Sensor and Ad Hoc Networks: Theoretical and Algorithmic Aspects (Lecture Notes in Electrical Engineering, Volume 7)

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Sensor and Ad Hoc Networks

Lecture Notes in Electrical Engineering Volume 7 Sensor and Ad Hoc Networks: Theoretical and Algorithmic Aspects S. Kami Makki, Xiang-Yang Li, Niki Pissinou, Shamila Makki, Masoumeh Karimi, and Kia Makki ISBN 978-0-387-77319-3, 2008 Current Trends in Intelligent Systems and Computer Engineering Oscar Castillo, Li Xu, and Sio-Iong Ao ISBN 978-0-387-74934-1, 2008 Recent Advances in Industrial Engineering and Operations Research Alan H. S. Chan, and Sio-Iong Ao ISBN 978-0-387-74903-7, 2008 Recent Advances in Communication Systems and Electrical Engineering Xu Huang, Yuh-Shyan Chen, and Sio-Iong Ao ISBN 978-0-387-74937-2, 2008 Time-Domain Beamforming and Blind Source Separation Julien Bourgeois, and Wolfgang Minker ISBN 978-0-387-68835-0, 2007 Digital Noise Monitoring of Defect Origin Telman Aliev ISBN 978-0-387-71753-1, 2007 Multi-Carrier Spread Spectrum 2007 Simon Plass, Armin Dammann, Stefan Kaiser, and K. Fazel ISBN 978-1-4020-6128-8, 2007

S. Kami Makki · Xiang-Yang Li · Niki Pissinou · Shamila Makki · Masoumeh Karimi · Kia Makki Editors

Sensor and Ad Hoc Networks Theoretical and Algorithmic Aspects

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Editors S. Kami Makki University of Toledo Toledo, OH USA [email protected]

Xiang-Yang Li Illinois Institute of Technology Chicago, IL USA [email protected]

Niki Pissinou Florida International University Miami, FL USA [email protected]

Shamila Makki Florida International University Miami, FL USA [email protected]

Masoumeh Karimi Florida International University Miami, FL USA [email protected]

Kia Makki Florida International University Miami, FL USA [email protected]

ISSN: 1876-1100 ISBN: 978-0-387-77319-3 DOI: 10.1007/978-0-387-77320-9

e-ISBN: 978-0-387-77320-9

Library of Congress Control Number: 2007941257 c 2008 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.

Printed on acid-free paper springer.com

Preface

Recent developments in mobile and wireless technology along with the availability of many smart and portable handheld devices facilitate the ubiquitous access to information. However, many limitations exist in these devices and the underlying network due to limited data transmission capability of these devices and the evolving and dynamic topology of mobile and wireless networks. The flexible structure of sensor and ad hoc networks has not only changed the formulation of the existing problems such as data communication for these networks, but has also involved the discovery of new solutions in a number of other areas such as reliability, scalability, energy efficiency, security, and interoperability. Research is currently underway to find solutions and techniques to address some of these issues such as the interoperability problem between sensor and ad hoc networks which use different routing mechanisms, and the adaptability problem which occurs between ad hoc and sensor networks that could very well be heterogeneous with respect to hardware characteristics and software systems. A self-adaptive system can evaluate the behavior of the system and change it (e.g., configuration, algorithm, design, etc.) when the result indicates that the system is not accomplishing what it was supposed to do, or when the performance of the system drops below a certain threshold. Scalability is also an important issue for these types of networks. As the applications of these networks for various tasks (e.g., collection of information in unfriendly and inaccessible terrains) suggest, the size of these networks can grow enormously. This can reduce the efficacy of almost all functions (e.g., routing, in-network aggregation, etc.) required by these networks. In addition, most existing mathematical models predict that these networks will become essentially incapable of operating effectively if they grow extremely large. Another challenge is the issue of reliability for these networks. This issue is complex and has many facets, such as coverage, routing, security, etc. The lack of fixed infrastructure and the mobility also makes reliable network operation very difficult, if not impossible. The security in these networks must also be investigated closely because of special characteristics and the usage of these networks for many sensitive and important applications in medicine, e-commerce, and the military. The major challenge is to secure these networks for existing and future vulnerabilities, although building a perfect secure system is always difficult. The lack of static infrastructure of these networks multiplies the security issues at hand, such as node authentication and secure routing. Furthermore, the ad hoc configurations v

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of these networks increase the complexity of detection and prevention of attacks by an order of magnitude. Therefore, there are many fundamental open questions in various areas related to ad hoc and sensor networks. These need to be answered and investigated before ubiquitous access becomes a fully workable and available technology. The aim of this book is to identify the areas that are in need of special attention and present a number of research findings, which correspond to noteworthy contributions in the areas of algorithmic aspects of sensor and ad hoc networks for current and future sensor and ad hoc networks. It is our hope that the diverse algorithms and protocols described in this book will give readers a good idea of the current state of the art in mobile and wireless technology. The authors of each chapter are among the leading researchers or practitioners in the field. S. Kami Makki Xiang-Yang Li Kia Makki Niki Pissinou Shamila Makki Masoumeh Karimi

Acknowledgement

This book would not have been possible without the wisdom and collaboration of the contributing authors. Special thanks to the personnel at the University of Toledo, Florida International University, IEEE Miami section, and National Science Foundation∗ for providing us with a stimulating environment for writing this book. We would also like to thank Alex Greene, senior Publisher and his staff, specifically Katelyn Stanne at Springer Science & Business for their strong support and encouragements. It was a pleasure working with Alex and Katelyn, who were incredibly patient, very responsible, and enthusiastic about this book. We also would like to express our sincere appreciation to the reviewers of this book, whose suggestions were invaluable. This book would not have been possible without the indulgence and infinite patience of our families during what often appeared to be an overwhelming task. They graciously accommodated the lost time during evenings, weekends, and vacations. As a small measure of our appreciation, we dedicate this book to them.

∗

This material is based upon work supported by the National Science Foundation under Grant No. 0437586. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Contents

1 Establishing New Research Initiatives for Theoretical and Algorithmic Aspects of Sensor and Ad Hoc Networks . . . . . . . . . . S. Kami Makki, Abdelmounaam Rezgui, Wuxu Peng, Kia Makki, Chung-Horng Lung, Niki Pissinou, Shamila Makki, Masoumeh Karimi, and Mohamed Eltowiessy

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2 Random Graph Models and the Limits of Scalability in Ad Hoc and Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Andr´as Farag´o 3 Analysis of Effective Connectivity in Mobile Wireless Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 J. David Haughsand Dongsoo S. Kim 4 Some Detectability Issues in Sensor Networks . . . . . . . . . . . . . . . . . . . . . 73 Wuxu Peng, Xinde Jia and Eric Reeves 5 Comparative Methods of Channel Assignment in Multivariate Wireless Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Xufei Mao, Xiang-Yang Li, and S. Kami Makki 6 Heterogeneous Wireless Networks: QoS-Aware Integration Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Ashraf Nusairat, Xiang-Yang Li, and S. Kami Makki 7 Distributed Energy-Aware Topology Control Algorithm for Wireless Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Zijian Wang and Jun Zhang 8 MFACE: A Multicast Backbone-Assisted Face Traversal Algorithm for Arbitrary Planar Ad Hoc and Sensor Network Topologies . . . . . . . 161 Hannes Frey and Franc¸ois Ingelrest ix

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9 Service-Driven Query Routing in Sensor-Actuator Networks . . . . . . . 181 Abdelmounaam Rezgui and Mohamed Eltowiessy 10 Multiscale Anchor-Free Distributed Positioning in Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Bastian Katz and Dorothea Wagner 11 Evaluation of Time Synchronization over Mobile Ad hoc Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Xiwei Zhao, Vinayak Ganapathy, Niki Pissinou, and Kia Makki 12 Universal Modular Framework for Sensor Networks . . . . . . . . . . . . . . . 237 Eli De Poorter, Benoˆıt Latr´e, Ingrid Moerman, and Piet Demeester 13 Application and Evaluation of Hierarchical Agglomerative Clustering in Wireless Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . 255 Chenjuan Zhou and Chung-Horng Lung 14 A Fault-Tolerant Scheme for Detection of DDoS Attack Patterns in Cluster-Based Wireless Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . 277 Zubair A. Baig and Asad I. Khan 15 Forming Energy-Efficient Bluetooth Scatternets for Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 Sain Saginbekov Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

Contributors

Zubair A. Baig Monash University, Melbourne, Australia, [email protected] Piet Demeester Department of Information Technology (INTEC), Ghent University – IBBT – IMEC Gaston Crommenlaan 8, bus 201, B-9050 Gent, Belgium Eli De Poorter Department of Information Technology (INTEC), Ghent University – IBBT – IMEC, Gaston Crommenlaan 8, bus 201, B-9050 Gent, Belgium, [email protected] Mohamed Eltowiessy The Bradley Department of Electrical and Computer Engineering, Virginia Technology, 4300 Wilson Blvd., Suite 750, Arlington, VA 22203, USA, [email protected] Andr´as Farag´o Department of Computer Science, The University of Texas at Dallas, Richardson, TX, USA, [email protected] Hannes Frey University of Paderborn, D-33098 Paderborn, Germany, [email protected] Vinayak Ganapathy Telecommunications and Information Technology Institute, Florida International University, Miami, FL 33174, USA, [email protected] J. David Haughs Department of Electrical and Computer Engineering, Indiana U. Purdue U. Indianapolis, IN, USA, [email protected] Franc¸ois Ingelrest ´ LCAV, I&C School, Ecole Polytechnique F´ed´erale de Lausanne, CH-1015 Lausanne, Switzerland, [email protected] xi

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Xinde Jia Texas State University, San Marcos, TX 78666, USA, [email protected] Jun Zhang School of Electronics and Information Engineering, Beihang University, Beijing, 100083, China, [email protected] Masoumeh Karimi Department of Electrical and Computer Engineering, Florida International University, Miami, FL 33174, USA Bastian Katz Universit¨at Karlsruhe, Karlsruhe, Germany, [email protected] Asad I. Khan Monash University, Melbourne, Australia, [email protected] Dongsoo S. Kim Department of Electrical and Computer Engineering, Indiana U. Purdue U. Indianapolis, IN, USA, [email protected] Benoˆıt Latr´e Department of Information Technology (INTEC), Ghent University – IBBT – IMEC Gaston Crommenlaan 8, bus 201, B-9050 Gent, Belgium Xiang-Yang Li Department of Computer Science, Illinois Institute of Technology, Chicago, IL 60616, USA, [email protected] Chung-Horng Lung Department of Systems and Computer Engineering, Carleton University, Ottawa, Ontario, Canada, K1S 5B6, [email protected] Kia Makki Telecommunications and Information Technology Institute, Florida International University, Miami, FL 33174, USA, [email protected] S. Kami Makki Department of Electrical Engineering and Computer Science, University of Toledo, Toledo, OH 43606, USA, [email protected] Shamila Makki Department of Electrical and Computer Engineering, Florida International University, Miami, FL 33174, USA Xufei Mao Department of Computer Science, Illinois Institute of Technology, Chicago, IL 60616, USA, [email protected] Ingrid Moerman Department of Information Technology (INTEC), Ghent University – IBBT – IMEC Gaston Crommenlaan 8, bus 201, B-9050 Gent, Belgium

Contributors

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Ashraf Nusairat Department of Computer Science, Illinois Institute of Technology, Chicago, IL 60616, USA, [email protected] Wuxu Peng Texas State University, San Marcos, TX 78666, USA, [email protected] Niki Pissinou Telecommunications and Information Technology Institute, Florida International University, Miami, FL 33174, USA, [email protected] Eric Reeves TeleNetwork Partners, LTD., San Marcos, TX 78666, USA, [email protected] Abdelmounaam Rezgui Department of Computer Science, Virginia Technology, 2050 Torgerson Hall (0106), Blacksburg, VA 24061, USA, [email protected] Sain Saginbekov Computer Engineering Department, Suleyman Demirel University, Almaty, 050043, Kazakhstan, Universit¨at Karlsruhe, sain [email protected] Dorothea Wagner Universit¨at Karlsruhe, Karlsruhe, Germany, [email protected] Xiwei Zhao Telecommunications and Information Technology Institute, Florida International University, Miami, FL 33174, USA, [email protected] Chenjuan Zhou Department of Systems and Computer Engineering, Carleton University, Ottawa, Ontario, Canada, K1S 5B6, [email protected] Zijian Wang School of Electronics and Information Engineering, Beihang University, Beijing, 100083, China, wang [email protected]

Chapter 1

Establishing New Research Initiatives for Theoretical and Algorithmic Aspects of Sensor and Ad Hoc Networks S. Kami Makki, Abdelmounaam Rezgui, Wuxu Peng, Kia Makki, Chung-Horng Lung, Niki Pissinou, Shamila Makki, Masoumeh Karimi, and Mohamed Eltowiessy

1.1 Introduction The rapid advances in mobile and wireless technology and the growing popularity of smart devices facilitate access to a variety of sources of information without the constraints of location and time. However, this availability of information does not provide the assurance of advancement in all areas of mobile and wireless technology as there are still many uncharted research areas. Many unanswered questions exist that require dedicated investigation by the enthusiastic researchers in this field. The workshop on “Theoretical and Algorithmic Aspects of Sensor and Ad Hoc Networks” held on June 28–29, 2007 in Miami, Florida, aimed to closely examine some of these research areas and investigate the opportunities for other uncharted research areas. To achieve these objectives, the technical program chairs and committee members meticulously selected the best and the most relevant submitted research papers for inclusion into the workshop program. These research papers covered different aspects of the sensor and ad hoc networks such as topology control, coverage and connectivity, scalability, routing, and security. These papers were presented by their respective participants. These presentations provided a platform for further discussions by the participants on various research directions and obstacles in this area. Not all participants agreed fully on whether a particular direction has been fully investigated. However, the discussions helped to clarify some of the underlying issues. This report intends to serve as a guidance for research in the area of theoretical and algorithmic aspects of mobile wireless sensor and ad hoc networks. S.K. Makki University of Toledo, Toledo, OH, USA e-mail: [email protected] This material is based upon work supported by the National Science Foundation under Grant No. 0437586. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

S.K. Makki et al. (eds.), Sensor and Ad Hoc Networks, C Springer Science+Business Media, LLC 2008 DOI: 10.1007/978-0-387-77320-9 1,

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Ad hoc networks originated early in the 1980s as packet radio networks in which the nodes could move freely while communicating over multihop wireless links. These networks are characterized not only by the nature of the medium, but also by the lack of infrastructure available for centralized computation and the timevarying topology. This unrestricted mobility and ease of deployment make ad hoc networks suitable for a wide range of applications, from military communication to disaster relief to personal-area networking. For example, Bluetooth is an example of a short-range wireless ad hoc network. Because of the wide range of applications for ad hoc networks, there is ongoing research on these types of networks for nearly 25 years. During this period, countless solutions for various problems in these networks have been proposed and innumerable papers have been published. Yet, these networks are not seen in the publicly available commercial domain. One of the main reasons is the lack of commercial usage of these types of networks. It should be mentioned that although these types of networks may not have commercial usages, many of the elaborate methodologies are quite useful in similar networks that seem to have a commercial future, such as wireless Local Area Networks (LANs), mesh, and sensor networks. In a sense, these networks are all descendant of ad hoc networks. For example, wireless sensor networks (SNETs) are composed of a large number of sensor nodes. However, since sensors are tiny and low cost devices, these types of network have stronger constraints such as power restrictions and limited computational capacity. Therefore, current architectures for sensor networks are either application specific or generic. Application-specific SNETs provide limited reusability. They are not cost effective and may require extensive reprogramming efforts to make the network capable of serving qnew applications. The generic SNETs usually require a sizeable code to be deployed on the nodes regardless of the specific requirements of the application at hand. More importantly, the SNETs may not be optimized to fully exploit the specific characteristics and query patterns of a given application. As sensor technologies mature and new applications proliferate, current design models for sensor-actuator systems seem increasingly unable to cope with the requirements of the next generation of open, ubiquitous, interoperable, multipurpose SNETs. Architectures for future sensor systems should serve different applications and adapt to different postdeployment query patterns. Networks from different providers should be individually programmed and also be able to interoperate efficiently. Though, both application-specific and generic architectures are obviously unable to satisfy these requirements, therefore, there is a need for new customizable architectures to enable the next generation of sensor actuator systems. We define customizable SNETs as readily configurable networks, and on deployment, are able to serve different types of applications with arbitrary query patterns. A node in a customizable SNET is an identifiable resource capable of being accessed by any entity, from within or outside the network. Customizable SNETs would provide developers with the flexibility to combine the resources provided by nodes in one or different (existing) SNETs to meet the requirements of new applications and yet expect the same levels of performance that would result from an applicationspecific deployment.

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The next section highlights some of the challenges for sensor and ad hoc networks, such as interoperability, adaptability, scalability, reliability, energy efficiency, security, and establishment of a standard testbed. Section 1.3 provides general recommendations for future research in this field. Finally, Section 1.4 provides concluding remarks for this report.

1.2 Challenges for Sensor and Ad Hoc Networks 1.2.1 Interoperability Ad hoc and sensor networks are the key components of the vision of pervasive computing. Developing pervasive environments is not possible without enabling interoperability among ad hoc and sensor networks. Given the constraints on resources in these networks (energy, memory, bandwidth, etc.), interoperability middleware developed for traditional networks is clearly not a viable option. Traditionally, ad hoc networks have been considered as isolated, standalone networks. In recent years, enabling the interoperability among ad hoc networks has been identified as the key requirement in many civilian and military applications. An example of this interoperability occurs in a disaster scenario where several teams of first responders (fire fighters, ambulance teams, police officers, etc.) are quickly deployed to the scene of the disaster and cooperate to save lives and property. Each team of first responders may have its own network of handheld devices. Often, effective disaster management plans require that the teams be able to share information among each other despite the heterogeneous hardware and software profiles of their networks. Interoperability in the context of ad hoc networks may have two forms: (1) ad hoc interoperability and (2) interoperability through an infrastructure (e.g., the Internet). In the first case, the problem is to enable different ad hoc networks to interact without relying on any infrastructure. In the second case, an infrastructure network is used as a backbone to interconnect several ad hoc networks. Research investigating the second form has been underway for many years [1]. Solutions providing the first form of interoperability are still the focus of intensive research. The complexity stems from the heterogeneity in hardware and software in devices used in ad hoc networks as well as from the diversity in the underlying networking technologies used in ad hoc networks. Indeed, the recent years have witnessed a significant increase in the number and types of wireless devices. Nodes in different ad hoc networks may need to interact while their underlying networks use two different network protocol stacks. Also, interaction may be necessary between ad hoc networks with different software components (different operating systems, different messaging Application Programming Interface (APIs), etc.). We distinguish two broad classes of ad hoc interoperability requirements: (1) network interoperability and (2) middleware interoperability.

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1.2.2 Network Interoperability In ad hoc networks the communication infrastructure must enable the interoperability of different devices that may use different network technologies. For example, different members of the different teams of first responders may have heterogeneous devices, such as laptops, PDAs, or cell phones, which may work with different network technologies such as Wireless Local Area Network (WLAN), Worldwide Interoperability for Microwave Access (Wi-Max), Wireless Wide Area Network (WWAN), satellite, or wired networks [2]. A particular challenge is to enable interoperability among ad hoc networks using different routing mechanisms. For example, commercial deployments available from NovaRoam use Ad hoc On Demand Distance Vector (AODV) and Temporally-Ordered Routing Algorithm (TORA) as routing protocols, whereas ad hoc networks available from Firetide use Topology Broadcast based on Reverse-Path Forwarding (TBRPF) as the routing mechanism [3]. In recent years, research has also investigated the use of the software reconfigurable radios (also called software defined radio, or SDR) to make radio interfaces interoperable across different standards and network types. A particular type of SDR that hold substantial promise in improving interoperability is cognitive radios. These SDRs dynamically retune their radio parameters based on the feedback they obtain from their surrounding environment. This functionality can allow the cognitive radio to discover other transmitting nodes in its vicinity and to selforganize into an information-sharing network. An example of this approach is SAFIRE, a multihop architecture that facilitates information exchange between first responders [4].

1.2.3 Middleware Interoperability Enabling interoperability between applications running on nodes of heterogeneous ad hoc networks has been mainly achieved through middleware. Two types of middleware have been investigated: (1) object-oriented middleware and (2) serviceoriented middleware. 1.2.3.1 Object-Oriented Middleware In object-oriented middleware, interoperability among heterogeneous devices is enabled through distributed object middleware such as Common Object Request Broker Architecture (CORBA) or Internet Communications Engine (ICE). The main challenge in this context is to lower the cost of embedding a distributed object middleware. Indeed, conventional distributed object middleware has high requirements in terms of power and memory and is therefore widely considered unsuitable for ad hoc networks. Several efforts, however, are underway to develop lighter versions of traditional middleware solutions that would be more suitable for ad hoc networks. An example is the prototype described in [5]. This proto-

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type supports interoperability among tiny heterogeneous wireless devices through a low-cost implementation of ZeroC ICE. On the standardization front, work has been done to develop interoperability standards suitable for ad hoc networks. For example, the Object Management Group (OMG) has adopted new standards regarding wireless access and terminal mobility [6]. However, only few implementations are currently available. This is due to the complexity of wireless network protocols, interoperation details, and also because the wireless technology field is still a controversial battlefield with each vendor trying to enforce its own solution to the market [7]. 1.2.3.2 Service-Oriented Middleware Interoperability middleware for ad hoc networks must be lightweight and flexible (i.e., easily adaptable to the resources and capabilities of specific nodes). Solutions derived from traditional middleware such as CORBA are yet to meet these two requirements. A promising direction emerged in recent years is based on serviceoriented middleware. In this approach, nodes in an ad hoc network are able to interact with other (wired and wireless) nodes through a middleware that consists of abstractions called services. Examples of this approach include PA-UWNT [8] and TinySOA [9]. PA-UNWT (Philadelphia Area Urban Wireless Network Testbed) is a mobile ad hoc network comprising mobile computers (PDAs, tablets, and laptops) and Web Service-based applications (situation awareness, sensors, tracking, data feeds, etc.). TinySOA is a TinyOS-based query system for sensor-actuator networks in which sensing and actuation capabilities of nodes are exposed to applications in the form of a collection of services. A service deployed on a node is a lightweight code unit that provides some functionality supported by the node. Services are deployed directly on top of the operating system and are directly accessible by applications. They may be individually invoked or combined in complex ways to form a “virtual” SNET with far richer sensing and actuation capabilities. Interoperability in TinySOA is possible because of the service abstraction through which the capabilities of any node in any network are perceived uniformly as homogeneous services.

1.2.4 Adaptability There are many different types of devices, algorithms, and application domains in ad hoc and sensor networks. These days, ad hoc and sensor networks could very well be heterogeneous with respect to hardware characteristics, software systems, and application requirements. In addition, newer techniques are evolving quickly in this field and application requirements are likely to change over time. Of late, self-adaptability or simply adaptability has emerged as a promising field. The selfadaptive systems evaluate the system behavior and change it (e.g., configuration, algorithm, design, and so on) when the result indicates that the systems are not accomplishing what they were supposed to do or when the performance of the

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systems drops below a certain threshold. For instance, if a clustering algorithm needs GPS location information and if the Global Positioning System (GPS) component of some nodes is malfunctioning, the nodes can exchange information and switch to a different method to conduct the clustering. Various scheduling methods could also be applied to different scenarios depending on power level, node degree, cluster size, and so forth to prolong the life of individual devices or the entire network. Therefore, adaptability is a crucial factor in system and software development, as it allows systems to cope with increasing complexity and difficult task of variability. To support adaptability during execution, three fundamental tasks of monitoring, analysis, and management need to be considered. Monitoring deals with mechanisms to collect and/or aggregate data obtained from various system elements or devices. The analysis phase is used to gauge and analyze the data that are collected from the monitoring step or to compare the collected data with existing historical data or preconfigured thresholds. Management is involved with the control mechanism based on the measurement and analysis results. A simple example could be sensors that collect data and forward the data to a base station. The base station conducts analysis by using the aggregated data and compares it with predefined data or knowledge. An action based on the results of the analysis and control mechanism may be taken subsequently. The description of adaptability and the basic tasks presented in the previous two paragraphs depend heavily on the intelligent design (ID) and the corresponding control mechanisms built into the system. In other words, the system has knowledge about design alternatives a priori and the application knows how to adapt to different contexts or scenarios based on previously specified rules. Another question is how to systematically and effectively incorporate various alternatives into the system. From the system design perspective, domain modeling and variability management advocated in software engineering could help adaptability. In domain modeling, commonalities and differences among a family of systems or applications are identified and analyzed. An architecture or framework that can accommodate different requirements in a family of systems is subsequently constructed based on the analysis. The architecture or framework, therefore, has the capability to support multiple contexts or diverse applications. Variability management is a critical task in domain modeling. The concept could improve adaptability due to differences in both hardware and software techniques. Differences in system artifacts of a product family are identified and analyzed. Those differences are called variation points. Each variation point has multiple potential variants that can be used for specific applications. System variability is the ability of a system or even an artifact to be adapted for a purpose in a particular context. A high degree of variability means the system is flexible to support a variety of applications in a broad context. Variation points could be at various levels, such as architecture, design, and implementation. The binding of a variant could also happen at different stages (e.g., design time, compile time, and runtime). Architectures with higher-level variation points could provide more leverage as more flexible design could be incorporated into a framework, while lower-level variation points are easier in terms of design and configuration. Binding of variants at the design stage could

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be more efficient than that of runtime, while binding at runtime generally provides more flexibility to support higher level of variability. Many clustering methods for Wireless Sensor Networks (WSNs) have been proposed. Each one has some assumptions as well as strengths and weaknesses. To increase the level of flexibility, variability analysis could be conducted on typical clustering methods. One variation point, for example, could be the input data type, that is, quantitative data or qualitative data. Quantitative data could further be divided into location information based on the GPS feature or the actual received signal strength (RSS) obtained from the system. Multiple clustering algorithms and various relevant parameters could be potential candidates for each data type. In other words, the clustering approach could become another variation point and each specific clustering algorithm is a variant. Data management at the application layer is another example. Various techniques are available on the server or base station to realize data management. To support the flexibility or to increase the level of variability, an analysis could be conducted to identify similarities and differences. An adaptation layer could then be built to support dynamic selection and adaptation of data management components. Layered architecture generally could be useful in supporting adaptability. An adaptation layer could be built to support a variation point, which consists of multiple variants. In addition to the layered approach, other techniques to support adaptation concept include wrapping, filters, and proxies. Consider PDAs as another example in an ad hoc environment. A PDA needs to support multiple protocols including Code Division Multiple Access (CDMA) and Global System for Mobile (GSM), and needs an efficient communication mechanism to support Web services. The decision of which protocol to use depends on the dynamic runtime detection of a particular protocol. This is closely related to variability modeling and flexible framework construction. The concept of filtering could be used in this situation to dynamically detect the protocol in use. In addition, PDAs may use proprietary protocols to communicate with the server or due to the resource and energy constraints, an efficient communication mechanism may be needed for this system. Simple Object Access Protocol (SOAP) is commonly used for service-oriented applications. However, SOAP messages have much higher overhead, which is undesirable for an energy-constrained PDA device. To support potential new protocols/standards like SOAP or to reduce communication cost, a proxy between PDAs and the server could be added. The communication between PDAs and the proxy is based on a legacy protocol(s) or a more efficient proprietary protocol for saving energy. However, the communication between the proxy and the server still uses SOAP with an aim to support the standard of Web services. Different adaptation policies or behaviors could exist for different concerns to technologies. Conflicts may occur between different adaptation policies or rules and may be detected statically during designing. A mechanism needs to be implemented to resolve the conflicts. However, conflicts may also happen during runtime depending on various states. Runtime conflicts could be resolved using microeconomic techniques or legal reasoning as advocated in [10]. In addition to the ID approach, another school of thought to support adaptability is the concept of evolutionary computation (EC). In ID, knowledge of alternatives

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and adaptation mechanisms have been identified, analyzed, and built into the system a priori as explained earlier. However, as the complexity of computing systems has grown dramatically, achieving the goal of ID generally may not be feasible for some circumstances. This issue has led researchers to investigate biologically inspired approaches. The idea is that natural organisms can adapt to unforeseen environments. Therefore, the goal of EC is to develop the ability of adaptability in such a way that individual nodes could mimic behaviors learned from natural organisms to evolve and handle unforeseen circumstances. The EC approach models natural organisms and the processes that generate their behaviors [11,12]. However, EC is a broad field and genetic algorithms, for instance, is one of the EC methods. A lot of research is still needed to build a system that can actually evolve and adapt to unforeseen environments.

1.2.5 Scalability Scalability is one of the key research challenges in the area of networks in general, and in sensor and ad hoc networks in particular. It transcends almost all functionalities required in these networks, for example, routing, in-network aggregation, key establishment, and so forth. Two major challenges pertain to scalability in sensor and ad hoc networks: (1) developing “scalable” applications and protocols and (2) proving the scalability of those applications and protocols. While claims of scalability abound in literature, proven research to show the scalability of applications and protocols is far less abundant. An example of research conducted to address the first challenge is scalable routing. Clustering is an almost canonical approach to improve scalability in routing protocols, and LEACH (Low Energy Adaptive Clustering Hierarchy) [13] is one example. This protocol forms clusters of sensor nodes based on the received signal strength. In each cluster, only a cluster head routes data to the sink. Data processing (e.g., data fusion and aggregation) is local to the cluster. Cluster heads change randomly over time to balance energy consumption among sensors. To address the second challenge (i.e., proving scalability), three approaches have traditionally been used: 1. Proving scalability through actual deployments – Due to the cost of high scale deployments, experiments proving scalability based on actual deployments are often limited in terms of number of nodes. For example, consider Trio, an outdoor sensor network that was deployed to evaluate robust multitarget tracking algorithms “at scale.” With only 557 solar-powered motes, Trio is said to be one of the largest solar-powered outdoor sensor networks ever constructed [14]. 2. Proving scalability theoretically – Theoretical research on scalability has focused on two aspects: (1) proving that some specific application or protocol scales up to large networks and (2) deriving theoretical boundaries on some properties of the network when its size increases asymptotically. For example, [15] derives scaling laws describing the achievable rate in worst case, that is, arbitrarily deployed, sensor networks. The paper shows that a sustainable rate of W(1= log2n) can be

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achieved in every network (of size n) even when nodes are positioned in a worstcase manner. The paper also shows that the best possible rate is Q(1= n). Another related challenge is to scale down, that is, apply asymptotic results (derived for large networks) on much smaller, but more practical, networks [16,17]. 3. Proving scalability through simulation – Given the cost and impracticality of actual deployment of networks with hundreds or thousands of nodes, most algorithms and protocols for sensor and ad hoc networks are shown to scale to large networks only through simulations. As manufacturing and deployment costs continue to decrease and the vision of pervasive computing takes shape, future sensor and ad hoc networks are expected to be much larger than current ones. This will push the limits for scalability analysis to networks far larger than those considered in current literature. As we do not expect actual testbeds to scale to common sizes of tomorrow’s networks, we believe that a new generation of simulators is needed to validate design and theoretical results on future networks with thousands or more nodes. Also, ad hoc networks do not scale well due to frequent change of network topology, lack of predefined infrastructure like routers (routing backbone), peerto-peer mode of communication, and limited radio communication range (typically 250 m). However, a scalable ad hoc network is an attractive means of establishing large networks without requiring a costly routing backbone. A large ad hoc network can be the primary communication infrastructure for metro areas/towns or can coexist with current Internet, which can also form a very good supplement to Internet.

1.2.6 Reliability The issue of reliability of ad hoc mobile networks and sensor networks presents a significant challenge due to several well-known reasons such as legal liability in medical applications. In case of ad hoc mobile networks, lack of fixed infrastructure and the mobility makes reliable network operation very difficult, if not impossible. For fixed sensor networks, where energy consumption is not a major issue, the reliability issue is somewhat easier to address [18]. However, recent trends in sensor network research indicate a move toward the application of large number of inexpensive sensors, each of which has limited energy capacity. If sensors are mobile, the mobility also presents challenges similar to ad hoc mobile networks. Furthermore, other performances such as computing cost and communication cost will also be affected. The issue of reliability is complex and has many facets, including routing, broadcasting, security, and coverage. Research on reliability of ad hoc mobile networks and sensor networks in recent years has centered on different aspects: i. Routing protocols – This research thread focuses on more efficient and reliable routing protocols. The main reliability parameter for routing protocols is

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the ratio of reliable message delivery over total messages sent. Some recent research results include energy-aware routing algorithm in limited mobility sensor networks [18,19] and ad hoc mobile routing algorithms based on forests [20]. ii. Broadcast protocols – As a basic interprocess communication, primitive broadcasting has many applications in network communications. This research thread studies algorithms and protocols for more efficient and reliable broadcasting. The main reliability measurement for broadcast protocols is whether a message initiated by any specific node in a network can reach all other nodes with fewer total incurred messages and within a shorter period of time [21,22]. iii. Security – Earlier, many Internet protocols (such as TELNET, FTP, and PING) were designed with the underlying assumption of well-mannered behavior of Internet users and applications. This assumption is no longer valid, and appropriately TELNET has been replaced by SSH and FTP has been replaced by SFTP. Any reliable network operation has to be secured. As in conventional computer networks, security research in ad hoc and sensor networks can be further divided into subthreads of key management, encryption schemes, and information assurance [23,24,25]. iv. Coverage algorithms – The coverage issue has emerged as a new challenging issue in ad hoc mobile and sensor networks. Research in this thread deals with how to cover a defined area efficiently. Research reported in references [26,27,28,29] provide very good introduction to this interesting topic.

1.2.7 Energy Efficiency Energy efficiency is one of the most discussed topics for WSNs [30,31,32,33]. Independent devices, which must be able to operate with batteries to support the fundamental requirement of mobility, are the building blocks of these networks. These batteries have limited life spans, which are generally much shorter than the life expectancies of the devices using these batteries. Therefore, there are two main research directions for energy efficiency, that is, either the given battery power must be used efficiently, or superior batteries must be created from modern materials with better characteristics that can enhance the life span of the batteries exponentially with reasonable cost. However, the latter research activities fall into empirical electrical engineering research, which is an ongoing active research area. There are indications that there will be new results to show changes in the selection of materials for construction of “smart” batteries, which will replace the conventional batteries. However, in the first research direction, the researchers have explored and considered a number of solutions in the areas such as efficient routing, information fusion, scheduling, and so forth, for efficient usage of the batteries [34,35,36]. In the area of routing, many algorithms have been created to reduce the redundancies that exist due to the distributed nature of these networks. For example, the directed diffusion

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algorithm improves upon the basic flooding algorithm by eliminating a number of unnecessary return messages or routing information from one node of the networks to the same nodes of the networks . Also, new directed diffusion algorithms have also improved the basic directed diffusion algorithm and have removed other redundancies inherent in previous solutions. For example, in information fusion applications, the sensor nodes are spread randomly over the terrain under scrutiny to collect data from their surroundings. Then each node processes its collected data and coordinates with nearby nodes to combine their information. The aggregate information is then forwarded to specialized gateway nodes or base stations (it needs to be mentioned that data transmission uses more battery power than local processing). This information fusion technique will reduce communication overhead and as a result decreases the consumption of battery power significantly. That is because a smaller amount of data needs to be transmitted in comparison with the traditional data transmission, which needs to transmit all the collected data. Resolving the issues related to data fusion efficiency still requires more research. Another area of reducing the consumption of battery life is scheduling. There are many research activities in this area. An example is the scheduling of network devices for doing different network operations [35]. This requires identification of a leader to achieve proper activity within the networks’ nodes [37]. Although the leader identification is not a new problem, there are new set of requirements (such as dynamic nature of these networks) in the sensor and ad hoc environment, which need to be satisfied. The results of these studies indicate sizeable improvements to the consumption of the battery power. Since most of these results were conducted using simulation of a scenario similar to the actual networks, some of the results may be unrealistic or outdated due to differences between the actual behavior of the simulated networks and the real networks. Therefore, more empirical studies using diverse devices should be conducted to measure the real value of energy consumption under various scenarios.

1.2.8 Security Security is the most important characteristic for most WSNs. In fact, security issues are also very important to the telecommunications industry and medical industry. However, in comparison with wired networks, security issues in ad hoc and sensor networks are more complicated and therefore, substantial research is required to find efficient solutions for the majority of these problems [38,39,40,41]. The constrained capabilities of hardware and their deployment characteristic make these networks more vulnerable to attacks. Also, detection and prevention of attack is very critical as security in these networks is relatively a new area of research, with a limited but rapidly growing set of research results. The attacks to these networks can be generally divided into two major types, physical and software. In the case of physical attacks, one or more nodes may be

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physically damaged or destroyed by adversaries. In software attacks, one or more nodes may be tampered with. The software attacks are further classified as outsider and insider attacks [47,48]. In an outsider attack, the attacker (to one or some nodes) is not an authorized participant of the network. There are a number of ways to prevent this type of attack, such as adopting various security techniques for usage of the networks. These measures can range from hierarchical authorization to the requirement of multiple passwords for each user to login to different sections of the networks, or forcing users to change their password periodically, or selection of hard-to-guess password in combination with the use of encryption of important informative files. The insider attack is generally the result of a compromised node. Since the compromised nodes may exhibit arbitrary behavior, it is hard to anticipate the behavior of these nodes. Due to inherent limitations and requirements of sensor and ad hoc networks, a number of different and new security mechanisms, schemes, and protocols are needed to be created. Attacks on ad hoc and sensor networks can occur on different layers of the network structure. For example, attacks that can reduce the availability of these networks can happen at the physical layer. This attack can take the form of jamming the radio frequency or tampering with the nodes of the network. At the data link layer, the attack can be in the form of resource exhaustion and unfairness service. At the network layer, attacks can include data alteration, selective forwarding, replays of routing information, spoofing, HELLO flood attacks, white hole attacks, sinkhole attacks, sybil attacks, wormholes, insulation, and corruption attacks. Flooding and desynchronization attacks are major attacks on the transport layer that reduce or disrupt availability. A number of solutions are provided for each of these attacks and research is on going to find more efficient solutions for them. Also, more research is needed in the following areas: i. Key management and cryptography – Techniques are especially important in sensor and ad hoc networks because of the limited memory for storage and battery power in these networks. Also, most security mechanisms require cryptography to provide confidentiality, integrity, and authentication services. ii. Provision of security for routing – The ad hoc and sensor networks can incur more routing attacks because of the low developed security measures for wireless communication with limited resources and inherent multihop routing requirement in these networks. Also, in contrast with traditional networks, the routing protocols in these networks face internal and external attacks. iii. Location security – Securing location information is very important because some other security mechanisms such as key management (and other applications such as reconnaissance) use location information. iv. Data fusion security – Each sensor node in these networks processes data and coordinates with nearby nodes to combine their information, since the nodes generally are spread randomly over the terrain. The collected information from each node will be aggregated by an intermediate node in order to reduce the communication overhead. Then it will be forwarded by a selected leader from

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these intermediate nodes to some specialized gateway nodes or base stations. This information processing model requires adoption of more security procedures and plans because each intermediate node can modify, forge or discard messages, or transmit false aggregation values, which can significantly alter the final result.

1.2.9 Testbeds and Benchmarks The research in sensor and ad hoc networks still lack two key elements: (1) testbeds and (2) benchmarks. Testbeds enable designers to accurately predict network parameters (e.g., lifetime, performance, and throughput) under different conditions. The use of physical testbeds for evaluating applications and protocols normally provides a high level of fidelity. However, given the cost of building testbeds for ad hoc networks, the majority of current research uses simulation as a substitute to experimental validation. A number of testbeds have been made publicly available. Examples include MoteLab [49], ORBIT [50], MiNT-m [51], Roofnet [52], and TWIST [53]. Although useful in many cases, these and other testbeds may not be readily usable for a large spectrum of research work because of limitations in one or more aspects. For example, MoteLab has only 190 TMote Sky sensor motes. In addition, motes in MoteLab are powered from wall power rather than batteries, which may invalidate the results of any experiment assuming battery-powered motes. Substantial efforts are still needed to provide more comprehensive, flexible, and reliable testbeds. Another element where efforts must be directed is the Development of benchmarks that the community may use for comparative studies. Indeed, in the absence of reliable benchmarks, much of the published results remain too subjective to be a basis of any comparative analysis. In turn, this makes it difficult to properly identify the superiority of any specific solution that may be proposed for any given problem in ad hoc and sensor networks research.

1.3 General Recommendations for Future Research The workshop participants generally agreed that majority of research in the ad hoc and sensor networks is based purely on analysis and simulation in which every proposed model makes use of some assumptions and limitations, as well as strengths. Many of these systems and algorithms have never been implemented in real environments, and the existing methods in use are adopted from the past or existing research works. Therefore, it can be concluded that an elaborate body of research is built on what must inherently be a fragile basis. The research in the field of sensor and ad hoc networks is multidisciplinary. For instance, technologies in software engineering are useful in modeling and managing variations and building tools to support the development of real applications. Biologically inspired

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techniques could be used to support self-organization or self-adaptability. Also, various models, such as mobility models require empirical validation using testbeds or real equipments. Publicly available large testbeds are needed instead of many dissimilar models built by various groups. These observations are particularly true because the general experience of those who have dealt with real deployments of ad hoc and sensor networks have revealed that they tend to be random, irregular, and hard to characterize. Therefore, with unpredictable behavior of these networks, researchers cannot solely rely on simulation or analysis. Furthermore, these networks in reality may contain many thousands of nodes. There are numerous papers describing ways to provide security for a range of protocols to handle routing in ad hoc and sensor networks. Reliability is also a critical issue in real-time applications such as ad hoc and sensor networks containing thousands of nodes in fields such as battlefield management or medical applications. Therefore, in these applications, the industry standard reliability requirements should be studied and established. However, if one accepts the fact that we do not have secure and reliable ad hoc and sensor networks, and also the other areas in wireless and mobile systems that have received much attention are in comparable situation, one must then try to discover what aspects of the earlier research failed to lead to solutions to these problems. The inherent heterogeneity of these networks requires efficient design, implementation, and operation. Therefore, a major recommendation that future research in these networks should be carried out on a realistic basis, with simulation being used to support the method for evaluation of a system but not as the only method. Further attention should be paid by researchers to the realities of research, rather than relying largely on archaic models that were built when it was only feasible to presume what might occur. A great deal of research should result in working prototypes. In addition, the majority of research should employ either live tests or modeling based directly on observed behavior of real users and systems working in the intended environment. While the National Science Foundation (NSF) has provided funds for profound theoretical research or early explorations in new areas, more emphasis should be put on solving the problems such as interoperability, scalability, reliability, security, and so forth in ad hoc and sensor networks is required. For example, interoperability is an important issue because of fastdeveloping technology. Recently, quality of service as a research area has also become relevant because of applications such as video and data integration with voice. The problem can gain momentum if the Internet service providers are shown how to make money by manipulating these technologies. Also, another interesting and important area of research is “broadcasting,” for example, convergence with full coverage. That is, how is it possible to reach all the nodes of a network in the minimum amount of time? Moreover, as mentioned earlier, the security is a complex issue in ad hoc and sensor networks and more research is required in many areas such as key management and cryptography, security requirement for routing, data fusion, and location security. For example, in data fusion, each intermediate node can modify, forge or discard messages, or simply transmit false aggregation values, which can significantly alter the final result.

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Another area where research can be directed is the development of benchmarks that the community may use for comparative studies. In absence of reliable benchmarks, many of the published results remain too subjective to be a basis of any comparative analysis. This, in turn, makes it difficult to properly identify the superiority of any specific solution that may be proposed for any given problem in ad hoc and sensor networks research. The recommendations are mainly based on the published papers , open discussions, and extensive discussions in the workshop on theoretical and algorithmic aspects of sensor and ad hoc networks (WTASA) held in Miami in June 2007.

1.4 Conclusion The advances in mobile, wireless, and Internet technology along with the availability of many smart and portable devices provide ubiquitous access to vast amount of information, which was only available through specific resources. For example, advances in sensor and ad hoc network technology provide information from inaccessible and hostile terrains. The ubiquitous access, which resulted from these advances, has not only improved the amount of information that can be accessed, but also eliminated the requirement for personal presence in some of these locations that gather the information. However, there are many fundamental open questions, which need to be answered and investigated before these ubiquitous accesses become a fully available and workable technology. This report provides the deliberations of the group of renowned experts in ad hoc and sensor environment who participated in the 2007 Workshop on theoretical and algorithmic aspects of sensor and ad hoc networks (WTASA), held in Miami, Florida in June 2007. The aim of the workshop was to present expert guidance to the National Science Foundation on priorities in research directions in the areas of algorithmic aspects of current and future sensor and ad hoc networks. Therefore, this report identified some of these shortcomings and highlighted some of the new research directions in this area. The suggestions contained here come from the published papers at the workshop, and the panel discussions, which were held at the second day of workshop among the workshop participants. In addition to the above recommendations, the authors of this report feel compelled to point out that these areas of research are underfunded. Without an increase in funding in research in these areas, important problems will remain unaddressed until they reach crisis proportions, and probably only after a real disaster has occurred.

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Chapter 2

Random Graph Models and the Limits of Scalability in Ad Hoc and Sensor Networks Andr´as Farag´o

2.1 Introduction 2.1.1 The Scalability Paradox It is generally expected that ad hoc and sensor networks will ultimately grow very large. On the other hand, most existing mathematical models on their fundamental limits point in the opposite direction – they predict that these networks will become essentially unable to usefully operate if they grow extremely large. Various models point out asymptotically either the per node throughput approaches zero or the expected delay grows to infinity or the network almost surely loses connectivity, etc. It is a rather paradoxical situation that, on the one hand, the ad hoc and sensor networking research community believes in scalability, while, on the other hand, their mathematical models apparently invalidate it. We analyze this “scalability paradox” and propose a common generalization of the various random graph models to exhibit a feature that is present in virtually all situations where the scalability breakdown occurs. The expectation of scalability is a natural motivation to explore the asymptotic behavior of ad hoc and sensor networks via appropriate mathematical models. This analysis can help finding out what are the fundamental limits, that is, in principle, what can and what cannot be accomplished if the network grows extremely large. Research interest in the fundamental limits had an upsurge after the publication of the seminal paper of Gupta and Kumar [10] on the capacity of wireless networks. Many results followed on how much traffic can an ad hoc network support in different modes of operation, which values of local parameters can guarantee global connectivity, what can topology control principally achieve, etc., see, e.g., [1,8,9,11,12,15,16,17,20,21,22,24,25,26,27,28,29] and a large number of others.

A. Farag´o Department of Computer Science, The University of Texas at Dallas, Richardson, Texas, USA e-mail: [email protected]

S.K. Makki et al. (eds.), Sensor and Ad Hoc Networks, C Springer Science+Business Media, LLC 2008 DOI: 10.1007/978-0-387-77320-9 2,

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Surprisingly, however, despite the optimistic general expectation of ultimate scalability, apparently all theoretical results seem to point in the direction of a scalability breakdown, in one way or another. This is what we call the scalability paradox of ad hoc and sensor networks. Let us first show this by briefly reviewing some results of the theoretical models (without aiming at completeness).

2.1.2 Some Fundamental Results The most important result in the paper of Gupta and Kumar [10] considers the achievable throughput per source–destination (S–D) pair in a large random network, where n nodes are placed independently and uniformly at random in a planar disk of unit area. Thus, the network topology is random, but static. The nodes have the same transmission radius, which can be chosen arbitrarily. They can transmit with a fixed maximum rate (bit/s), but they are allowed to divide the channel into subchannels without any constraint, in any domain (e.g., frequency, time, code). The nodes communicate using arbitrary protocols for channel access and routing, with the only restriction that there is a minimal requirement of interference avoidance in the same (sub)channel to ensure successful receptions. The considered traffic pattern is that each node has a randomly chosen destination in the network. The authors prove that in this general model the achievable throughput per S–D pair is Θ(1/ n log n). Regarding scalability, the key message of this result is that the achievable throughput per S-D pair tends to zero as the network size grows to infinity. We call this the vanishing throughput effect It means, the network is fundamentally not scalable, since it becomes unable to usefully operate when it grows extremely large. It is then a natural question to investigate how robust is the vanishing throughput effect against changing model. Is it merely an artifact due to some special modeling assumptions, or is it a fundamental phenomenon that remains true in any reasonable model? Already in their original paper [10] Gupta and Kumar point out that if the area where the nodes are located is the surface of a sphere rather than a planar disk, the results still remain in effect. The authors also show that no essential change results even if instead of random node placement, the nodes are located optimally and their transmission radii are also chosen optimally. For three-dimensional network topology (random node placement in a unit cube) Toumpis and Goldsmith [26] show that, although the rate of vanishing is different, the per node throughput still tends to zero. Similar results are obtained by Gupta and Kumar in [12]. Various other static network scenarios were also analyzed by different authors. For example, Yi et al. [29] show that the use of directional antennas, although can increase the capacity, still does not invalidate the vanishing throughput effect. Peraki and Servetto [20] prove that even if the nodes can generate multiple beams in parallel, aimed at multiple receivers, the achievable improvement is still insufficient to sustain positive per node throughput in the limit. Kozat and Tassiulas [15] consider the scenario when the ad hoc network has infrastructure support, that is, besides the ad hoc operation, it can also use a cellular-like infrastructure. They show

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that although this support can bring an exponential improvement in the capacity, the per node throughput still asymptotically vanishes, although at a much slower rate. Infrastucture-based hybrid scenarios were also considered by Liu [17] and Toumpis [25], all pointing in the direction that vanishing throughput remains in effect, given that the infrastructure size is not overwhelming compared to the ad hoc network size. A closely related issue is network connectivity Naturally, to send any message to an arbitrary destination in a static network, a minimum requirement is that the network needs to be connected. Unfortunately, however, there is an asymptotically very high price for connectivity. Before we analyze it in more detail in later sections, let us just mention here that all investigations on connectivity (e.g., [7,11,21,22,24,27,28]) show that the node degree, that is, the number of neighbors, has to grow to infinity if we want to provide connectivity in the limit, with high probability. This is bad news again, since in any reasonable scenario, an infinitely growing neighborhood is prone to performance breakdown.

2.1.3 Escapes from the Vanishing Throughput Effect At this point one may wonder has any model been found at all for large random ad hoc networks in which constant (i.e., nonvanishing) per node throughput can be maintained in the asymptotic regime? The answer is yes, but unfortunately, with serious reservations. One possibility is to consider the effect of mobility, since all the above results refer to random, but static networks. Grossglauser and Tse [9] analyze the mobile version of the Gupta–Kumar [10] model, assuming that the nodes move randomly and independently with uniform stationary distribution over the unit disk. The key advantage of mobility in this setting is that either a source node can get close to its destination and send the data directly, or it can spread the packets among other nodes, which relay the data to the destination whenever they get close to it. A typical general state of this network is that each node buffers many packets destined to different destinations and whenever a node gets close to another node, it sends the data, if any, waiting for that destination. Grossglauser and Tse [9] prove that in this setting it is possible to maintain asymptotically constant per session throughput. The problem is, however, that it comes at the price of infinitely growing delay. Gamal et al. [8] analyzed the trade-off between throughput and delay and found that with bounded node movement speed (it is certainly bounded at least by the speed of light) the average delay grows to infinity with the network size. Note that each packet travels at most 2 hops in this network (either directly to the destination or through a single relay node), so the delay is due to waiting to get close to the destination. Another problem is that mobility in the Grossglauser–Tse model is not an option, it is an obligation: essentially, the nodes must be on the move all the time to make the solution workable. Another possible escape from the vanishing throughput effect is to restrict the traffic pattern in the random static network. Li et al. [16] argue that the random destination scenario in Gupta–Kumar model can be regarded as a worst-case traffic

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distribution. The authors find that if the traffic tends to be local, in the sense that the expected route hop-length is bounded, then constant throughput can be maintained in the static random network. This is still not sufficiently reassuring, since it would be desirable that the network can handle any traffic pattern, rather than only a small subset of the possibilites. Furthermore, if we do not want to replace the network with a multitude of small local networks that are disconnected from each other, then the problem of the infinitely growing node degrees still remains. Another approach to improve the asymptotic throughput scaling is to apply more sophisticated physical layer solutions such as multiple input multiple output ¨ ur et al. [18] shows that with intelligent, hierar(MIMO). A recent paper of Ozg¨ chical node cooperation, and MIMO techniques, it is possible to achieve an aggregate throughput of Ω(n 1− ) for n randomly placed nodes, where > 0 is an arbitrarily small constant. This translates into a per S–D pair throughput of Ω(1/n ). If is chosen small enough, then it is close to the ideally sought constant throughput per node. Nevertheless, since must be a fixed positive constant, no matter how small it is, the per node throughput will still vanish as n → ∞. In the next section we point out a common reason of the notorious vanishing throughput effect. Since mobility raises different problems that are outside the scope of this chapter, we focus on large, random static networks, which is the most frequently discussed case in the literature on the fundamental limits of ad hoc and sensor networks.

2.2 Why Does the Throughput Vanish? To better understand a fundamental reason for the vanishing throughput, let us briefly discuss what causes it and how it is caused in the Gupta–Kumar model [10]. One may observe that the transmission radius r of nodes has two opposite effects. If r is small, then more hops are needed to deliver a packet to its destination, since in each hop the packet can advance at most a distance of r toward its destination. Therefore, small r causes a growing burden of nodes to serve as relays, which decreases the end-to-end throughput. This would justify choosing r as large as possible. On the other hand, large transmission radius increases the interference which causes the throughput to decrease again, so interfence reduction would require choosing r as small as possible. The detailed analysis of the above conflicting tendencies in [10] shows that the forwarding burden is proportional to 1/r , since the average route hop-length is proportional to 1/r. On the other hand, the interference increases quadratically with the radius, due to the area involved, which is proportional to r 2 . Balancing the two effects yields the conclusion that r has to be chosen as small as possible, as the interference reduction, due to its quadratic nature, brings more benefit than what is lost by longer routes. Specifically, the joint effect results in the formula 1 , (2.1) λ(n) = O nr (n)

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where n is the number of nodes, λ(n) is the throughput in bit/s for each S–D pair, and r (n) is the transmission radius (as a function of n). It is clear from (2.1) that if we want to avoid λ(n) → 0, then r (n) has to tend to 0 at least as fast as 1/n, so that nr (n) does not grow to infinity. There is, however, an effect that does not allow to choose the transmission radius arbitrarily small. This is the requirement that the network topology must be connected, since otherwise communication between certain endpoints sbecomes impossible. The discussed model uses an earlier result of the same authors [11] about the needed transmission radius for asymptotic connectivity. They show that if the nodes are placed uniformly at random in a unit disk, then the network is connected with probability approaching 1 if and only if the transmission radius satisfies πr 2 =

ln n + c(n) n

(2.2)

with c(n) → ∞. According to (2.2), it is necessary for connectivity that ln n r> πn holds for all large enough values of n. Combining it with (2.1), we obtain ⎛ ⎞ 1 1 λ(n) = O ⎝ ⎠ = O √ n ln n n lnnn clearly showing the vanishing throughput effect. The fundamental formula (2.2) plays a role in all discussed theoretical models of large, random, static ad hoc networks. The lower bound on the transmission radius, enforced by the network connectivity requirement, can be viewed as a key cause of the vanishing throughput effect, since without it the transmission radius could be chosen small enough to gain more from reduced interference than what is lost by longer hop-distances, as discussed earlier. To obtain a graph theoretical view of the network topology, we can translate (2.2) into the expected node degrees. If the nodes are placed uniformly at random in a unit disk, then πr 2 is the expected number of nodes that fall in the range of a node that is not at the border of the disk, so that its range is fully in the domain. This is also the probability that a random node falls in this range, so the expected number of neighbors is nπr 2 . Since only a vanishing fraction of nodes are close to the border, we can asymptotically ignore the border effect and reformulate (2.2) in the following way. For the Gupta–Kumar model, connectivity requires that the node degrees grow to infinity at least logarithmically with the network size. It is worth mentioning that infinitely growing node degrees alone, even without the capacity analysis, can kill scalability, since the processing requirements of a node are likely to grow at least proportionally with the size of the neighborhood.

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Based on the above arguments, we formulate the following thesis: If a model for random, static ad hoc or sensor networks requires infinitely growing node degrees for connectivity, then it results in a scalability breakdown, i.e., it becomes asymptotically inoperable.

Of course, in this form, this is not a formal theorem, just an observation that we have made while studying the models known to us for large, random, static networks. Note that the randomness of the network is an essential point here. If we consider large, but nonrandom network topologies, such as an infinite grid, then we can easily have connectivity without infinitely growing node degrees. The aforementioned thesis leads to the question: which general properties of a random network model can enforce infinitely growing node degrees as a price for connectivity? Note that in the Gupta–Kumar model it is derived in a rather special situation: the node positions are chosen uniformly at random in a unit disk and each node has the same transmission radius. It leaves open, however, a number of questions. What if the domain is more complicated? What if the distance is not Euclidean? What if the distribution is not uniform? What if the existence of a link depends on the locations of both end-nodes, in a possibly complicated way, rather than their distance only? In the next sections we attempt to give a general answer to such questions.

2.3 Previous Results on Connectivity Let us first review some existing results on the connectivity of random network models. In our context, the typical model in the literature is the following: n nodes are placed randomly and independently in a regularly shaped domain, which is most often a square or a disk in the Euclidean plane. Each node has a transmission radius of r , and two nodes are connected with a link if and only if their distance is at most r . The radius is typically a function of n in the asymptotic analysis. Note that this geometric random graph model is different from the more traditional independent-edge random graph model (also called Erd¨os–R´enyi random graphs), since in the geometric setting the edges are correlated. Many results are available for the independent-edge model (see, e.g., [4]), but they are not directly applicable to ad hoc networks, for which the geometric setting, involving edge correlations, is more suitable. As one of the early results on ad hoc network connectivity, Philips et al. [24] proved the following. Assume the nodes are chosen in a square of area A from a planar Poisson process of constant density D. (This is asymptotically equivalent to choosing the points independently at random from the uniform distribution over the domain.) The area A of the square grows to infinity, while the density remains constant, so the number of nodes also grows to infinity. A result of [24] is that for any > 0, if r≤

(1 − ) ln A/π D

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then the network gets disconnected with probability approaching 1, as A → ∞. It implies that the transmission radius r cannot remain bounded if we want connectivity with a growing number of nodes that are placed with constant density in a growing area. If we want to keep the entire domain constant, it can be achieved by normalizing the quantities with the domain size. As already mentioned in the previous section, Gupta and Kumar [11] analyzed the situation when the nodes are placed uniformly at random in a unit disk in the plane. They investigated the critical transmission range, that is, the minimum transmission radius needed for connectivity. They obtained that the network is asymptotically connected with probability 1 if and only if the transmission radius satisfies πr 2 =

ln n + c(n) n

with c(n) → ∞. Wan and Yi [27] extended the results to k-connectivity on a unit disk and square. The aforementioned result of Gupta and Kumar [11] can also be deduced from Penrose’s formula [21,23] on the asymptotic distribution of the longest edge of a minimum spanning tree in a random geometric graph, since the longest edge length in a minimum spanning tree is known to be equal to the critical transmission range [23]. Penrose analyzes a rather general setting, including a large class of probability density functions, allowing the nodes to be placed in an irregularly shaped area, in a (possibly) high dimensional normed space. This model allows the incorporation of many different distance concepts. It is assumed, however, that the considered distance is derived from a norm. This excludes many distance options that could take radio propagation characteristics and other practical features into account. This problem was remedied in the Generalized Geometric Random Graph model of Farag´o [7] that is based on the concept of a premetric space, allowing much more general concepts of distance. The node degree required for connectivity was analyzed by Xue and Kumar [28] in a somewhat different model. They place n nodes uniformly at random in a unit square in the plane, but the edges are not defined via a transmission radius. They consider the graph that arises if each node is connected to its φn nearest neighbors. That is, an edge between nodes i, j exists, if either i is among the φn nearest neighbors of j or j is among the φn nearest neighbors of i. The arising graph is denoted by G(n, φn ). Note that this model is somewhat different from the transmission radius-based geometric random graph model. For example, in the latter it may happen with positive probability that a node is isolated. On the other hand, by definition, no node can be isolated in G(n, φn ) for φn > 0. This models the situation when each node adjusts its transmission radius individually until it has the desired number of neighbors. It is shown in [28] that G(n, φn ) is asymptotically almost surely connected (i.e., the probability that it is connected tends to 1 as n → ∞), if φn > 5.1774 ln n. On the other hand, if φn 0.074 ln n, then the graph will be asymptotically almost surely disconnected. Thus, the critical number of neighbors is on the order of ln n, but the gap between the upper and lower bounds is significant,

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their ratio is close to two orders of magnitude. The upper bound was improved by Wan and Yi [27] to αe ln n, where e ≈ 2.718 is the base of the natural logarithm and α > 1 is any real constant. The issue of connectivity is closely related to the minimum degree in geometric random graphs. Penrose [22] shows that if the points are chosen uniformly at random in a d-dimensional unit cube ( d ≥ 2) and the edges are added one by one in the order of increasing length, then the graph becomes k-connected almost surely whenever all nodes reach degree ≥ k. This can be interpreted that for large geometric random graphs, almost surely, the sole reason for not being k-connected is the trivial reason that at least one node does not have sufficient degree. For simple connectivity it means the graph is connected asymptotically almost surely if and only if the transmission radius is chosen large enough so that there are no isolated nodes. All this holds not only with the Euclidean distance, but also for all l p , 1 ≤ ∞ distances. For the l∞ distance, Appel and Russo [2] determined the exact asymptotics of the minimum transmission radius rn needed to eliminate isolated nodes. They obtain rn ∼

ln n 2dn

1/d ,

where d ≥ 1 is the dimension of the space in which the nodes are chosen uniformly at random from the unit cube. The combination of this with the aforementioned results of Penrose on the degrees yields precise asymptotics for the needed transmission radius for k-connectivity, if the nodes are placed uniformly at random in a d-dimensional unit cube ( d ≥ 2) and the distance is based on the maximum norm ( l∞ distance). For Euclidean distance in the plane the asymptotics for the needed transmission radius for simple connectivity ( k = 1) was derived earlier by Dette and Henze [6].

2.4 A Common Generalization of Models 2.4.1 Motivation One may consider many different variants of the random ad hoc network topology model, of which the Gupta–Kumar model is only a very special case. In general, the nodes can be located in a different domain, not only a planar unit disk or square. The distance can be measured in many different ways, not only by the Euclidean distance. The probability distribution can also be arbitrary, rather than uniform. It is not even necessary that the links are defined merely by distance, the existence of a link can also be a more complex function of the variables that describe its end-nodes, expressing, for example, location and/or direction-dependent propagation characteristics. In this section we present a model that can be viewed as a common generalization of all

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these possibilities. Then in the next section we prove a condition that captures what is necessary for connectivity in this general network model.

2.4.2 The Random Vertex Model (RVM) To specify the class of considered ad hoc network models, we define a general random graph model to capture as many special random network models as possible in a unified framework. We call it Random Vertex Model (RVM), as the randomness in this model is primarily focused in the vertices. For brevity, a random graph generated by our Random Vertex Model is called an RVM random graph. In the following text, we define separately the underlying model and the random graphs generated by it. Definition 1 A Random Vertex Model (RVM) is given by the following: • A set S with a probability measure P on it. • A sequence of functions f n : S × S → [0, 1], n = 2, 3, ..., that is, each f n maps any two elements x, y ∈ S into a real number in [0, 1]. Definition 2 An n-vertex RVM random graph (a random graph generated by the Random Vertex Model) is defined as follows: • First we draw n random elements X 1 , ..., X n independently from S, according to the probability measure P. The random variables X i are called vertex variables, they represent the vertices. • Given a realization X i = xi , ..., xn = X n of the vertex variables, an edge is drawn with probability f n (xi , x j ) for any i = j between the two respective vertices. That is, the function f n assigns an edge probability between any two given vertices and, therefore, we call f n the edge function. Note • If no ambiguity arises, we may omit the n subscript from f n (xi , x j ) and simply talk about the edge function f , understanding that it may depend on the number n of nodes. • In this chapter the edge function is assumed symmetric, that is, f (x, y) = f (y, x) always holds, because we restrict ourselves in this chapter only to undirected graphs. • In our analysis we are going to consider the asymptotic behavior, that is, when n → ∞. To avoid unnecessary mathematical difficulties that would only obscure the main message, we simply assume that all sets and functions that occur in the analysis are measurable and the expected values exist whenever needed. Before going into the analysis, let us show, via a few examples, how RVM random graphs contain many existing models of interest.

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2.4.3 Examples We present some basic examples as follows. They should convince the reader that many more examples can be created along similar lines, to cover most interesting cases of homogeneous random ad hoc and sensor networks. • Geometric random graphs: It is clear that the Gupta–Kumar random network topology model and other similar geometric random graphs are all included as a special case, since we can take a planar unit disk for the underlying set S, take X i as a uniformly distributed point in the disk, and choose the edge function as f n (x, y) =

1 if |x − y| ≤ r 0 if |x − y| > r,

where r = r (n) is the transmission range. • Independent-edge random graphs: The classic independent-edge model G(n, p) (also called Erd¨os–R´enyi random graphs) arises as another direct special case. In these graphs each edge is put independently in the graph with some probability p = p(n). As an RVM random graph it can be obtained if X i is arbitrary and f n (X i , X j ) = p(n), independently of X i , X j . Note that while many deep results are available for the independent edge model (see, e.g., [4]), these graphs generally do not model ad hoc networks, since the latter links are not independent, due to the geometric setting. There are, however, some possible exceptions. For example, in some networks it may happen that all nodes are in the range of each other, but random obstacles prevent certain pairs of nodes from receiving each other’s transmission. In this case an independent edge model may be appropriate, see, e.g., [13]. • Generalized geometric random graphs: If in a geometric random graph model the area is an irregular domain rather than a unit disk, or it is higher dimensional, or the distance is not Euclidean, or the probability distribution is different from uniform, then all these cases can be directly cast in our framework by changing the respective parts of the model. These are also captured by our earlier, premetric space based model in [7], but that model does not directly incorporate the classic Erd¨os–R´enyi random graphs. The RVM model provides a common generalization that includes both. • More complex random network scenarios: More complex ad hoc networking scenarios can be captured, too. For example, assume each node has a random location in a possibly irregular domain and the node is not always available for use. The probability of availability may be location dependent. There are also obstacles in the area that are not transparent to radio propagation (e.g., hills). Let the probability that a link exists between two nodes be a function h of their locations, given that the two nodes are both available and they are not separated by an obstacle. Let Yi be the random location of node i and Ai be its availability indicator (=1 if available, 0 otherwise). If u, v are two locations, then let L(u, v) = 1 if no obstacle separates u, v (they are in line of sight) and set

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L(u, v) = 0 otherwise. Then the vertex variables can be chosen as X i = (Yi , Ai ) and a possible edge function is f (X i , X j ) = Ai A j L(Yi , Y j )h(Yi , Y j ), where the function h, 0 ≤ h(u, v) ≤ 1, can be derived from radio propagation characteristics. The aforementioned edge function is interpreted in the following way. If two nodes are not separated by an obstacle and they are both available, then the probability of having a link between them is determined by their locations through the function h(Yi , Y j ). If the nodes happen to be separated by an obstacle (depending on their locations), or at least one of them is unavailable, then no link can exist between them. Note that even though availability probability may also be location dependent, the vertex variables are still independent, since the depedence is only among the components of the same vertex variable. • Interrelation of traffic and network topology: We can capture some features of traffic-dependent network characteristics, as well. Let the vertex variables be of the form X i = (Yi , λi ), where Yi is a random location and λi a random traffic demand for the node (both chosen from an arbitrary probability distribution and may possibly depend on each other). Then we can express the condition that a link exists between two nodes if they are within a certain range r = r (n) and the traffic does not block the link, that is, it is still available to carry more traffic. For simplicity, we may compute blocking probability via Erlang’s wellknown formula, assuming a capacity of C units on the link and its load is taken as the sum of its end-nodes traffic load λi + λ j . Then we obtain the edge function ⎧ (λi +λ j )C /C! ⎪ ⎨ 1 − C (λ +λ )i /i! if d(Yi , Y j ) ≤ r j i=0 i f n (X i , X j ) = ⎪ ⎩ 0 if d(Yi , Y j ) > r, where d(., .) is a distance function. • Battery levels: This is another example where the node variables represent more than mere location and their relationship expresses more than geometric distance. Assume the nodes are located in the plane. Let xi , yi be the coordinates of the ith node. Furthermore, we also characterize a node with its battery level E i > 0. E i represents the remaining energy, assuming the node is not fully out of energy. Thus, a node is represented by a triple (xi , yi , E i ), these are now the node variables. Let d(E i ) be the distance over which a node can communicate, given its energy level E i . (The function d(E i ) can be derived from the physical characteristics of the node and from radio propagation conditions.) Now we can introduce an (abstract) distance function as ρ (xi , yi , E i ), (x j , y j , E j ) =

(xi − x j )2 + (yi − y j )2 . min{d(E i ), d(E j )}

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With this we can define the edge function by f n (x, y) =

1 if ρ(x, y) ≤ r 0 if ρ(x, y) > r.

(2.3)

If we take r = 1, then this expresses the condition that a link exists if and only if its end-nodes are at most at a distance that can be bridged by the energy levels of both nodes. Note that the distance function ρ does not satisfy the triangle inequality, so it would not fit in the usual geometric setting. • Log-normal shadowing: A typical phenomenon in the radio environment is fading. An example of fading is a relatively slow random fluctuation in the signal strength, which occurs even if the locations are fixed. Measurements show that this random variation can be accurately modeled by a log-normal distribution (see, e.g., [19]). Hence the name log-normal shadowing, which is widely used for this phenomenon. To capture it in our model, let us characterize a node i by a triple wi = (xi , yi , ξi ), where xi , yi represent a random position in the plane and ξi is an infinite sequence of independent, log-normally distributed random variables: ξi = (ξ (i) j ; j = i, i + 1, i + 2, ...). Let us define a distance by ρ(wi , w j ) = ξb(a) (xi − x j )2 + (yi − y j )2 where a = min{i, j} and b = max{i, j}. (The reason we need an infinite sequence of log-normal random variables is that this way we can have independent log-normal shadowing for every link.) With this distance (which does not satisfy the triangle inequality, so it is not geometric) we can define the edge function the same way as in (2.3). In this way, we can express the fact that from the radio commnunication point of view one really perceives an “effective distance,” which is a log-normally modulated random variant of the physical distance.

2.5 Analysis We prove that the introduced general model, under a mild regularity condition (defined as follows), still has the following fundamental limit: if we want the graph to stay connected as n → ∞, then the expected node degrees must grow at least logarithmically. Thus, it is a necessary condition for asymptotic connectivity that the node degrees tend to infinity. Then, of course, the same holds for all covered ad hoc network models. We can prove this claim under an assumption, which we call geometric consistency. Essentially, this condition formalizes the usual requirement that the range of a

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node is small when compared to the entire domain. Since in a general RVM random graph we may not have any geometry and, consequently, in an abstract setting there may be no natural definition of node range, we express the condition via the relationship between the probabilities of the events that nodes remain isolated. Definition 3 (Geometric Consistency) Let G n denote the n-node random graph generated by a Random Vertex Model. Let Ai(n) denote the event that node X i is isolated in G n . Then the model is called geometrically consistent if there is a sequence αn → 1 such that for every i, j ≤ n, i = j (n) (n) Pr(Ai(n) ∩ A(n) j ) ≤ αn Pr(Ai ) Pr(A j )

holds. Before proceeding further, it is worth explaining this condition. Let us take first (n) αn = 1. Then the requirement is equivalent to Pr(Ai(n) |A(n) j ) ≤ Pr(Ai ). This means, if we condition on a node X j being isolated, then it can only decrease the probability that another node X j is also isolated. This is a quite natural assumption for the following reasons. If we think in terms of traditional node transmission ranges, then the condition that node X j is isolated means that no other node falls in the range of X j . Therefore, the nodes are restricted to the rest of the domain, in which X i too resides. In any reasonable ad hoc network model we can expect that this cannot decrease the chance that a node falls in the range of X i , since by “pushing out” the nodes from the range of X j to the rest of the domain, which includes X i , the chance that a random node falls in the range of X i is expected to increase. The sequence αn only serves to weaken the requirement, in the sense that it is enough if it holds asymptotically, it does not have to be precisely satisfied for a given finite n. In our more general model there may be no transmission ranges defined, but we may still require the aforementioned condition for the Ai(n) events to stay consistent with the geometry-based view. We postulate this requirement, as it will be needed in the proof and, although it is consistent with geometric intuition, it would not automatically follow from the general model of RVM random graphs. Now we can present the result which shows that it is necessary for the expected node degrees to grow logarithmically to ensure asymptotic connectivity in all covered models. As we are going to see, the proof is purely probabilistic and does not rely on the specifics of geometry. This is what makes it possible to achieve a much higher level of generality. Theorem 1 Let G n denote the n-node random graph drawn from a geometrically consistent Random Vertex Model. Assume there exists a function 0 ≤ c(n) ≤ ln n with c(n) → ∞ such that the expected degree of each node in G n is bounded by ln n − c(n). Then lim Pr(G n is disconnected) = 1

n→∞

holds and the number of isolated nodes in G n tends to infinity with probability 1 as n → ∞.

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Before proving the theorem, let us note that the ln n − c(n) bound is still logarithmic, despite c(n) → ∞, since c(n) can tend to infinity arbitrarily slowly. For example, if c(n) = 0.001 ln n, then it follows from the theorem that a degree bound of 0.999 ln n yields asymptotic disconnectivity with probability 1. Of course, we can have bounds that are even closer to ln n, such as ln n − ln ln n. Proof By the definition of the model, if we fix particular node variable realizations, say, X 1 = x1 , ..., X n = xn , then the probability of edge existence between the ith and jth nodes under this realization is f n (xi , x j ), which depends on the node realizations. On the other hand, for the random ith and jth nodes X i , X j the probability that an edge exists between them is pn = E( f n (X i , X j )), which is the same value for all i, j, since all node variables are independent and identically distributed (i.i.d.). (Note, however, that the edges are generally not independent.) Let pn (xi ) be the probability that an edge exists between X i and X j in G n , conditioned on the event {X i = xi }. That is, pn (xi ) = E( f n (xi , X j )). Note that pn (xi ) depends on the particular realization xi of X i , but not on the The realization of X j , since that is averaged out with the expectation. value of pn (xi )is related to the unconditional edge probability pn via E pn (X i ) = pn . Once we condition on {X i = xi }, the edges adjacent to X i become conditionally independent, since the other endpoints of these edges are chosen independently. Recall that Ai(n) denotes the event that X i is isolated among the n nodes. Then we have n−1 . Pr(Ai(n) |X i = xi ) = 1 − pn (xi ) Observe now that the function g(x) = (1 − x)n−1 is convex for 0 ≤ x ≤ 1, so we can use Jensen’s inequality to obtain a lower bound for Pr(Ai(n) ). Jensen’s well-known inequality saysthat for any variable ξ and for any convex random function h the inequality E h(ξ ) ≥ h E(ξ ) holds, which is a consequence of the definition of convexity. Thus, we can write Pr(Ai(n) ) = E Pr(Ai(n) |X i ) = E (1 − pn (X i ))n−1 ≥ n−1 n−1 1 − E( pn (X i )) = 1 − pn . Since each edge exists with probability pn , therefore, by the linearity of expectation, the expected degree of a node is (n − 1) pn , even if the edges are not independent. The expected degree is bounded by ln n − c(n) (by assumption), so we have . Substituting this in the aforementioned lower bound for Pr(Ai(n) ) pn ≤ ln n−c(n) n−1 yields Pr(Ai(n) )

ln n − c(n) n−1 ≥ 1− . n−1

2 Random Graph Models and the Limits of Scalability

33

Let us now use the fact that (1 − xnn )n ∼ e−xn holds for any sequence xn whenever xn → 0 (see, e.g.,[14]. Choosing xn = ln n−c(n) n we have xnn = ln n−c(n) → 0, so n n−1 n−1 there is a sequence an → 1 such that ln n−c(n) xn n−1 xn n 1 n ≥ 1− = an e− n−1 n = an n −1− n−1 e n−1 c(n) Pr(Ai(n) ) ≥ 1 − n n holds, which implies n

Pr(Ai(n) ) ≥ an n − n−1 e n−1 c(n) . 1

n

i=1

Since limn→∞ n − n−1 = limn→∞ e− n−1 ln n = 1 and an → 1, c(n) → ∞, therefore, we obtain 1

1

lim

n→∞

n

Pr(Ai(n) ) = ∞.

(2.4)

i=1

(n) Note that even if now we know that i Pr(Ai ) tends to infinity, this does not (n) necessarily imply that infinitely many of the Ai events occur with probability 1, since these events are not independent. We need more work to prove that in fact infinitely many of them occur with probability 1. Let us consider the random variable η=

n

I A(n) . i

i=1

Here we used the notation that for any event A the random variable I A is the indicator of A, that is, I A takes the value 1 if A occurs and 0 otherwise. Then E(I A ) = Pr(A). n (n) The expected value of η is E(η) = i=1 Pr(Ai ). We can now bound the deviation of η from its expected value via the Chebyshev inequality as Pr (|η − E(η)| > E(η)) ≤

var(η) 2 (E(η))2

where var(η) = E(η2 ) − (E(η))2 is the variance of η and > 0 is a constant. Substituting the expression of η and E(η) yields n n n n (n) var I i=1 Ai Pr I A(n) − Pr(Ai(n) ) > Pr(Ai(n) ) ≤ 2 . i (n) n i=1 i=1 i=1 2 i=1 Pr(Ai )

34

A. Farag´o

Since E I A(n) I A(n) i

var

j

= Pr Ai(n) ∩ A(n) , therefore, we can express j

n

I A(n) i

=

Pr

Ai(n)

∩

A(n) j

i, j≤n

i=1

−

n

2 Pr(Ai(n) )

.

i=1

Now we are going to use the following claim: Claim 1 lim inf n

Pr(Ai(n) ∩ A(n) j ) 2 ≤ 1. (n) i≤n Pr(Ai )

i, j≤n

(2.5)

We first show how to prove the theorem using Claim 1 and then we prove Claim 1 itself. Using the expression of the variance, Claim 1 implies (n) (n) n var i, j≤n Pr Ai ∩ A j i=1 I Ai(n) −1≤0 lim inf 2 = limn inf 2 n n (n) (n) n Pr(A ) Pr(A ) i=1 i=1 i i and since the above quantity cannot be negative, it is equal to 0. Thus, taking = 1/2 in the Chebyshev inequality, we obtain n n n 1 (n) (n) I A(n) − Pr(Ai ) > Pr(Ai ) = 0. (2.6) lim inf Pr i n 2 i=1 i=1 i=1 Let us now introduce a sequence Bn of events by n n 1 (n) I A(n) Pr(Ai ) Bn = i 2 i=1 i=1 Then (2.6) implies lim inf Pr(Bn ) = 0. n

From this it follows that there is an infinite sequence n 1 < n 2 < ... < n j < ... of natural numbers for which ∞ j=1

Pr(Bn j ) < ∞

2 Random Graph Models and the Limits of Scalability

35

holds. Then, by the first Borel–Cantelli lemma,1 it follows that with probability 1 only finitely many of the Bn j occur. That is, with probability 1, the complement B n j must occur for all but finitely many n j . By the definition of Bn , this means that nj

1 (n ) ≥ Pr(Ai j ) 2 i=1 nj

I A(n j )

i=1

i

n j holds for all but finitely many n j , with probability 1. Thus, the sum i=1 I A(n j ) i must diverge with probability 1 as j → ∞, due to (2.4). If n is not in the sequence n {n j }, then n j < n < n j+1 holds for some j and since we have i=1 I Ai(n) ≥ n j n i=1 I Ai(n) must also diverge with i=1 I A(n j ) , with j → ∞ as n → ∞, therefore, i n (n) probability 1. As i=1 I Ai(n) is precisely the number of occuring Ai events for a given n, that is, the number of isolated nodes when there are n nodes, we conclude that the number of isolated nodes must tend to infinity with probability 1. Then, of course, the graph is also disconnected with probability 1. This proves the theorem. What remains is to prove Claim 1, which we do next. Proof of Claim 1 Set Sn =

Pr(Ai(n) ∩ A(n) j )

i, j≤n

and Qn =

2 Pr(Ai(n) )

.

i≤n

(For simpler notation, from now on we do not show the bound “ ≤ n” for the summation indices, but it is always meant to be there.) What we have to prove is lim infn (Sn /Q n ) ≤ 1, since this is the same as (2.5). Let us reformulate Sn and Q n as Pr(Ai(n) ∩ A(n) Pr(Ai(n) ) Sn = j )+ i = j

Qn =

i = j

1 The

Pr(Ai(n) ) Pr(A(n) j )+

i

2 Pr(Ai(n) ) .

i

first Borel–Cantelli lemma says that if the sum of probabilities of an infinite sequence of events converges, then with probability 1 only finitely many of the events occur. This remains true even if the events are not independent (see any advanced textbook on probability theory, e.g., [3])

36

A. Farag´o

Let us now recall that by the assumed geometric consistency (Definition 3) there is a sequence αn → 1 such that for i = j (n) (n) Pr(Ai(n) ∩ A(n) j ) ≤ αn Pr(Ai ) Pr(A j )

holds for every n. Hence, we can upper bound Sn as follows: Sn ≤ αn

Pr(Ai(n) ) Pr(A(n) j )+

i = j

Pr(Ai(n) )

i

We can bound Q n from below by removing the second sum in its expression: Qn ≥

Pr(Ai(n) ) Pr(A(n) j ).

i = j

Using the upper bound on Sn and the lower bound on Q n yields αn Sn ≤ Qn

i = j

(n) Pr(Ai(n) ) Pr(A(n) i Pr(Ai ) j )+ (n) (n) i = j Pr(Ai ) Pr(A j )

= αn + i = j

i

Pr(Ai(n) )

Pr(Ai(n) ) Pr(A(n) j )

.

(2.7)

Observe now that

Pr(Ai(n) ) Pr(A(n) j )=

i = j

=

2 Pr(Ai(n) )

i

≥

Pr(Ai(n) )

=

Pr(Ai(n) )

2

i

2

i

− −

Pr(Ai(n) )

i

Pr(Ai(n) )

i

Pr(Ai(n) )

−1 .

i

By substituting this into (2.7), we obtain 1 + 1/ i Pr(Ai(n) ) Sn . ≤ αn + (n) Qn i Pr(Ai ) − 1

2 Random Graph Models and the Limits of Scalability

37

(n) Since αn → 1 and we already know from (2.4) that i Pr(Ai ) tends to infinity as n → ∞, therefore, lim infn (Sn /Q n ) ≤ 1 follows, as desired, which completes the proof.

2.6 On Sufficiency We have seen that under very general conditions it is necessary for the node degrees to grow at least logarithmically to ensure asymptotic connectivity with probability 1. It is natural to ask: is this condition also sufficient? Specifically, if the expected node degrees are at least ln n + c(n) with c(n) → ∞, then does this guarantee asymptotic connectivity with probability 1? In some special cases it does. This is the case in Erd¨os–R´enyi random graphs [4] and also in certain geometric settings, for example, if the nodes are uniformly distributed points in a unit disk and the edges are defined via Euclidean distance [11]. The following example shows, however, that having superlogarithmic expected degrees is not sufficient for asymptotic connectivity in general RVM random graphs. Let S = {0, 1} and for each vertex variable Pr(X i = 0) = Pr(X i = 1) = 1/2. Define the edge function such that f (1, 1) = 1 and f (x, y) = 0 for all (x, y) = (1, 1). Then the expected degree of each node is (n − 1)/4, but at the same time, each node is isolated with probability 1/2, so the graph will not have asymptotic connectivity with probability 1.

2.7 Discussion 2.7.1 Node Degrees vs Asymptotic Connectivity We have seen that connectivity requires that the expected node degrees grow to infinity at least logarithmically with the network size, under very general conditions. This shows that the scalability breakdown is quite robust in the Gupta–Kumar model and other related models. If we change some elements of the model, such as the shape of the domain, the probability distribution, the distance, etc., it is quite unlikely to invalidate the lack of scalability. Does it mean that it is hopeless to get rid of this fundamental problem? Apparently it does, as long as we stick to the approach that the existence (or the probability) of a link is fully determined by the status of its end-nodes. On the other hand, if we allow that the existence of a link may also depend on other nodes, then the situation may change. Is it realistic to assume such a crossdependence? Under certain circumstances it is. For example, a node may apply power control to adjust its transmission power, so that it has at least a certain number of neighbors. In such a case, the existence of a link depends not only on its end-nodes, but also on the distance of the end-nodes to other nodes.

38

A. Farag´o

This type of situation was analyzed by Xue and Kumar [28], as we have already mentioned in Section 2.3. They place n nodes uniformly at random in a unit square in the plane and consider the graph that arises if each node is connected to one of its φn nearest neighbors. This model is different from the transmission radius– based geometric random graph model. For example, in the latter it may happen with positive probability that a node is isolated. On the other hand, by definition, a node can never be isolated in G(n, φn ) for φn > 0. This captures the situation when each node adjusts its transmission radius individually until it has the desired number of neighbors. It is shown in [28] that G(n, φn ) is asymptotically almost surely connected if φn > 5.1774 ln n, while for φn < 0.074 ln n the graph will be asymptotically almost surely disconnected. Thus, the critical number of neighbors to connect for global connectivity is in the order of ln n. If we compare this with our general model, then we can see both a similarity and a dissimilarity. The similarity is that having significantly less than ln n neighbors causes almost sure disconnectivity in both. On the other hand, in the Random Vertex Model, disconnectivity is always accompanied (and, in fact, caused) by an infinitely growing number of isolated nodes, while in the Xue–Kumar model there are no isolated nodes at all. Yet, it still requires infinitely growing degrees, so it does not resolve the scalability breakdown. One may wonder at this point: can it happen at all in any random graph model that asymptotic global connectivity does not require infinitely growing node degrees? Interestingly, the answer is yes, although with reservations. Cooper and Frieze [5] prove the following. Assume there are n nodes and for each pair of nodes a length is assigned from [0, 1], independently at random. Let us refer to these numbers as distances (though they do not satisfy the triangle inequality). Let us define a graph such that each node connects to its three nearest neighbors, in terms of the random distances. Cooper and Frieze [5] prove, among other things, that the arising graph is connected with probability approaching 1, as n → ∞. This is quite interesting, since the average degree in the arising random graph is a small constant. If we compare the Xue–Kumar and Cooper–Frieze models, it is clear that they behave very differently. The former needs infinitely growing node degrees for connectivity, while the latter does not (although at the price of being farther from geometry, which can justify some reservations about its applicability to ad hoc networks). Nevertheless, it shows that the way of defining the edges does make a difference in those models in which the existence/probability of the edges is not restricted to depend only on the endpoints. This might give some hope to overcome the scalability paradox by developing more refined ad hoc and sensor network models.

2.7.2 Other Parameters vs the Limits of Scalability As we have seen and analyzed, under very general conditions, node degree remains a “badly behaving” parameter from the viewpoint of connectivity, as it cannot be kept bounded if we want asymptotic connectivity. It is natural to ask at this point if

2 Random Graph Models and the Limits of Scalability

39

there is any other local parameter with similar “bad behavior?” The answer is yes, although quite nontrivial. We have proved in [7] that a new parameter called link dynamics has this property. We briefly summarize this result. Link dynamics is defined as the worst case length ratio of the longest and shortest link adjacent to the same node. It is reasonable to assume that under practical conditions link dynamics should remain bounded for the following reasons. It is clear that the practical length of a link is bounded from above by limitations on transmission power and receiver sensitivity. It is less obvious, but is still the case, that the link length is also bounded from below by practical constraints. The reason for the lower bound can be explained as follows. A node in typical models is represented by a point and the link length is the distance between two such points. While two points can get arbitrarily close to each other in theory, the pratical node is a threedimensional body with positive volume. If the idealized point representation of the node corresponds, say, to the center of gravity of the real node (or its antenna, which is also a body with positive volume), then these points cannot get arbitrarily close to each other, due to practical limits on equipment miniaturization. If we measure distance in relative units, say, as multiples of the shortest link length, then we can express the aforementioned considerations such that the link dynamics is expected to remain bounded in practice, even if the number of nodes grow arbitrarily large. Using the concept of link dynamics, we have proved in [7] a new fundamental limit of topology control: if the number of nodes grow to infinity, but the link dynamics remains bounded, then the network gets disconnected almost surely (i.e., with probability approaching 1). Moreover, the disconnection is essential in the sense that the number of isolated nodes will also tend to infinity. This result was proved in a model that is similarly general as the one analyzed in this chapter. Nevertheless, the two models are not identical. It seems an interesting open question to characterize those parameters that have a similar ”antiscalable” behavior as the node degree and the link dynamics.

2.8 Conclusion We have analyzed the paradoxical situation that in ad hoc and sensor networks, despite the existing general belief that these networks will grow ultimately very large, the theoretical models predict a scalability breakdown, in the form of vanishing per session throughput. We identified that the infinitely growing node degrees, required by asymptotic connectivity, is a key reason for the scalability breakdown. We have proved that in a new model, which is significantly more general than previous models, it is still necessary that the node degrees must grow at least logarithmically with the network size to avoid asymptotically almost sure disconnectivity. This led us to the conclusion that we can only hope for a resolution of the scalability paradox if the network model considers more complex conditions for link existence or probability than a restricted dependence only on the end-nodes of the link.

40

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Acknowledgments This work has been supported in part by NSF Grants ITR 0220001 and CCF 0634848.

References 1. A. Agarwal and P.R. Kumar, “Improved Capacity Bounds for Wireless Networks”, Wireless Communications and Mobile Computing, 4(2004), pp. 251–261. 2. M.J.B. Appel and R.P. Russo, “The Minimum Vertex Degree of a Graph on Uniform Points in [0, 1]d ”, Advances in Applied Probability, 29(1997), pp. 582–594. 3. P. Billingsley, Probability and Measure, Wiley, 1979. 4. B. Bollob´as, Random Graphs, Second Edition, Cambridge University Press, 2001. 5. C. Cooper and A. Frieze, “On the Connectivity of Random K th Nearest Neighbour Graphs”, Combinatorics, Probability and Computing 4(1996), pp. 343–362. 6. H. Dette and N. Henze, “The Limit Distribution of the Largest Nearest Neighbour Link in the Unit d-Cube”, Journal of Applied Probability, 26(1989), pp. 67–80. 7. A. Farag´o, “On the Fundamental Limits of Topology Control in Ad Hoc Networks”, Algorithmica, 49(2007), pp. 337–356. 8. A.E. Gamal, J. Mammen, B. Prabhakar and D. Shah, “Throughput-Delay Trade-off in Wireless Networks”, IEEE INFOCOM’04, Hong Kong, March 2004. 9. M. Grossglauser and D. Tse, “Mobility Increases the Capacity of Adhoc Wireless Networks”, IEEE/ACM Transactions on Networking, 10(2002), pp. 477–486. 10. P. Gupta and P.R. Kumar, “The Capacity of Wireless Networks”, IEEE Transactions on Information Theory, 46(2000), pp. 388–404. 11. P. Gupta and P.R. Kumar, “Critical Power for Asymptotic Connectivity in Wireless Networks”, In: Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming, Edited by W.M. McEneany, G. Yin, and Q. Zhang, Birkhauser, Boston, 1998, pp. 547–566. 12. P. Gupta and P. Kumar, “Internets in the Sky: The Capacity of Three Dimensional Wireless Networks”, Communications in Information and Systems, 1(2001), pp. 39–49. 13. P. Jacquet and A. Laouti, “Analysis of Mobile Ad Hoc Network Routing Protocols in Random Graph Models”, INRIA Technical Report No 3835, 1999. 14. K. Knopp, Theory and Application of Infinite Sequences, Dover Publications, New York, 1990. 15. U.C. Kozat and L. Tassiulas, “Throughput Capacity of Random Ad Hoc Networks with Infrastructure Support”, ACM MOBICOM’03, Sept 14–19, San Diego, California, pp.55–65. 16. J. Li, C. Blake, D.S.J. De Couto, H.I. Lee and R. Morris, “Capacity of Ad Hoc Wireless Networks”, ACM MOBICOM’01, Rome, Italy, 2001, pp. 61–69. 17. B. Liu, Z. Liu and D. Towsley, “On the Capacity of Hybrid Wireless Networks”, IEEE INFOCOM’03, San Francisco, California, April 2003, pp. 1543–1552. ¨ ur, O. L´ev´eque, ’eque and D. Tse, “Hierarchical Cooperation Achieves Optimal 18. A. Ozg¨ Capacity Scaling in Ad Hoc Networks”, Technical Report, arXiv:cs.IT/0611070v3, Feb 12, 2007. 19. K. Pahlavan and P. Krishnamurty, Principles of Wireless Networks, Prentice Hall, 2002. 20. C. Peraki and S.D. Servetto, “On the Maximum Satble Throughput Problem in Random Networks with Directional Antennas”, ACM MOBIHOC’03, Annapolis, Maryland, June 1–3, 2003, pp. 76–87. 21. M.D. Penrose, “The Longest Edge of the Random Minimal Spanning Tree”, Annals of Applied Probability, 7(1997), pp. 340–361. 22. M.D. Penrose, “On k-connectivity for a Geometric Random Graph”, Random Structures and Algorithms, 15(1999), pp. 145–164.

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23. M.D. Penrose, “A Strong Law for the Longest Edge of the Minimal Spanning Tree”, Annals of Applied Probability, 27(1999), pp. 246–260. 24. T.K. Philips, S.S. Panwar and A.N. Tantawi, “Connectivity Properties of a Packet Radio Network Model”, IEEE Transactions on Information Theory, 35(1989), pp. 1044–1047. 25. S. Toumpis, “Capacity Bounds for Three Classes of Wireless Networks: Asymetirc, Cluster and Hybrid”, ACM MOBIHOC’04, Roppongi, Japan, May 24–26, 2004, pp. 108–116, 133–144. 26. S. Toumpis and A. Goldsmith “Ad Hoc Network Capacity”, Asilomar Conference on Signals, Systems and Computers, 2000. 27. P.-J. Wan and C.-W. Yi, “Asymptotic Critical Transmission Radius and Critical Neighbor Number for k-Connectivity in Wireless Ad Hoc Networks”, ACM MOBIHOC’04, Roppongi, Japan, May 2004, pp. 1–8. 28. F. Xue and P.R. Kumar, “The Number of Neighbors Needed for Connectivity of Wireless Networks”, Wireless Networks, 10(2004), pp. 169–181. 29. S. Yi, Y. Pei and S. Kalyanamaran, “On the Capacity Improvement of Ad Hoc Wireless Networks Using Directional Antennas”, ACM MOBIHOC’03, Annapolis, Maryland, June 1–3, 2003, pp. 108–116.

Chapter 3

Analysis of Effective Connectivity in Mobile Wireless Communications J. David Haughs and Dongsoo S. Kim

3.1 Introduction Ad hoc wireless networks are formed by a group of wireless mobile nodes. The wireless nodes can be any sort of microprocessor device with the ability for wireless communication. By nature, a wireless adhoc network lacks any fixed network infrastructure. Users are provided connectivity with unrestricted mobility due to the self-organizing, rapidly deployable architecture of wireless ad hoc networks. Because a node in a wireless ad hoc network is connected with unrestricted mobility, the topology of the network is dynamic. Realistic mobility modeling becomes very critical for analyzing node behavior and network performance. Common mobility models are the random walk and random way point mobility models [1, 4, 5, 9]. The random walk mobility model was derived from the Brownian motion, which is a stochastic process that models random continuous motion [8]. In this model, a mobile node moves from its current location with a randomly selected speed in a randomly selected direction. The new speed and direction are both chosen from predefined ranges, [vmin , vmax ] and [0, 2π ), respectively [5]. The new speed and direction are maintained for an arbitrary length of time randomly chosen from(0, tmax ]. At the end of the chosen time the node makes a memoryless decision of a new random speed and direction. In the random waypoint mobility model, a mobile node chooses a random destination within the deployed area. With the destination chosen, the mobile node randomly chooses a speed at which to travel arbitrarily from [vmin , vmax ]. Upon reaching the destination, a mobile node will pause for a random time before determining a new destination and speed. In the random waypoint model, mobile

J.D. Haughs Department of Electrical and Computer Engineering, Indiana U. Purdue U. Indianapolis, Indiana, USA e-mail: [email protected] This research was supported in part by the National Science Foundation under grant CCF-0514975.

S.K. Makki et al. (eds.), Sensor and Ad Hoc Networks, C Springer Science+Business Media, LLC 2008 DOI: 10.1007/978-0-387-77320-9 3,

43

44

J.D. Haughs, D.S. Kim

nodes have a tendency to concentrate to the middle of the deployment region [4, 12, 14], indicating that this model does not present a truly uniform node distribution. Both mobility models presented earlier are used regularly in the simulation of wireless mobile nodes [6, 7, 10, 13, 14, 15]. In addition to choosing the appropriate mobility model, one must also understand the coverage of a mobile node (MN) under a given situation. It is common to assume that a node has a uniform coverage area independent of its location within the deployment area without full understanding of the impact of the transmission range in that deployment area [3, 10]. This chapter will present the dependency of location and transmission power on the coverage of a MN and provide an analytical method for describing this behavior and analyzing connectivity of MNs.

3.2 Effective Node Coverage The effective coverage of a mobile node describes the number of MNs that can communicate with a given node in the deployment region. Effective coverage is dependent on the location of the node and its transmission power in relation to the size of the deployment region and nodal density. For simplicity, it is assumed that a MN has a uniform circulartransmission area that directly corresponds to its transmission power. The transmission power of a MN has a range of length r and can therefore be represented as the radius of the circular transmission area centered at the MN with a total transmission area of πr 2 . This is commonly assumed but is not always true. As a MN moves about the deployment region, the transmission area could be affected by the boundary effect. The boundary effect occurs when a MN is at a distance less than r from one or more boundaries of the deployment region. At this distance, a portion of the MN’s total transmission area extends beyond the boundary of the deployment region. This portion of transmission area is considered unusable by the MN as there cannot exist a MN to communicate with beyond the boundary. Therefore, the effective coverage area of the affected MN is less than πr 2 . Figure 3.1 illustrates this behavior. The figure shows two identical nodes near one corner of a deployment region. The solid dot in the middle of the shaded circle is the MN, the shaded circle represents the transmission area of the MN. The dashed line in the figure is located a distance r from the boundary. This line represents a thre shold into a region of cutoff for a MN’s effective coverage area. As can be seen in the figure, the MN that has crossed this threshold line and is nearing the boundary has a portion of its transmission area extending beyond the boundary of the deployment. This hatched area serves no benefit to the MN. The boundary effect can have a major impact on the coverage area of a MN. When analyzing node connectivity in ad hoc networks, it is important to take into account the boundary effect to prevent an overestimation of coverage area. Total transmission area data can beskewed by the cutoff areas at the boundaries.

3 Analysis of Effective Connectivity in Mobile Wireless Communications

45

Fig. 3.1 Illistration of boundary effect using two identical nodes. One node’s coverage extends beyond the boundary of the deplyment region

3.3 Effective Connectivity Model The purpose of this model is to predict node connectivity based ontransmission range and to model the behavior of nodes under different simulations. An average effective connectivity area in two dimensional space, μ(r ), is given as μ(r ) = S(r,x,y) × p(x,y) d x d y, (3.1) where x and y represent the location of the node, p(x, y) is the probability that a node is located at the point (x, y), and S(r, x, y) denotes the effective coverage of the node with the transmission range r and at the location (x, y). The analytical model is computed by considering a node’s effective coverage area in different sections, or regions, of the deployment area. Figure 3.2(a) illustrates the regions in a L × L deployment area when r ≤ L2 . The regions are created based on the transmission range, r , of a MN. The distance r creates the various regions in side the deployment area. As r nears 0, region A will dominate the deployment;

(a) r ≤ L2

(b) L2 r < L2 ≤

Fig. 3.2 Regional division of deployment area for computation of effective connectivity

46

J.D. Haughs, D.S. Kim

conversely, as r nears L2 , regions C will dominate. For the casewhere L2 < r ≤ L, one must refer to Fig. 3.2(b). As r increases beyond L2 , the lines representing the regions will cross paths and continue in opposite directions decreasing region C and creating two new regional divisions, D and E. All of the regions from A to E represent differing levels of effective coverage area and create different calculations for S(r, x, y). The functions for S(r, x, y) for each region are explained in the following subsections.

3.3.1 Region A Nodes lying within Region A do not have coverage areas intersecting any boundary and therefore, are able to utilize their entire coverage area. The coverage area of a node that is residing in Region A is given as S A (r, x, y) = πr 2

(3.2)

3.3.2 Region B In Region B a node’s coverage area will extend beyond one and only one boundary of the deployment area. Figure 3.3 demonstrates this single edge boundary effect for a node within Region B1 of Fig. 3.2. It also shows how the effective area is broken into slices to obtain a function for effective coverage for a node within this region. For B1 the coverage area is π x πr 2 − arccos + . S B1 (r, x, y) = x r 2 − x 2 + r 2 2 r 2

(3.3)

Because B1 , B2 , B3 , and B4 are symmetric, (3.3) can be used to represent each of the four regions of B. Therefore, S B (r, x, y) = S B1 (r, x, y)

Fig. 3.3 Single edge boundary effect for a node within Region B1

3 Analysis of Effective Connectivity in Mobile Wireless Communications

47

3.3.3 Region C The coverage area of a node within Region C will intersect two of the deployment area’s boundaries. There are two cases to take into consideration for a node located in this region. The first case, shown in Fig. 3.4(a) as Case C1 , occurs when a node is located no more than a distance of r from the corner of the deployment area. The second case, shown in Fig. 3.4(b) as Case C2 , occurs when a node is located a distance greater than r from the corner but still within the bounds of region C. This distance r from the corner forms an arc inside of Region C as seen√ in Fig. 3.5. Within the region labeled C3 in Fig. 3.2, the arc is defined as r 2 − x 2 . For a node located withinC3 the first case of the coverage area for r ≤ L2 is SC3 (r, x, y) =

The second case for r ≤ SC3 (r, x, y) =

1 x πr 2 r2 π + x r2 − x2 + − arccos 4 2 2 2 r 2 1 2 π y r + y r − y2 + − arccos + xy 2 2 2 r L 2

(3.4)

generates the equation

1 x 1 2 πr 2 r2 π + x r2 − x2 + − arccos + y r − y2 4 2 2 2 r 2 2 1 r π 1 y + x r 2 − x 2 + y r 2 − y2 + − arccos 2 2 r 2 2 x y r2 π − arccos − arccos (3.5) + 2 2 r r

(a) Case C1

(b) Case C2

Fig. 3.4 Double edge boundary effect for a node within Region C3

Fig. 3.5 Arc formed from r in region C3

48

J.D. Haughs, D.S. Kim

As with S B (r, x, y), the regions of SC (r, x, y) are symmetric. For the case of r > with in Region C shown in Fig. 3.2(b) only the first of the aforementioned cases exists. For the effective connectivity in this region (3.4) is used again; however, the limits of integration will change when calculating μ(r ). L 2

3.3.4 Region D Region D only exists when L2 < r < L. In this region a MN’s coverage area intersects three of the deployment region’s boundaries. Like Regions B and C, Region D is also symmetric. Figure 3.6 illustrates the coverage of a node within Region D. From this figure it can be seen that the coverage area of a node within this region is dependent on r , x, and y and the following equation can be obtained 1 S D1 (r, x, y) = x L + (L − y) r 2 − (L − y)2 2 L−y y 1 r2 π − arccos − arccos + y r 2 − y2 + 2 r r 2

(3.6)

3.3.5 Region E Region E emerges when L2 < r and continues to grow and take over the entire deployment region as r approaches L. The coverage area of nodes within Region E intersect the deployment region at all four boundaries. There are, however, four subcases to this region that are separated depending on the value of r . While it is true that all nodes within Region E will intersect all four boundaries of the deployment, they do so in different ways dependingon location and transmission range. The Figs. 3.7(a) through 3.7(b) display the four subcases of Region E. In each of these figures, the arcs represent the distance r from each of the four corners of the deployment region. The centralized square box represents Region E from

Fig. 3.6 Tripple edge boundary effect for a node within Region D1

3 Analysis of Effective Connectivity in Mobile Wireless Communications

(a) Subcase E1

(b) Subcase E2

(c) Subcase E3

(d) Subcase E4

49

Fig. 3.7 Subcases for Region E

Fig. 3.2(b) bounded by L − r and r on both the x and y axis. As r increases the figures demonstrate the four subcases created as the arcs begin to overlap the centralized box and begin to further intersect themselves. These actions result in the four subcases explained in the following subsections.

3.3.5.1 Subcase E1

√ √ Subcase E 1 , as shown in Fig. 3.7(a), is valid for L2 < r ≤ (2 − 2)L. (2 − 2)L is the point at which the arc of radius r meets the corner of the Region E. Nodes within this subcase will expand beyond all four sides of the deployment region but will not overlap the corners of the deployment region as can be seen in Fig. 3.8. Within the bounds of this subcase, the formula for coverage area within E 1 is given as S E1 (r, x, y) = πr 2 + x r 2 − x 2 + y r 2 − y 2 + (L − y) r 2 − (L − y)2 x y L−x 2 2 2 − r arccos − r arccos − r arccos r r r L − y (3.7) − r 2 arccos r

50

J.D. Haughs, D.S. Kim

Fig. 3.8 Boundary effect for a node within E a

3.3.5.2 Subcase E2

√ For subcase E 2 , the valid range for r is (2 − 2)L < r ≤ 58 L. 58 L is the point at which the intersection of the arcs meets the boundary of Region E. As shown in Fig. 3.7(b), subcase E 2 is further broken into two subregions with separate calculations named E 2a and E 2b . S E2 (r, x, y) = S E2a (r, x, y) + S E2b (r, x, y). The breakup of Region E 2a is identical to that of subcase E 1 and is therefore calculated in the same manner but with differentlimits of integration. It was found that Region E 2a must be further subdivided into two zones to perform the calculation. The functions for zones are the same,however, they have different limits of integration. Fig. 3.9(a) shows the lower left quarter of Region E from Fig. 3.7(b) and how it is further divided into subregions and zones for calculations. To simplify

(a) Region E2a division

Fig. 3.9 Subcase E 2

(b) Boundary effect for a node within Eb

3 Analysis of Effective Connectivity in Mobile Wireless Communications

51

the calculations, the curved line labeled Line 1 in Fig. 3.9(a) is assumed to be a straight line with minimal error. The coverage area of a MN in these zones is S E2a (r, x, y) = 4 · S E2a1 (r, x, y) + 4 · S E2a2 (r, x, y).

(3.8)

Nodes in E 2b again expand not only beyond all four sides of the deployment region, but also expand beyond one corner of the deployment region as can be seen in Fig. 3.9(b). The representative equation for nodes within this region is given as S E2b (r, x, y) =

x 2 πr 2 + xy + r − x 2 + (L − y) r 2 − (L − y)2 2 2 x y 2 r2 + (L − x) r 2 − (L − x)2 + r − y 2 − arccos 2 2 r y 2 r L−y L−x − r 2 arccos − arccos . − r 2 arccos r r 2 r (3.9)

3.3.5.3 Subcase E3 Subcase E 3 , shown in Fig. 3.10, is used when

5 L 8

< r ≤

√L . 2

At the point that

r= the arcs generated from opposing corners of thedeployment region begin to overlap creating regions to be described in subcase E 4 . As one can see, subcase E 3 is broken into three subregions, consisting of three separate calculations, which have been named E 3a ,E 3b , and E 3c . Region E 3a , like region E 2a , is similar to subcase E 1 and is therefore calculated the same, but with different limits of integration. Region E 3b is similar to that of E 2b in subcase E 2 . Nodes in the region represented by E 3c continue to overlap all four sides of the deployment area, but now they also overlap two of the four corners ofthe deployment area. E 3c is calculated based on Fig. 3.10 and is given as √L , 2

Fig. 3.10 Boundary effect for a node within E 3

52

J.D. Haughs, D.S. Kim

S E3c (r, x, y) =

x 2 πr 2 L −x 2 + yL + r − x2 + r − (L − x)2 2 2 2 x r2 + (L − y) r 2 − (L − y)2 − arccos 2 r L − y L − x − r 2 arccos . (3.10) − r 2 arccos r r

3.3.5.4 Subcase E4 The final subcase, subcase E 4 , shown in Fig. 3.11 represents the case where √L2 < r ≤ L. There are four subregions within subcase E 4 named E 4b , E 4c , E 4d , and E 4e . The calculation for E 4b is similar to that of subcase E 2b and the calculation for E 4c is similar to that of subcase E 3c . Subcase E 4 presents two new subregions, E 4d and E 4e . Nodes within E 4d are represented by Fig. 3.11 and the equation for these nodes is given as S E4d (r, x, y) =

L − y 2 πr 2 + y L + x(L − y) + r − (L − y)2 4 2 L −x 2 r2 L−y 2 + r − (L − x) + arccos 2 2 r r2 L−x + arccos . 2 r

(3.11)

Subregion E 4e is the case in which a node’s coverage area expands beyond the entire deployment region and is therefore equal to the area of the deployment region S E4e (r, x, y) = L 2

Fig. 3.11 Boundary effect for a node within E 4

(3.12)

3 Analysis of Effective Connectivity in Mobile Wireless Communications

53

Fig. 3.12 Effective Transmission area due to border effect

The functions for the various regions presented earlier are independent of each other and therefore, μ(r ) can be calculated separately for each region and summed together for the final result as follows: μ(r ) = μ A (r ) + μ B (r ) + μC (r )μ D (r ) + μ E (r ). Figure 3.12 demonstrates the boundary effect by representing the recently described S(r, x, y) as the number of neighboring mobile nodes within the transmission range of a node moving away from a corner of the map (Region C). The x and y axes of the figure represent the node’s location in one quarter of a deployment map and the z axis shows the number of nodes in a given transmission range. The figure shows that as the node moves away from a corner or a map edge, the number of nodes connected directly to the node increases until it reaches a constant.

3.4 Random Walk Analytical Model In the previous chapter, (3.1) was introduced as a model for effective connectivity. This section outlines the adaptation of the effective connectivity model for use with the random walk mobility model. Section 3.2 outlined the regional differences for calculating S(r, x, y). These functions for S(r, x, y) along with the probability p(x, y) ofa node’s location under the random walk mobility model will be used in this adaptation.

54

J.D. Haughs, D.S. Kim

MNs under the random walk mobility model remain distributed uniformly during the entire simulation [5, 12]. Therefore, the function p(x, y) associated with (3.1) can be found by once again referring to Figs. 3.2(a) and 3.2(b). The probability that a node is located at a given (x, y) is identical for every point within a region. This function is derived from the uniform density of the random walk mobility model. Therefore, it is equivalent to the ratio of the area of a region to the area of the entire deployed region. When r ≤ L2 , the probabilities are as follows: r 2 p A (x, y) = 1 − 2 L

(3.13)

rr p B (x, y) = 4 1 − 2 L L

(3.14)

pC (x, y) = 4 When

L 2

r 2 L

.

(3.15)

< r ≤ L, the probabilities are: r 2 pC (x, y) = 4 · 1 − L

(3.16)

r r −1 p D (x, y) = −4 · 2 − 1 · L L

(3.17)

2 r p E (x, y) = 2 − 1 . L

(3.18)

These probabilities are then used along with the functions, S(r, x, y), for coverage area given in the Section 3.2 and inserted into (3.1) to determine the effective connectivity. μ(r ) is divided into separate calculations for each region and summed together at the end for the resulting random walk effective connectivity model.

3.4.1 Region A For Region A, (3.2) and (3.13) are brought together with 3.1 to form the following completed equation r 2 μ A (r ) = πr 2 · 1 − 2 . L

(3.19)

3 Analysis of Effective Connectivity in Mobile Wireless Communications

55

3.4.2 Region B Because (3.3) for Region B is dependent on x, when this equation and (3.14) are inserted into (3.1), μ B must be integrated with respect to x over 0 to r to determine an equation for effective connectivity based on r . Integrating this region results in a volume and therefore, must include a division by r , the length of x, to return this function to an area. When the integration is performed on μ B (r ) =

L−r

r

r 0

S B (r, x, y) · p B (x, y) d x, dy r

the resulting equation for Region B is μ B (r ) =

4r 3 (3π − 2)(L − 2r ) . 3L 2

(3.20)

3.4.3 Region C Region C for r ≤ L2 was previously divided into twoseparate cases. These two subcases, Case C1 and Case C2 , containedwithin C both utilize the same probability shown in (3.15) but have different equations. Because these functions are integrated with respect to both x and y, thefinal product of μC must be divided by the area of Region C, r 2 , so that μC represents an effective area. The resulting equations for Region C when r ≤ L2 are Case C1 √r 2 −x 2 r μC3 (r ) =

0

0

r

r

SC3 (r, x, y) · pC (x, y) d y d x r2

Case C2 μC3 (r ) =

√ r 2 −x 2

0

SC3 (r, x, y) · pC (x, y) d y d x r2

.

Upon integration and summation of μC3 (r ) from Case C1 and Case C2 , the resulting equation for Region C when r ≤ L2 is μC (r ) =

r 4 (13π − 10) . 4L 2

(3.21)

When L2 < r ≤ L, the final function must still be divided by the area of Region C so that it represents an effective area; however, this area has changed and is now (L − r )2 . The probability for this subcase is shown in (3.16). As was mentioned

56

J.D. Haughs, D.S. Kim

in Section 3.2, Region C for L2 < r ≤ L is only based on the first case of C. The resulting equation for Region C when L2 < r ≤ L is L−r L−r μC3 (r ) =

0

0

and after integrating, Region C for μC3 (r ) =

L 2

SC3 (r, x, y) · pC (x, y) d x d y (L − r )2 < r ≤ L is represented as

L −r 3L 3 + 4L 2 −L (L − 2r ) − 9r L 2 − 3Lr 2 π − 8L −L (L − 2r )r 2 3L L −r L −r L + 9r 2 L + 6Lr 2 arcsin + 9πr 2 L − 6r 2 arccos r r L −r − 11r 3 − 9πr 3 + 3r 3 π + 12r 2 −L (L − 2r ) − 6r 3 arcsin r L −r . (3.22) + 6r 3 arccos r

3.4.4 Region D The portion of the random walk effective connectivity formula relatedto Region D comes from (3.6) and (3.17). Once again the area that the region covers will beincluded in the denominator so that the final function results in the effective area of Region D. The area of Region D is(2r − L)(L − r ). After combining the area and the two equations mentioned earlier with (3.1) the resulting function is r μ D (r ) =

L−r

L−r 0

S D (r, x, y) · p D (x, y) d x d y (2r − L)(L − r )

and Region D after integration is L −r −2 (L − r ) 3 2 2 μ D (r ) = 3 L − 9 L r + 6 Lr arcsin + 6 Lr 2 + 3 r 2 π L 3L 2 r − 3 r 2 π L − 2 (−L (L − 2 r ))3/2 + 6 r 2 −L (L − 2 r ) L −r 3 3 3 + 3 r π − 6 r arcsin − 6r π . (3.23) r

3 Analysis of Effective Connectivity in Mobile Wireless Communications

57

3.4.5 Region E The portion of the effective connectivity formula for Region E is made up of Region E’s subcases as detailed in Section 3.2. The calculation of μ E (r ) is highly dependent on r and each subcase is only used in the final equation for a specific range of r . As done for the previous regions, these functions must be multiplied by the probability from (3.18) and divided by the area of Region E, (2r − L)2 . These two factors are constants in the integration as they are completely independent of (x, y). 3.4.5.1 Subcase E1

√ The range for this region was defined as L2 < r ≤ (2 − 2)L in Section 3.2 and it was also explained that there was only one formula for this subcase. The function for μ in this first subcase is r μ E1 (r ) =

r

L−r

L−r

S E1 (r, x, y) · p E (x, y) d x d y (2r − L)2

After integration, Region E for L2 < r ≤ (2 −

.

√ 2)L is

−L + r −r 2 μ E1 (r ) = 2 (2 r − L) 4 r arcsin L r −L + r − Lπ + 4 L (2 r − L) . − 4 L arcsin r

(3.24)

3.4.5.2 Subcase E2 From Section 3.2 it is known that subcase E 2 involves two subregions, E 2a and E 2b , that sum together to form the equation for subcase E 2 . To simplify the calculations, Region E was divided into four symmetric quadrants. The limits of integration for E 2a and E 2b are derived from Fig. 9(a). Each of the functions includes a factor of 4 to allow for √ all four symmetric quadrants. The resulting equations for Region E when (2 − 2)L < r ≤ 58 L are L L 2 2 4 · p E (x, y) μ E2 a (r ) = · S E2 a1 d x d y √ (2r − L)2 L−r 2Lr −L 2 √

+

2Lr −L 2

L−r

4 · p E (x, y) · μ E2 b (r ) = (2r − L)2

L 2

√ −x+L−r + 2Lr −L 2

√ −x+L−r + 2Lr −L 2

√

S E2 a2 d y d x

2Lr −L 2

SE2 b d y d x L−r

L−r

58

J.D. Haughs, D.S. Kim

that upon integration, result in the following two equations to be used when √ (2 − 2)L < r ≤ 58 L. √ 2 Lr − L 2 r2 2 2 μ E2 a (r ) = 2 r π − 2 r arcsin L r √ − 2 Lr − L 2 + L 2 − 2 r arcsin r √ 2+L 2 Lr − L − + 8 2 Lr − L 2 arcsin L − 6 r −L (−2 r + L) r −r + L + 2 r Lπ − 6 r 2 + 2 2 Lr − L 2 L − 2 Lr L + 6 r 2 arcsin r √ 2 Lr − L 2 + 2 −L (−2 r + L)L + 4 arcsin L2 r −r + L −r + L 2 − 8 r 2 Lr − L arcsin − 4 r L arcsin r r √ √ 2 Lr − L 2 − 2 Lr − L 2 + L − 8 arcsin Lr − 8 arcsin Lr r r − 6 r 2 − 2 Lr + L 2 2 Lr − L 2 + 4 π Lr − L 2 π − 4 2 Lr − L 2 Lπ −r + L 2 + 8 2 Lr − L 2 −L (−2 r + L) + 8 2 Lr − L L arcsin r 2 2 2 + 6 r + 2 2 Lr − L L − 2 Lr 2 Lr − L (3.25)

√√ t −t + 2 r −t + r 3 3 − 24 r arcsin t t − 24 r arcsin r r −t + r 2 −t + r t + 9 r 4 arcsin + 12 r 2 arcsin r r √ 3/2 2 − 10 t r −t + 2 r √ √√ − 12 t 5/2 −t + 2 rr + 18 r 3 t −t + 2 r − 120 t 2 r 2 + 80 t 3 r − 20 t 4 √ √ √√ 5/2 + 8t r 2 − 2 t r + 2 t 3/2 −t + 2 r −t + 2 r − 6 r 3 π t −t + 2 r √ √ √ t −t + 2 r 3 3 2 3/2 + 8t r − 2t r + 2t −t + 2 r − 24 r t arcsin r −t + r √ √ t −t + 2 r + 24 r 3 arcsin r

−1 μ E2 b (r ) = 6L 2

t−

3 Analysis of Effective Connectivity in Mobile Wireless Communications

+ 24 r t arcsin 3

−t +

59

√√ t −t + 2 r r

√ √ √ + 8 t r r 2 − 2 t r + 2 t 3/2 −t + 2 r −t + 2 r + 4 t 7/2 −t + 2 r −t + r √ − 24 r 2 t 3/2 arcsin −t + 2 r r √ √ t −t + 2 r 2 2 + 12 r t arcsin r √ √√ + 26 r 2 r 2 − 2 t r + 2 t 3/2 −t + 2 r t −t + 2 r √ − 18 r 2 π t 3/2 −t + 2 r √√ √ −t + t −t + 2 r 2 3/2 −t + 2 r arcsin − 24 r t + 24 r 3 π t + 80 t r 3 r √ − 24 t 2 r 2 − 2 t r + 2 t 3/2 −t + 2 rr √√ t − t −t + 2 r 4 − 6 r arcsin r √ √ √ t −t + 2 r 2 4 2 3/2 −t + 2 r t − 3 r arcsin − 26 r r − 2 t r + 2 t r √√ t − t −t + 2 r 3/2 √ (3.26) −t + 2 r − 5 r 4 + 24 r 2 arcsin t r 3/2

These two equations show how rapidly the complicated subcases of Region E grow into vastly complicated formulas for the effective coverage of the random walk mobility model. The following two subcases, E 3 and E 4 , quickly become even more complex and for this reason the result of their integrations will not fit on these pages.

3.4.5.3 Subcase E3 For 58 L < r ≤ √L2 subcase E 3 becomes the function for Region E. This subcase was previously defined in Section 3.2 and is made up of three separate subregions. As with the previous subcases, the equations for S E3 must be inserted into the equation for μ and integrated. Choosing limits of integration becomes rather complicated in this subcase. Figure 3.13 represents the lower left quarter of Region E for this subcase. This figure is used to determine the limits of integration. The dashed lines in this figure are the arcs located a distance of r from the corners of the deployment as explained in Section 3.2. These lines are curved, but are estimated as straight lines for the purpose of simplifying the integrations. This can be done with minimal error. From this figure, the functions for these dashed lines are

60

J.D. Haughs, D.S. Kim

Fig. 3.13 Subcase E 3

Line1 y (x) = Line2

2 tr −

√ 2 tr − t 2 − t + r +[ ] (x − t + r ) √ t − r − 2 tr − t 2

t2

−1 [2 xr 4 r 2 − t 2 − 4 xtr + 4 xr 2 y (x) = √ 4 −t + tr − − (−2 r + t) tr + 2 4 r 2 − t 2 t − 3 4 r 2 − t 2 tr + 2 4 r 2 − t 2 − (−2 r + t) tr + 2 r t 2 − 2 tr 2 ].

Using the figure and the previous formulae for the lines in the figure, the equations for Region E when 58 L < r ≤ √L2 are L L 2 2 4 · p E (x, y) · S E3a d x d y μ E3a (r ) = √ 2 (2r − L)2 r 2 − L4 r 2 −x 2 L x 2 p E (x, y) · 8· S E 3b d y d x μ E3b (r ) = 2 (2r − L) L−r L−r L L L 2 2 2 −4· S d y d x − 8 · E √ 3 b L2 r 2−

4

8 · p E (x, y) · μ E3c (r ) = (2r − L)2

−(

line1

L 2

√

−(

r 2 −(L−r )2 −L)

r 2 −(L−r )2 −L)

Line2 L−r

S E 3b d y d x

Line2 L−r

S E3c d y d x.

The above multipliers of either 4 or 8 are inserted into the function based on the symmetric regions. Once again referring to Fig. 3.13, it can be seen that the equation for subregion E 3a is integrated over a quarter of the subregion and therefore, this equation must be multiplied by 4 to include the entire subregion. Subregions E 3b and E 3c shown in this figure are integrated over just 18 of their entire area and are therefore multiplied by 8. Subregion E 3b was calculated by integrating it over the

3 Analysis of Effective Connectivity in Mobile Wireless Communications

61

entire area under the line y = x and then subtracting out the portions outside of E 3b . This proved to be the most efficient way to calculate this subregion.

3.4.5.4 Subcase E4 The final subcase for Region E is for √L2 < r ≤ L and is made up of four subregions. These subregions were defined in Section 3.2 and shown in Fig. 3.7(d).As with subcase E 3 , choosing the limits of integration for this subcase proved to be a challenge. Figure 3.14 shows the breakup of the subregions for this subcase. As was the case in the previous figures, this figure is the lower left quarter of Region E. The dashed lines are the arcs located a distance of r from the corners of the deployment. The two dotted lines are displayed for reference. From this figure, the functions for these dashed lines are Line3 y(x) =

L−

Line4 y(x) = L −

√

1 −L 2 + 4 r 2

L 2 − 2 −L 2 + 4 r 2 L − L x + −L 2 + 4 r 2 x + 2 r 2

r2 − xx

Line5 y(x) = L − r +

√ 2 r2 − L2 (x − t + 2 Lr − L 2 ) √ √ 1 L − 2 Lr − L 2 + 2 2 r 2 − L 2 L 2

1 2

−r +

1 2

As shown in the Figure 3.14, E 4c is further divided into two zones, E 4c1 and E 4c2 , for ease of computation. As occurred in the previous subcase, subregion E 4b will be integrated under the line y = x from the corner, (L − r ), to the dotted line dividing the subregion E 4c in two. This will be followed by subtracting the function S E4b integrated over the bounds of subregion E 4c2 . This was found to be the least complicated method. The integration of subregion E 4d is performed similar to that of E 4b . With the use of these considerations the functions for Region E for subcase E 4 are

Fig. 3.14 Subcase E 4

62

J.D. Haughs, D.S. Kim

L − 1 √2r 2 −L 2 x 2 2 8 · p E (x, y) μ E4b (r ) = · S E 4b d y d x 2 (2r − L) L−r L−r L − 1 √2r 2 −L 2 Line5 2 2 − S E 4b d y d x √ L− 2Lr −L 2

μ E4c1 (r ) =

8 · p E (x, y) · (2r − L)2

8 · p E (x, y) μ E4c2 (r ) = · (2r − L)2

μ E4d (r ) =

L 2

L 2

√ 1

−2

L 2

− 12

Line4

2r 2 −L 2

L−r

√

2r 2 −L 2

√ L− 2Lr −L 2

S E 4c d y d x

Line5 L−r

S E 4c d y d x

L x 2 · p E (x, y) · 8 · S E 4d d y d x √ 1 L 2 2 (2r − L)2 L−r 2 − 2 2r −L −4·

μ E4e (r ) =

L−r

L 2

2 L− r 2 − L4

4 · p E (x, y) · (2r − L)2

L 2

Line3

S E 4d d y d x − 8 ·

L 2

2 L− r 2 − L4

L 2 L 2

− 12

√

2r 2 −L 2

Line4 L−r

S E 4d d y d x

L 2

Line3

S E 4e d y d x

After performing all the necessary calculations for the effective connectivity of the random waypoint mobility model, we are left with the following complex formula ⎧ μ A (r ) + μ B (r ) + μC (r ) ⎪ ⎪ ⎪ ⎪ ⎪ μ C3 (r ) + μ D (r ) + μ E 1 (r ) ⎪ ⎪ ⎨ μ (r ) + μ (r ) + μ (r ) + μ (r ) C3 D E2 a E2 b μ(r ) = μ (r ) + μ (r ) + μ (r ) + μ ⎪ C D E a E 3 b (r ) + μ E 3 c (r ) 3 3 ⎪ ⎪ ⎪ ⎪ μ (r ) + μ (r ) + μ (r ) + μ C3 D E4 b E 4 c−1 (r ) ⎪ ⎪ ⎩ +μ E4 c2 (r ) + μ E4 d (r ) + μ E4 e (r )

if 0 < r ≤ L2 √ if L2 < r√≤ (2 − 2)L if (2 − 2)L < r ≤ 5L 8 if 5L < r ≤ √L2 8 if

√L 2

It has been found that this model can be simplified to just the first three regions and expanded over the entire range of r instead of limiting them to r ≤ L/2. This drastically simplifies the model. The resulting equation for effective connectivity in the random walk mobility model is

μ(r ) =

4r 3 (3π − 2)(L − 2r ) r 4 (9π − 5) πr 2 (L − 2r )2 + + L2 3L 2 3L 2

(3.27)

3 Analysis of Effective Connectivity in Mobile Wireless Communications

63

Equation (3.27) can be converted into a relative mean effective connectivity model by dividing it by the deployed area, L 2 , so that it becomes unitless. The substitution ρ=

r L

can be made so that (3.27) becomes a function of the transmission range and the deployment area 8 11 − π ρ 4 − ρ 3 + πρ 2 . (3.28) μ(ρ) = 3 3 The resulting relative mean effective connectivity function, (3.28), can be plotted over a range of transmission ranges to give us a visual representation of how node connectivity will be effected as transmission range is increased.

3.5 Random Waypoint Analytical Model In a similar manner to the previous section regarding random walk, this section will outline the adaptation of the effective connectivity model for use with the random waypoint mobility model. The functions outlined in Section 3.3 for calculating S(r, x, y) will again be used in this implementation along with the probability p(x, y) of a node’s location under the random waypoint mobility model. The random waypoint mobility model lacks the uniform distribution of the random walk model. Because of this, the spatial node density must be taken into consideration. Many researchers have worked to derive functions for the random waypoint spatial density [2, 4, 11, 12]. This research uses the simplified function presented in [12] for this adaptation of the effective connectivity model to the random waypoint model. Figure 3.15 represents the resulting distribution of the random waypoint model using [12]. The effective connectivity of nodes within these regions is calculated similarly for this model as it was for the random walk model, with the inclusion of the spatial node density function from [12]. Due to this inclusion, S(r, x, y) becomes not only a function of area, but also a function of density. S(r, x, y) = f (A(r, x, y), p(x, y))

(3.29)

Computing the probabilities for this model involve the use of the spatial density function from [12] discussed earlier. To simplify the calculations, a zero pause time is assumed and no node is stationary at the beginning of the simulation. The resulting simplified spatial density function is f (x, y) = 36x y(x − 1)(y − 1)

(3.30)

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Fig. 3.15 Spatial Distribution of Random Waypoint

and is based on a unit square map. The actual probability that a node is located at a given (x, y) becomes a function of the area under (3.30). This will result in an equation for effective connectivity in the random waypoint mobility model that is based on the unit square. The resulting function is similar to that for random walk, that is, it is a function of transmission range versus deployment area. Again, μ(r ) is calculated separately for each of the regions and combined in the end for the final result. Due to the accuracy of the simplified random walk model and the complexity of the full version of the random walk analytical model, only the simplified version of the random waypoint analytical model has been calculated.

3.5.1 Region A Region A again comes from Fig. 3.2(a) and is calculated by combining the (3.2), (3.29), and (3.30). The new combined equation is a function of both x and y and is therefore integrated over r to L − r for both x and y. The equation for Region A is μ A (r ) = r

L−r

L−r

S A (r, x, y) · [36x y(x − L)(y − L)]2 d xd y,

r

which upon integration, the equation becomes μ A (r ) =

36 2 288 432 6 864 r π− π r5 + r π− π r 7 + 576 π r 8 25 5 5 25 9936 10 5184 11 5184 12 r π− r π+ r π. − 1728 r 9 π + 5 5 25

(3.31)

3.5.2 Region B Again Region B is symmetric and therefore, one needs only to derive a calculation for one of the B regions. As was the case in the calculation for Region B under the

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random walk analytical model, using region B1 from Fig. 3.2(a). In this analytical equation, Region B is dependent on both the x and y variables and must be integrated over both. It can be seen in Fig. 3.2(a) that Region B is to be integrated with respect to x over 0 to r and with respect to y over r to L − r . By combining (3.3), (3.29), and (3.30), Region B is L−r r S B (r, x, y) · [36x y(x − L)(y − L)]2 d xd y, μ B (r ) = 4 · r

0

the resulting equation becomes 384 4608 405 6 864 288 5 π− r − πr + π− r7 μ B (r ) = 5 25 5 25 875 1536 2304 8 − 1152 π r + 3348π − r9 + 5 5 50688 19062 − π r 10 + 175 5 27648 10044 55296 10368 11 π− r + − π r 12 . + 5 175 875 25

(3.32)

3.5.3 Region C As with the previous derivation of the random walk analytical model, Region C of this model is not only symmetric but also broken into the same two subcases, C1 and C2 . Both these functions use the same limits of integration as was used for the random walk analytical model, however, they are now combined with (3.29) and (3.30) to form Case C1

√ r 2 −x 2

μC1 (r ) =

μC2 (r ) =

SC3 (r, x, y) · [36x y(x − L)(y − L)]2 d xd y

0

0

Case C2

r

r √ r 2 −x 2

r

SC3 (r, x, y) · [36x y(x − L)(y − L)]2 d yd x

0

after integrating and combining the two formulae, the equation for Region C is 1578 9531 93984 60048 8 μC (r ) = π+ r + − π r9 20 175 1225 35 742248 431649 6258496 74889 10 π− r + − π r 11 + 224 1225 13475 10 10886404 760707 + π r 12 . + (3.33) 67375 5600

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Now that all the required calculations have been performed for the random walk analytical model, the individual regional functions are combined to form the full model. μ (r ) =

384 5 27 4608 7 36 π r2 − r + π r6 − r 25 25 5 875 55338 1989 470496 4212 − π r8 + − + π r9 + 175 20 1225 35 6849 387432 114021 165184 + π r 10 + − π r 11 + − 1225 1120 539 70 15144196 400509 − π r 12 . + (3.34) 67375 5600

Because this function is based on the unit square, the transmission range, r , in this model is already the ratio of transmission range to map length, r/L. Therefore, r can be substituted with ρ in (3.34) to match the random walk analytical model. μ (ρ) =

36 384 5 27 4608 7 π ρ2 − ρ + π ρ6 − ρ 25 25 5 875 55338 1989 470496 4212 8 + − π ρ + − + π ρ9 175 20 1225 35 387432 114021 165184 6849 10 + π ρ + − π ρ 11 + − 1225 1120 539 70 15144196 400509 − π ρ 12 . + (3.35) 67375 5600

Both this model and the random walk analytical model will be analyzed and compared to simulated data in the next section.

3.6 Analysis 3.6.1 Random Walk Analytical vs Simulated Section 3.4 presented two versions of the random walk analytical model. The first version is a complete implementation of the effective coverage analytical model over the range of 0 < r ≤ L made up of several parts. The second version is an expansion of the simpler beginning part of the lengthy first version. This function was originally intended to represent the effective coverage of the random walk mobility model from 0 < r ≤ L/2. However, once it was implemented, the range was experimented with and its output was found to be nearly identical to that of the lengthier version all the way to the extreme end of the range, L. Figure 3.16 shows both of these equations plotted together on the same graph. As one can see

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Fig. 3.16 Complete and Simplified

from the figure, the two functions are nearly identical all the way to about r = 750. At this point, the simplified version produces a slightly lower estimation than the full version. Figure 3.17 shows both of these versions plotted with the results of a simulation. In this figure, it is clear that both models slightly deviate from the simulated data with the full version slightly overestimating and the abbreviated version slightly underestimating. The differences at this level of r are negligible as these

Fig. 3.17 Complete, Simplified and Simulated

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levels of transmission range versus deployment region are not realistic. Therefore, the simplified version provides functional results. To compare the model with the simulated data, multiple random walk simulations were run with the total number of simulated nodes ranging from 20 to 300 in increments of 20. Each of these simulations was conducted with a map size of 1000 × 1000 m, a simulation time of 900 s, minimum node speed of 0.1 m/s, maximum node speed of 10 m/s, and a uniformly distributed duration of [0,100] s. Data from every simulation was then analyzed, at transmission ranges from 25 m to 1000 m, for the average number of nodes within one node’s transmission range. The data was plotted as the average percentage of nodes in the simulation that are within the transmission range of one node. As the transmission range increased, the curves of all simulations followed the same shape regardless of the number of nodes in the simulation. The random walk simulation data was plotted with the random walk analytical model and can be seen by once again referring to Fig. 3.17. From this figure, one can see that the random walk simulation data and the random walk analytical model are nearly identical. The most noticeable difference in the analytical model as compared to the simulation data occurs at the upper bounds of the transmission range. This is attributed mainly to the approximation used in the analytical model. The analytical model is accurate up to approximately r = 3L/4, this is where the simplified model deviates from the full model and the curve is slightly skewed. The fourth curve in Fig. 3.17 represents the behavior of node coverage if no cutoff is taken into consideration, that is, a uniform coverage area is assumed. For a relatively small transmission range this assumption could be acceptable, but as the transmission range increases the assumed and actual node coverage differ greatly. The analytical model and the uniform model are compared with the random walk simulation data and the difference is plotted in Fig. 3.18. From this figure, it can be seen that the level of error increases at an exponential rate for the uniform distribution as r is increased, However, the analytical model retains a very small level of error throughout all values of r . From this data, it can be concluded that the uniform distribution can be used with a 95% confidence level if r ≤ 75 and with a 90% confidence level if r ≤ 125. These confidence levels decrease at a rapid rate beyond r = 125. However, using the analytical model, the confidence level never drops below 95% and is actually better than 97.5% for r ≤ 900.

3.6.2 Random Waypoint Analytical vs Simulated As with the random walk simulations, multiple simulations were run for the random waypoint model. The number of nodes, simulation map size, and simulation time was the same as in the random walk simulations. However, duplicate simulations were run with different speed ranges. The first simulation set was run with a minimum and maximum speed identical to that of the random walk simulations. The second simulation set was configured with a minimum and maximum speed of 5 m/s. The maximum rest time for a node in both simulation sets was set to zero. Again data from each simulation was analyzed, at transmission ranges, from 25 m

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Fig. 3.18 Error of Random Walk

to 1000 m, for the average number of nodes within one node’s transmission range. This data was also plotted and as was the case with the random walk model, all plots were the same irrespective of the total number of nodes in the simulation. The two speed variations in the simulations resulted in very similar plots as well. The data from the simulation was plotted with the analytical model and can be seen in Fig. 3.19. The random waypoint simulation data and the analytical model are very similar in shape. There are a few slight variations that can be seen in the figure and these can be attributed to the approximation of the area under the spatial density used in the calculation of the analytical model. The random waypoint analytical

Fig. 3.19 Comparison of Random Waypoint

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(a) Error of Variable Speed

(b) Error of Constant Speed

Fig. 3.20 Random Waypoint Error

model proves to be much more accurate than the uniform model in the higher regions of r . The two are very similar in the lower regions of r . Figures 3.20(a) and 3.20(b) show the random waypoint (RWP) model and uniform model error as compared to the simulated data. The RWP model has a confidence level of greater than 90% for L/2 < r . The error is greater below L/2 and is attributed to the lower overall connectivity in these ranges. A slight deviation in the percent of nodes in range for a low value already equates to an unfairly large percentage of error. Simulations themselves can and do vary by a small amount due to the randomness of their behavior. Regardless of the unfair percentage of error analysis, this model is a very reasonable estimate of the random walk mobility model’s effective coverage.

3.7 Conclusion In this paper we have shown that the location and transmission range of a mobile node can have a considerable effect on expected node connectivity and density. We presented a mathematical model to predict the behavior of node coverage. The model was extended to the random walk and random waypoint mobility models and examined for accuracy in each. It was shown that as the transmission range, r , of a node is increased, the effective mean coverage also increases, but not in a uniform manner. Extensive simulations were conducted to verify these mathematical findings and to demonstrate the importance of the boundary effect. Future work for effective coverage includes adaptations to additional mobility models, including group mobility models. In addition to adaptations, further refining the spatial node density of the random waypoint model could reduce the variations between the simulated and analytical results. Likewise, comparisons between

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the presented analytical models, simulated data, and real world data could prove extremely useful to the research community.

References 1. Bai, F., Sadagopan, N., Krishnamachari, B.: Modeling Path Duration Distributions in Manets and Their Impact on Reactive Routing Protocols. IEEE Journal on Selected Areas in Communications. Vol. 22 (7), 1357–1373. December (2004) 2. Bettstetter, C., Wagner, C.: The Spatial Node Distribution of the Random Waypoint Model. Proceedings 1st German Workshop Mobile Ad Hoc Networks (MWAM). 41–58. March (2002) 3. Bettstetter, C.: On the Connectivity of Wireless Multihop Networks with Homogeneous and Inhomogeneous Range Assignment. VTC’02. Vol. 3, 1706–1710. September (2002) 4. Bettstetter, C., Resta, G., Santi, P.: The Node Distribution of the Random Waypoint Mobility Model for Wireless Ad Hoc Networks. IEEE Transactions on Mobile Computing. Vol. 2 (3), 257–269. July–Sept (2003) 5. Camp T., Boleng, J., Davies, V.: A Survey of Mobility Models for Ad Hoc Network Research. Wireless Communication & Mobile Computing (WCMC): Special Issue on Mobile Ad Hoc Networking: Research Trends and Applications. Vol. 2 (5), 483–502 (2002) 6. Kim, D.S., Hwang, S.K.: Behavioral Group Mobility Model in Ad hoc Wireless Networks. In 9th International Conference on Cellular and Intelligent Communications (CIC2004), Seoul. October (2004) 7. Kwak, B., Song, N., Miller, L.: A Canonical Measure of Mobility for Mobile Ad Hoc Networks. In IEEE Military Communications Conference (MILCOM). October (2003) 8. Lawler, G.F.: Introduction to Stochastic Processes. Chapman & Hall. Probability Series. (1995) 9. Lin, G., Noubir, G., Rajaraman, R.: Mobility Models for Ad hoc Network Simulation. Proceedings of the 23rd Conference of the IEEE Communications Society (INFOCOM 2004). March (2004) 10. McDonald, A.B., Znati, T.: A Path Availability Model for Wireless Ad Hoc Networks. In Proceedings of the IEEE Wireless Communications and Networking Conference. 35–40. September (1999) 11. Navidi, W., Camp, T.: Stationary Distributions for the Random Waypoint Mobility Model. IEEE Transactions on Mobile Computing. Vol. 3 (1), 99–108. (2004) 12. Resta, G., Santi, P.: An Analysis of the Node Spatial Distribution of the Random Waypoint Mobility Model for Ad Hoc Networks. Proceedings on the 2nd ACM International Workshop on Principles of Mobile Computing. 44–50. (2000) 13. Royer, E., Melliar-Smith, P., Moser, L.: An Analysis of the Optimum Node Density for Ad hoc Mobile Networks. In IEEE International Conference on Communications. June (2001) 14. Yoon, J., Liu, M., Noble, B.: Random Waypoint Considered Harmful. Proceedings of 21st Conference of the IEEE Computer and Communications Society (INFOCOM 2003). 1312–1321. April (2003) 15. Zonoozi, M., Dassanayake, P.: User Mobility Modeling and Characterization of Mobility Patterns. IEEE Journal on Selected Areas in Communications. Vol. 15 (7), 1239–1252. (1997)

Chapter 4

Some Detectability Issues in Sensor Networks Wuxu Peng, Xinde Jia and Eric Reeves

4.1 Introduction Sensor networks have found applications in broad areas such as environment sensing and monitoring, vehicle tracking, battlefield surveillance, and inventory tracking. Recent hardware advances make inexpensive microsensors and embedded sensors available. These extremely affordable microsensors have made it possible to deploy large number of sensors in relatively large space. There are many reasons to believe that the future of sensor networks is bright and sensor networks will be ubiquitous [1,5,11,12,17,25]. Research on sensor networks has been explosive in recent years. Many important issues such as power management, target tracking, localized coordination, and security have received much attention and extensive research [18,20,28,33]. Most of the recent research focused on sensor networks that are covered completely. However, in many cases, the geographical space of interests is not completely covered by the sensor network. Issues in such sensor networks have been largely left un-addressed. In this research, we consider the situation where one or more sensor will try to infiltrate or pass through an area protected by an incomplete sensor network. We study such incomplete sensor networks and investigate the issue of how to timely and efficiently detect intruders that attempt to infiltrate the monitored area. We consider various issues related to the performance and solutions to the problem, including fixed verse mobile sensors, deployment pattern of fixed sensors, movement patterns of mobile sensors, mobile sensors that self-adjust their movements in response to events of intrusion of group intruders, and broadcast in incomplete sensor networks, and applying existing learning theories and models in multiagent systems to guide sensor movements and cooperations.

W. Peng Texas State University, San Marcos, TX 78666, USA e-mail: [email protected]

S.K. Makki et al. (eds.), Sensor and Ad Hoc Networks, C Springer Science+Business Media, LLC 2008 DOI: 10.1007/978-0-387-77320-9 4,

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Research on incomplete sensor networks has broad practical implications. In many circumstances there are simply not enough sensors to completely cover a region to be monitored. Therefore, the next best we can do is to utilize whatever is at hand to prevent intruders from infiltrating the monitored region without being detected. Such circumstances can result from an unexpected battleground encounter or a sudden change of battleground plan. In other cases, the areas to be monitored are simply too large to deploy sufficient sensors to provide complete coverage. For example, we may want to monitor a border area to prevent large volume of illegal drug trafficking and we simply do not have enough manpower and equipment to cover the whole border area. A marine area being monitored by a group of submarines may simply be too large to have enough submarines to cover every corner of the whole area, not to mention providing coverage redundancy. In cases where a monitored region is initially completely covered, even with possible redundancy in coverage, it is still possible that some unexpected events may reduce complete coverage to incomplete coverage. For instance, some of the sensors can become inoperative due to unexpected hardware and/or software failures. In many applications, the deployed microsensors have very limited battery capacity. Unforeseen events such as heavy communications may easily exhaust batteries at some sensors. All these unfavorable events can degrade an initially completely covered sensor network to an incompletely covered network. Strategies that maximize coverage until replacement sensors are deployed and/or fresh batteries are reinstalled can be an integrated part of all these applications. The reverse of the problem, which we term as the problem, is also important. For instance, we would like to know the best strategies for our soldiers to infiltrate an area under enemy’s incomplete surveillance. Finally in a complete static sensor network where energy consumption is a major concern, turning on all sensors all the time will be problematic. Those sensors that are turned on at any particular instance may form an incomplete sensor network. The effect of sensor turning-on and turning-off among the static sensors is similar to moving sensors. Strategies/protocols of effective sensor movements can be used to systematically turn on and turn off group of sensors to maximize detectability. The pattern of turning on/off provides a virtual sensor movement. By controlling the rate of sensors on/off, the virtual sensor movement can achieve better detectability while conserving the energy. The rest of this paper is presented as follows: Section 4.2 briefly reviews related work. In Section 4.3, we present our preliminary findings of detectability in incomplete sensor networks. Section 4.4 contains detectability under various deployment and movement patterns. Section 4.5 discusse the effectiveness of various sensor deployment and movement patterns. The notion of effectiveness of detectability is significant. The effectiveness of a deployment and movement model is characterized by two properties. The first property is the detectability with a given number of sensors. The second is the increase or decrease in detectability in response to the increase or decrease of the total number of sensors. A good sensor deployment/movement model should possess both properties to be effective. Concluding remarks are given in Section 4.6.

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4.2 Related Work The research in [8,26] discussed many problems and challenges of topology control in sensor networks. The authors survey a collection of modern solutions for topology control, including location, direction, and/or neighbor-based approaches. Liu and Towsley characterized the asymptotic behaviors of grid-based sensor networks, where sensors are randomly deployed in a square lattice [19]. The sensors studied there were not mobile and only randomly distributed sensors were considered. The work in [9] considered the issue of how to deploy sensors to detect a moving target. The authors proposed the concept of unauthorized traversal problem and an algorithm to solve it. We notice that the sensors considered there were fixed, and were deployed randomly. Long before the concept of sensor networks was proposed, the notion of Brownian motions and the issue of detecting were proposed and studied [21]. If the intruders can move continuously with a random speed and random direction at any point, then the intruders are called in Brownian motion. If the intruders can only move in discrete steps with limited number of directions (chosen randomly though), then the intruders are called random walkers. Brownian motion is a stochastic process in which the random variable moves continuously and follows a random walk with normally distributed, independent increments. Brownian motion is of great interest and has been studied extensively in literature. A random walk can be regarded as the discrete version of a Brownian motion. It also has been studied extensively by researchers in sciences and mathematics. While many results are now available, there are still a great deal of questions left unanswered. In the discrete random walk case, most research focused on the asymptotic behavior of the random walkers (the intruders in our case) as the walking time or the number of walking steps approaches infinity, see for instance Donsker and Varadhan [3,10]. There is no known information about how fast the asymptotic behavior would be stabilized at the limit position [4,14,15]. Coverage problem in sensor networks is fundamental and has received much attention. Meguerdichian and et al. in [20] addressed the issue of both worst and best coverage problems in sensor networks. The sensor networks considered there were completely covered and the best problem was to find a path from a given source spot to a given destination spot in the covered area such that the maximum distance to the closest sensors is minimized. Li and et al. in [18] improved the work in [20] by providing a distributed optimal best algorithm. They also considered the issue of energy conservation with respect to coverage problem. The research in [30] proposed a node scheduling scheme that can reduce overall energy consumption and hence prolong complete coverage. The research in [28] proposed to divide sensors into mutually exclusive sets, called disjoint covers. A heuristic algorithm was proposed to activate those disjoint covers at different times to enable savings in energy consumption. The study proposes coverage, signal attenuation, and sensor density as the main parameters by which the balance is measured. The work in [6] proposed the notion of disjoint dominating sets. The authors showed that the maximum number of disjoint dominating sets is greater than or equal to the

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maximum number of disjoint covers, and hence their algorithm improved over the work in [28]. Tracking mobile objects is another important research topic in sensor networks. Aslam and et al. studied the computational power of binary sensor networks with respect to tracking applications [2]. They proposed a binary sensor model, where each sensor’s value is converted reliably to one bit of information that indicates whether an object is moving toward the sensor or away from the sensor. Zhang and others studied the issue of tracking mobile targets in sensor networks by using optimizing tree reconfigurations [33]. Two schemes were proposed to minimize energy consumption for data collection and to reduce reconfiguration overhead, respectively. Sensors in their work are assumed stationary. The work in [16] studied the power-saving operations in both surveillance and tracking states and proposed a trade-off between the two states. Estrin and et al. were among the first to point out the importance of scalable and localized coordination in sensor networks and they proposed the notion of directed diffusion as a simple communication model for describing localized algorithms [12]. Cerpa and Estrin studied an adaptive self-configuration topology mechanism, named ASCENT, for distributed wireless sensor networks [7]. Shakkottai and others studied connectivity and coverage issues of unreliable sensor grid networks [27]. They presented the necessary and sufficient conditions for the random grid network to cover the unit square region as well as to ensure that the active nodes are connected. They also showed an expression for the diameter of the random grid. Peng and others developed a heuristics-based protocol for more efficient routing in wireless mobile ad hoc networks [22]. In a subsequent work, Peng and others proposed a security mechanism for wireless mobile ad hoc networks [23]. Jia, Yan, and Ellis [32] recently studied the connectivity problem of a wireless network with mobile stations at random locations. In a recent paper, Jia and Gu proved an algorithm to find optimal locations for sensors in sensor networks. While the research there deals with a different problem, the ideas are helpful in our proposed research.

4.3 Detectability – Theory and Practices A sensor network within a geographical region is incomplete if there are areas within the given region that are not sensible. Formally we define detectability as the probability that an infiltration into an incomplete sensor network is detected. In this section we briefly present some of our preliminary findings about detectability in several different scenarios. We present three cases: randomly deployed, but static sensors; arranged mobile sensors; and randomly mobile sensors. In all three cases there is a single intruder enters the monitored area at a random entry point on the south border of a rectangle area and moves straight toward north. In the next section we consider more factors that affect detectability. More details can be found in [24].

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4.3.1 Randomly Deployed Fixed Sensors Let R be an a × b rectangular area. We assume that k sensors are in R with uniform distribution. All the k sensors are static once they are deployed. We also assume that each sensor can monitor a circular area with itself being the center and radius λ. Therefore, a sensor can monitor an area of π λ2 . As shown in Fig. 4.1, let R¯ denote the region that the sensors can possibly cover. Then R¯ is an (a + 2λ) × (b + 2λ) rectangle with round corners. In fact, each corner of R¯ is one fourth of the circular ¯ = ab + λ2 π + 2λ(a + b). If an disk of radius λ. Clearly the total area of R¯ is | R| ¯ intruder q is randomly placed in R, then it is easy to see that the probability that q is being detected by at least one of the sensors is 1− 1−

λ2 π 2 ab + λ π + 2λ(a + b)

k

=1−

ab + 2λ(a + b) ab + λ2 π + 2λ(a + b)

k .

(4.1)

4.3.1.1 Straight Moving Intruders We now consider the probability that a single intruder travels in a straight line parallel to one of the edges of R, say, the vertical edge of R. For the purpose of illustration and simplification of computation, we consider only the case where the straight line the intruder travels on goes through R, as shown in Fig. 4.2. Let x be the distance between the intruder and the left vertical edge of R. If we use E to denote the event that the intruder is being detected by at least one of the sensors. For convenience, let F1 , F2 , and F3 be the events 0 ≤ x ≤ λ, λ ≤ x ≤ a−λ, and a − λ ≤ x ≤ a, respectively. It is easy to see that

2λ Pr[E | F2 ] = 1 − 1 − a

k .

R

b ¯ R

a

Fig. 4.1 Partially protected R and randomly placed sensors

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a

x R

b R

Path of the intruder

Fig. 4.2 An intruder is crossing the region R

The conditional probability Pr[E | F1 ] can be computed as follows: x +λ k 1− 1− dx a 0 x +λ k a 0 x +λ 1− = 1− d 1− λ λ a a k+1 λ a 2λ k+1 1− = 1− − 1− . (k + 1)λ a a

1 Pr [E | F1 ] = λ

λ

Similarly, we have a Pr[E | F3 ] = 1 − (k + 1)λ

λ k+1 2λ k+1 1− − 1− . a a

Obviously, Pr[F1 ] =

λ , a

Pr[F2 ] =

a − 2λ , a

and

Pr[F3 ] =

λ . a

Therefore, the probability that the intruder is being detected by at least one of the sensors is

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λ a − 2λ λ · Pr[E | F1 ] + · Pr[E | F2 ] + · Pr[E | F3 ] a a a k+1 λ a λ 2λ k+1 = · 1− 1− − 1− a (k + 1)λ a a k 2λ a − 2λ · 1− 1− + a a a λ k+1 2λ k+1 λ 1− − 1− + · 1− a (k + 1)λ a a k+1 k+1 λ 2λ 2 k−1 1− 1− = 1− − . k+1 a k+1 a

Pr[E] =

(4.2)

Figure 4.3 shows the prediction of (4.2) and result of a corresponding simulation. The simulation result matched the prediction closely. The simulation was done with our NS2-based simulation software on a 150 by 50 grid area. The single intruder entered the grid area at a random point at the bottom edge and moved upward along a straight line at a speed of 0.004 unit per move. Equation (4.2) shows that in case of continued sensing, the detectability is not related to the intruder’s travel speed. However, simulation software are discrete events driven. To maximize accuracy, we decided to let the intruder travel at extremely low speed. For each given number of sensors 5, 10, 20, . . . , 100, . . . , 200, the detection probability was calculated by counting the number of detected travels in 1000 travel attempts. Detectability 100

: Theory

: Simulation

90 80 70 60 50 40 30 20 10 20

40

60

80

100

120

140

160

180 200 Number of sensors

Fig. 4.3 Theoretical and simulation results of randomly deployed static sensors and a single straight moving intruder

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It is clear that predictions like (4.2) depend on both the sensor distribution and intruder’s movement patterns. In our proposed research, we will find optimal or near optimal strategies for the deployment of the sensors to provide maximum protection of R by using both mathematical computation and computer simulations.

4.3.2 Mobile Sensors We now consider the case where all the sensors are mobile. There are two cases: the movement of the sensors are random, or arranged. When the sensors are in Brownian motion or performing random walks in the region R, the survival probability of the intruders may become very sophisticated to compute explicitly. We shall use computer simulations extensively in this case. Obviously, the intruders are more likely to be detected if the sensors are on the move all the time. However, one drawback is that the sensors have to be much more complex and require more power to operate because of their mobility. Of course if they offer much greater protection, the cost might be justified. Here we will use both mathematical manipulation and computer simulation to articulate optimal and balanced strategies for the mobility of sensors and the capability of protection. 4.3.2.1 Arranged Moving Sensors and Straight Moving Intruders For the purpose of illustration, we only consider one specific arranged moving sensors: we assume that all the k sensors are first placed into the region R at random, and then they move horizontally at a fixed constant speed s. They may start their movement at either direction. When they reach either side of R, the sensors change to the opposite direction and continue to move at the constant speed s. As before, we assume that each sensor can detect intruders within a circular area with itself as the center and radius λ, as shown in Fig. 4.4.

R

b

xk (t) sk

bk

b2 q

b1

y(t)

Lk

x2 (t) s2

x1 (t) s1

L2 L1

0 Path of the intruder

Fig. 4.4 All k randomly placed sensors are moving horizontally at speed s

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Let si denote the ith sensor (i = 1, 2, . . . , k). Assume that at time t, sensor si is at location xi (t) on the respected horizontal line L i . In order to write xi (t) in terms of time t, we need the following definitions first. For every t ∈ [0, ∞), define, for every i : 1 ≤ i ≤ k, " ! 1 xi (0) cos θ + st + (1 − cos θ ), τi (t) = a 2 where x is the floor function of x, which is equal to the greatest integer that is less than or equal to x, and θ is the direction of the ith sensor’s initial movement, i.e., θ = 0 or π . Define, for every i : 1 ≤ i ≤ k, ! " xi (0) cos θ + st xi (0) cos θ + st − . ηi (t) = a a Then it is not difficult to verify that xi (t) =

a 1 − (−1)τi (t) + (−1)τi (t) aηi (t) 2

for i = 1, 2, . . . , k.

Suppose a single intruder q enters the region R from the bottom edge at point ξ , the distance to the left edge of R when the time is t = 0. Then the intruder moves upward at a constant speed v. We now want to find the probability that the intruder q is being detected by at least one of the moving sensors. We know that the intruder q moves upward toward the sensors at speed v and the sensors move only horizontally at speed s. As shown in Fig. 4.5, if we consider the intruder as a reference point, the movement of the sensors can be considered as a combination of two motions: one is the downward movement at speed v, and the other is the horizontal movement at speed s. With this combination of movements, each sensor will “hit” the bottom edge of R and will have an “impact” on the bottom edge. The impact by the ith sensor is actually an interval, denoted by Ii . It is easy to

xi (t) si

q

Fig. 4.5 The relative movement of a sensor si with respect to the intruder q

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see that the intruder q is being detected by the ith sensor si at some point if and only if the entry point of q on the bottom edge is covered by the interval Ii .Therefore, the probability that the intruder q is being detected by at least one of the sensors is the probability that a randomly picked point (the intruder’s entry point on the bottom edge of the region R) is covered by at least one of such intervals. All the intervals created by the sensors on the bottom edge of the region R are random and uniformly distributed on the edge. In order to compute the probability that an intruder q on the edge is being detected, we must first compute how wide each of such intervals is. As shown in the Fig. 4.6, the width of the interval by si is equal to D E, which is twice D B. Suppose that it takes time t for the ith sensor si to travel from A to B, then C B = st

and

AC = vt.

Therefore, AB =

v 2 + s 2 · t.

Hence, DB =

λ2 + (v 2 + s 2 )t 2 ,

(4.3)

which implies that DC = D B − C B =

λ2 + (v 2 + s 2 )t 2 − st.

On the other hand, DC =

λ2 − v 2 t 2 ,

we see that

λ2 + (v 2 + s 2 )t 2 − st =

λ2 − v 2 t 2 ,

A λ

D

vt

C

st

Fig. 4.6 The interval created by sensor si

B

E

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which implies that λs t= √ . v v2 + s 2 It then follows from (4.3) that DB =

λ2 + (v 2 + s 2 )t 2 = λ ·

1+

s2 . v2

Therefore, the interval created by the ith sensor si on the bottom edge of R has length s2 D E = 2 · D B = 2λ · 1 + 2 . v In particular, if the sensors’ horizontal speed is 0, we see that the interval created by each sensor has length 2λ, which is the case we discussed earlier in the proposal. Now we can consider the problem in this way. There are k intervals (one by each sensor) randomly placed on the number line with the centers of the intervals being inside the interval [0, a]. The intruder q is a point in [0, a]. The probability that the intruder is being detected by at least one of the sensors is the probability that the point q is covered by at least one of the intervals. This computation is similar to our earlier computation for the case where sensors are randomly placed without movement and the intruder travels along a straight line upward. The difference is that here the sensors can detect a larger area, namely the diameter here is s2 λ = λ 1 + 2. v Therefore, it follows from (4.2) the probability that the intruder is being detected by at least one of the sensors is k+1 k+1 s2 k−1 s2 λ 2λ 2 1+ 2 − 1+ 2 . 1− 1− 1− k+1 a v k+1 a v s As expected, the region R will have a better protection when the ratio is larger. v If the intruder’s moving speed is known to the sensors, well-arranged sensors will provide a better protection. However, without knowing the speed of the intruder, it seems randomly placed sensors provide very good protection for the region R according to our preliminary testing. In many cases, mathematical computation becomes too complex to provide meaningful solutions to the problem. Well-thought and strategically designed computer simulations will provide near optimal good solutions to the problem.

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:Random mobile sensors

:Randomly deployed static sensors

100 90 80 70 60 50 40 30 20 10 10

30

50

70

90

110

130

150

170

190 Numberof sensors

Fig. 4.7 Fixed but randomly deployed sensors versus randomly moving sensors

4.3.2.2 Randomly Moving Sensors and Straight Moving Intruders We assume all the sensors are moving randomly and uniformly in the region R. In this case, the speed of the intruders and the speed of the moving sensors affect the outcome greatly. For the purpose of illustration, we only consider the case where all the sensors have the same speed. With the assumption as we did earlier, an analytical result similar to (4.2), although more complex, can be obtained [24]. To save space, we only present our simulation result here. Figure 4.7 shows detectability of both randomly deployed static sensors and randomly moving sensors with respect to a single straight-moving intruder. In the simulation, the speeds of the sensors and intruder are assumed the same. It can be seen that when the number of sensors is small, randomly moving sensors outperform randomly deployed static sensors by about 5 to 10 percent. However, when the number of sensors is 130 or more, randomly moving sensors perform almost the same as randomly deployed static sensors. This can be explained by reasoning that, when the number of randomly moving sensors reaches certain threshold value (in this specific simulation case, the threshold is about 130), the gains in covered area due to random movements are offset by the overlapping in covered area. Our other simulation results, not shown here due to space limit, confirm intuition that when the speed of sensors increases, the detectability also increases, while increasing the intruder’s speed decreases detectability.

4.4 Various Factors Many factors can affect incomplete sensor networks. In this section we consider results for several more interesting cases.

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The sensors deployed in all networks have the hardware and software architectures necessary to communicate wirelessly. The sensors that populate this area are of heterogeneous sensing capacity, energy consumption models, and means of communication [29]. Radio propagation is achieved using the two-ray ground reflection model. The two-ray ground model considers propagation by both line-of-sight and a ground reflection path [13]. At a distance of d, the received power is predicted by Pr (d) =

Pt G t G r h 2t h r2 , d4 L

where L = 1, h t is the height of the transmitting antenna, h r is the height of the receiving antenna, and G t and G r are the gains of the transmitting and receiving antenna, respectively. The simulation area is two dimensional. The length of the simulation area along the X axis is 150 m. The length of the simulation area along the Y axis is 50 m. No geological or artificial obstacles exist such that the paths of protecting sensors are inhibited. It is assumed that any bodies that exist can otherwise be traveled through or over. All sensors have exactly the same receive and transmit threshold. These thresholds are by majority 1 m; however, some simulations will require an increase in these parameters. These circumstances are clearly indicated. Sensors are given a small range of communication so the effects of the mobility model are easier to discern. Both defending sensors move at a speed of 1 m/s unless otherwise noted. All protecting sensors are able to distinguish another defender from an intruder; however, those mechanisms are not discussed in detail. The length of the simulation is determined by its scope; since the objective is to determine the rate at which intrusions are detected, the simulation ends when either the intruder has been detected or when it has successfully reached the opposite boundary. Thus, the maximum time at which the simulation runs is equal to the distance divided by the velocity of the intruder. Since the velocity of the intruder is 1 m/s, the simulation runs for as many seconds as the length of the intruder’s traversal. In some scenarios, the distance traveled by an intruder is of variable length and thus the simulation time is based on the maximum distance a sensor could travel along its traversal path. Each simulation places an intruder against k defending sensors, where k = 10, 20, 40, 50, 70, 100, 120, 150, 170, 200 sensors. Each simulation is run by average 1000 times and at the end of the 1000th simulation, the number of detections is divided by 1000 to determine the rate of detection.

4.4.1 Vertical Intruder, Uniform Sensor Deployment Four different scenarios are examined in which a vertically moving intruder faces various detector deployments. In each scenario the detecting sensors’ positioning strategy is the same; however, the movement patterns differ. Detectors are deployed at 10 sensors per row where the number of rows is determined by the total number of sensors in the environment. Furthermore, detectors are initially deployed

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horizontally from the middle of the area. The formula that dictates these coordinates is as follows. Let maxY be the maximum Y coordinate of the two-dimensional area, and let maxX be the maximum X coordinate. numberOfNodes indicates the number of nodes protecting the area. The number of sensors expands at ten per row from the middle of the area toward the boundaries Y = 0, Y = maxY as more sensors are deployed. y Div = maxY/((number O f N odes/10) + 1) x Div = max X/(10 + 1). A single intruder begins at coordinates (rand,0), where rand is a random coordinate within the boundaries of the X axis. The intruder stays on this X coordinate while moving toward the maximum Y coordinate. Once both the intruder and the detecting sensors are deployed, the simulation begins. Once the simulation begins all sensors simultaneously begin moving as dictated by their assigned behavior. The behaviors assigned to the sensors are as follows. • Randomly moving defenders: Sensors move in a random direction at a statically assigned interval. At every 10 time units of the simulation, the sensor moves in a new randomly chosen direction. The interval between assignments is intentionally short to inhibit the sensor from exhibiting predictable behavior. • Random straight line defenders: Sensors move toward one of the area boundaries. The boundary is chosen at random. Once a sensor has reached the boundary of the area, a new and different boundary is randomly chosen and the sensor begins its movement along that path. Sensors under this mobility model travel boundary to boundary until the simulation is complete. • Area constrained defenders: Sensors move at random, however, they do not move outside the area surrounding their point of deployment. The size of area is proportional to the number of detecting sensors in the area such that the entire environment is subject to the presence of a detector. The goal of this simulation is to create a medium between the static and earlier random movers scenarios. Area constrained sensors are only deployed in simulations with uniform sensor distribution. • Sine wave movement patterns: This simulation employs another scenario: defending sensors that move in a sine wave pattern. This pattern is performed along the X axis of the simulation area; in other words, defending sensors are moving from their deployment coordinates to x = 0 or the maximum x coordinate. A horizontal movement is chosen with the intention of intercepting an intruder’s path. Given that our simulated habitat is rectangular, we desire a sensor having more space to cover before encountering an area boundary and patrol the same region more than once. The sine wave movements in this scenario are controlled by many parameters. The two most common attributes of sine waves are their frequency and amplitude. Frequency determines how many times a cycle appears within a unit of time while amplitude is a nonnegative measure of the maximum disturbance during a wave cycle [31]. Both the amplitude and frequency should have a large influence on

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the results of the simulation due to the control each has on the behavior of the movements: the maximum y-distance from which defending sensors will travel and how frequently defending sensors will approach the maximum y-distance. y = α + sin(2 ∗ π ∗ λ). The velocity of a defending sensor can be measured by one of two methods. A common way of measuring the velocity of traveling entities is by the length of the arc produced by the current location and the next location. In order for the velocity to be properly and accurately measured the arc length must be constant. Likewise, the velocity may also be measured relative to the simulation area’s X axis. Simulation results are shown in Fig. 4.8. It can be seen that as the number of detecting sensors in the area increases the benefit of statically deployed sensors grows at a higher rate than that of the other three scenarios. Simulation results show that deploying a low number of static sensors into the area is ineffective. The scenario in which sensors move in a straight line at a random direction yields the highest rate of detection at the maximum number of sensors, yet at lower sensor counts is not as effective. It is particularly interesting to point out that our results indicate that sensors constrained to a small area are not as effective as other three cases. This is somewhat against our original intuitions. Intuitively when sensors are moving randomly, there are probabilities that a large number of them may move to a relatively small region, and hence leave relatively large areas unsensible. Constrained movement should prevent these type of sensor configurations. However, our simulation shows that the rate of detecting intruders in constrained sensor movement is considerably lower than the other three scenarios. Also since the energy expenditure of this scenario is the same as the random mover scenario, the lower probability of detection affords no advantage to constraining the movements of a sensor to the area surrounding its point of deployment. We observe that in our current study only one intruder participates. In cases where multiple intruders are possible, our conclusion may change.

Detection Rate (%)

Vertical Intruder, Uniform Sensor Deployment 100 90 80 70 60 50 40 30 20 10

Static Rnd Walk Rnd Line Area SW (Arc Len) SW (X-Axis)

0 0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Sensors

Fig. 4.8 Vertical intruder, uniformly deployed sensors

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Sensors that move in a sine wave pattern with a constant velocity along the X axis yielded the highest rate of detection for all scenarios; however, sensors with a constant velocity along the sine wave arc performed at less than both static sensors and random boundary sensors. From the perspective of a single sensor moving in a sine wave pattern with constant X axis velocity the chances of detecting an intruder are more promising due to the movement along both the X and Y axes. In addition, as a sensor increases and decreases acceleration to maintain the constant dimensional velocity its speeds go above 1.0 m/s, giving it somewhat of an advantage over the other designated movement patterns. Without this constant velocity sine wave patterns offer no additional utility against a vertically moving intruder.

4.4.2 Vertical Intruder, Random Sensor Deployment In this case we investigate four different scenarios in which a vertically moving intruder faces various detector deployments. These scenarios differ from the previous simulations where a vertically moving intruder faces uniform deployments of detecting sensors. Defending sensors are deployed randomly than are either static or mobile, employing a particular pattern of movement. Random deployments have the potential to create high concentrations of defending sensors in a particular area, highly increasing the probability of detecting intruders in those areas. This observation gives way to creating heuristics used to guess an intruder’s point of deployment, exit point, and movement patterns. As more intruders are detected, the history of those parameters are stored; from those statistics heuristics can be created. The simulation results are shown in Figs. 4.9 and 4.10. The results for static defenders, as well as both random movers and random straight-line movers indicate that random deployments are more effective than uniform deployments when coupled with these movement patterns. Surprisingly,

Detection Rate (%)

Vertical Intruder, Random Sensor Deployment Static Rnd Walk Rnd Line SW (Arc Len) SW (X-Axis)

100 90 80 70 60 50 40 30 20 10 0 0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Sensors

Fig. 4.9 Vertical intruder, randomly deployed sensors

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Detection Rate (%)

Sine Wave Movement By Sensor Speed 100 90 80 70 60 50 40 30 20 10 0

Arc Len, 1.0 m/s Arc Len, 1.5 m/s X-Axis, 1.0 m/s X-Axis, 1.5 m/s

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Sensors

Fig. 4.10 Vertical intruder, randomly deployed sensors: sine wave movements by sensor velocity

the rate of detection for random moving and random straight-line moving detectors are more similar than in simulations deployed according to uniform coordinates. Protecting the area with fixed sensors yields a slightly lower rate of detection when deployed with uniform coordinates. In these simulations the detection rate for random movers and random straightline movers are very similar yet are not as effective as when deployed in uniform distribution. Despite their decreased detection rates both patterns produce more detections than static sensors, who thus far have performed better in uniform deployments. Sine wave movements for which the velocity is measured by X axis were most successful, due largely in part to the sensors, coverage along the X axis, and improved coverage along the Y axis. In addition, the fluctuations in the y coordinate distance allow defending sensors to either detect intruders preemptively or detect intruders after they have crossed the y coordinate of a defender’s point of deployment.

4.4.3 Random Intruder, Uniform Sensor Deployment Here we examine three different scenarios in which a randomly deployed intruder faces static, random moving, random straight-line moving, and sine wave movement patterns. The intruder is placed at any position at one of the four boundaries of the simulation area, and moves in a straight line to any boundary other than the one at which it was deployed. The intruder moves in a straight line to minimize the time it spends in monitored territory. Random entry and exit coordinates afford intruders the benefit of a variable length traversal through the protected area; this places the intruder at more of an advantage than in previous scenarios; however, this behavior is more realistic. For example, a sensor deployed in the northwest corner of the simulation area may choose to cross the area and exit at the nearby boundary on the west side (so long as the origin of the intruder is on the north boundary), or it

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may choose to exit at some point near the southeast corner. The possibility that an intruder is deployed at the bottom of the simulation area and moves vertically in a straight line does still exist albeit the chances are quite small. Unlike the intruder, detecting nodes are deployed according to uniform positioning and begin their assigned movement behavior when the simulation begins. Given the nature of the three movement patterns assigned to the protectors, a randomly deployed intruder that is inside the monitored area for the same amount of time as a vertically moving intruder faces the same probability of it being discovered. The only advantage the former has over the latter is that the distance between origin and destination is of variable length. The opportunity for higher rates of detection exist when that variable length is longer than the length of traversing a straight line from Y = 0 to the maximum Y coordinate. As intruders are deployed at one boundary and exits the area at another they are subject to increased risk of detection; If a vertically moving intruder is within the communication range of a static defender, the intruder will be detected by the first defender at that X coordinate. Likewise, diagonal movements across the area place the intruder closer to the communication ranges of more defenders. As can be seen from Fig. 4.11, static defenders perform very well, yielding a higher rate of detecting randomly deployed intruders than random straight-line defenders and random moving defenders across simulations with all quantities of sensors. The results of this simulation indicate that defenders moving in a sine wave pattern with constant X axis velocity create the highest percentage of detection when the area is populated with 200 sensors. Yet, static defenders offer a higher rate of detection for all lesser node densities. Realistically the nature of a sensor network create difficulties in maintaining 100% node density, and as sensors become inoperable they will require a collective strategy that will account for variable numbers of defenders. Thus, static defenders are the obvious choice. Static deployments perform better than the other three strategies and their relatively small energy expenditure increases their life expectancy, ease of tracking, and replacement. Therefore, static sensor deployments maintain higher node densities for longer periods of time.

Detection Rate (%)

Random Intruder, Uniform Sensor Deployment 100 90 80 70 60 50 40 30 20 10 0

Static Rnd Walk Rnd Line SW (Arc Len) SW (X-Axis)

0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Sensors

Fig. 4.11 Random intruder, uniformly deployed sensors

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4.4.4 Random Intruder, Random Sensor Deployment We again study three different scenarios in which a randomly deployed intruder faces each of the five movement strategies. The intruder is placed at any position at one of the four boundaries of the simulation area, and moves in a straight line to any boundary other than the one at which it was deployed. As previously indicated, an intruder will move in a straight line to minimize the time it spends in monitored territory. This behavior affords intruders the benefit of a variable length traversal through the protected area by providing the intruder more of an advantage than in previous scenarios. The simulation results are shown in Fig. 4.12 Sensors protecting the monitored area are deployed at random location throughout the area. Given the nature of the three movement patterns assigned to the protectors, a randomly deployed intruder that is inside the monitored area for the same amount of time as a vertically moving intruder faces the same probability of it being discovered. The only advantage the former has over the latter is that the distance between origin and destination is of variable length. The opportunity for higher rates of detection exist when that variable length is longer than the length of traversing a straight line from Y = 0 to the maximum Y coordinate. Intruders entering and leaving the monitored area at randomly chosen boundaries face the highest rate of detection against randomly generated, static defenders. Uniform deployment of static sensors still produces a higher detection rate against randomly deployed intruders, however, are still vulnerable to infiltration when a horizontally moving intruder maintains a constant Y coordinate or when a vertically moving intruder maintains a constant X coordinate. Random moving and random straight-line defenders are much less effective than both their static relatives and identically moving defenders in a uniformly deployed environment.

Detection Rate (%)

Random Intruder, Random Sensor Deployment 100 90 80 70 60 50 40 30 20 10 0

Static Rnd Walk Rnd Line SW (Arc Len) SW (X-Axis)

0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Sensors

Fig. 4.12 Random intruder, randomly deployed sensors

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4.5 Effectiveness of Sensor Deployment and Movement We have presented both theoretical and simulation results on detectability on various combinations of behaviors of the defenders and intruders. In this section we evaluate three of five deployment and movement models. The effectiveness of a deployment and movement model is characterized by two properties. The first property is the detectability with a given number of sensors. The second is the increase or decrease in detectability in response to the increase or decrease of the total number of sensors. Effectiveness is the most desirable property for detecting infiltration in incomplete sensor networks. In the following, we use VI to represent the vertically moving intruder and RI the randomly moving intruder. Likewise, we use US to denote uniform sensor deployment and RS random sensor deployment.

4.5.1 Static Sensors Static sensors perform best when randomly deployed in areas where an intruder moves in a straight line from any one boundary to the other, as shown in Fig. 4.13. They perform similarly well against randomly deployed intruders when positioned with uniform distribution. An apparent vulnerability is the probability of intrusion detection when low sensor densities are coupled with random distribution, as very large areas can be left completely unprotected. The only ways to cover unprotected areas are with more random sensor deployments or larger communication ranges.

4.5.2 Randomly Moving Sensors Randomly moving sensors yield the highest rate of detection when a vertically moving intruder infiltrates the bottom of the monitored area and exits through

Detection Rate (%)

Static Sensor Performance 100 90 80 70 60 50 40 30 20 10 0

VI, US VI, RS RI, US RI, RS

0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Sensors

Fig. 4.13 Performance of static sensors

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Detection Rate (%)

Random Walking Sensor Performance 100 90 80 70 60 50 40 30 20 10 0

VI, US VI, RS RI, US RI, RS

0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Sensors

Fig. 4.14 Performance of randomly moving sensors

the top, as shown in Fig. 4.14. Random distributions of these sensors against a vertically moving intruder yield higher percentages of detection. Simulation results suggest that intruders traveling through random entry and exit points have a significantly higher chance of traversing the area without being detected. As such, random moving sensors are not recommended against this class of intruder.

4.5.3 Random Straight-Line Moving Sensors Similarly, Fig. 4.15 shows that random straight-line sensors also perform well when infiltrated by a vertically moving intruder. Uniform and random deployment of these sensors perform equally well. A randomly deployed intruder has a higher success rate when evading random straight-line sensors. Random straight-line sensors share

Detection Rate (%)

Random Straight Line Sensor Performance 100 90 80 70 60 50 40 30 20 10 0 0

VI, US VI, RS RI, US RI, RS

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Sensors

Fig. 4.15 Performance of random straight moving sensors

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the same shortcomings that affects randomly moving sensors – intruders with random entry and exit points are noticeably more successful at infiltration.

4.5.4 Sine Wave Moving Sensors Sensors that move in a sine wave pattern with constant velocity perform somewhat well against both classes of intruder, as shown in Fig. 4.16. However, in this case, random deployments against an intruder with a random entry and exit point are not quite as effective. Despite these sensors guided by this method of mobility are somewhat of a general purpose solution when the cost of higher energy expenditure is not a point of concern. Figure 4.17 shows that sensors which move in a sine wave pattern with a constant velocity along the X axis perform well against both classes of intruder; however, the variable amount of acceleration to maintain the X axis velocity raises large concerns

Detection Rate (%)

Sine Wave (Arc Length) Sensor Performance 100 90 80 70 60 50 40 30 20 10 0

VI, US VI, RS RI, US RI, RS

0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Sensors

Fig. 4.16 Performance of sine wave (arc length) moving sensors

Detection Rate (%)

Sine Wave (X-Axis) Sensor Performance 100 90 80 70 60 50 40 30 20 10 0

VI, US VI, RS RI, US RI, RS

0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Sensors

Fig. 4.17 Performance of sine wave (X axis) moving sensors

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regarding the amount of energy required to fuel these movement patterns. Nonetheless, random distribution of these sensors against a vertically moving intruder succeeds in detection more than any other type of intruder and deployment method. What these results have shown is that static sensors can provide a competitive rate of detection coupled with comparatively low energy consumption. However, one weakness lies in the detection rate yielded by low sensor densities. Thus, when the quantity of deployed sensors is low, static sensors do not provide a viable means of detecting infiltration. Only at a quantity of 150 sensors do static sensors provide an equal or greater amount of detectability than random moving sensors, and only at 200 sensors do static sensors produce a higher rate of detection than sensors moving in a straight line toward randomly chosen boundaries. Conversely, static sensors yield much higher detection rates when the intruder enters the area at a randomly chosen boundary. Random moving and random boundary sensors are unable to match the performance of static sensors against this class of intruder, regardless of the area’s sensor density. The significance of these discoveries is that a sensor does not necessarily have to be mobile to be effective – against certain classes of intruder and certain types of infiltration, static sensors do provide adequate means of protection. Areas of interest having no designated entry and exit points benefit the most from static sensors. Yet, consider a scenario in which a border between two independent areas is under surveillance. Many borders are divided by naturally occurring geographic bodies such as rivers, channels, streams, forests, etc. An intruder enters the boundary separating both ends of the border at one side then moves to the boundary at the opposite side. Static sensors would not perform optimally in this environment. Random boundary sensors would provide the second greatest probability of detection, just as under sine wave sensors with constant X axis velocity. Overall randomly moving sensors do not provide scenario-based benefits that random boundary and static sensors provide. At low sensor quantities this mobility model performs approximately equal to or better than random boundary sensors; however, at 70 sensors or greater its performance begins to normalize and does not increase at the rate of mobile boundary sensors. The constraints of maintaining sensor quantities at a narrow range between the minimum and maximum values can become burdensome. Tables 4.1, 4.2, 4.3, 4.4, and 4.5 shows the percentage by which the rate of detectability increases as the quantity of sensors increases. The increase in percentage from one quantity to the next shows that as the number of sensors increase the additional percentage of additional detectability increases. The results show that as deployments surpass 120 sensors the percentage by which the detection rate increases is significantly lower than the rates afforded by lower sensor quantities. This is significant because the threshold between large and small improvements is known for a particular area and scenario developers may calculate the range of desired sensor quantities. In the context of a vertically moving intruder against uniformly deployed sensors, one can initially deploy more than 120 sensors, however, if the quantity drops below that threshold, then the benefit of restoring a quantity of more than 120 sensors produces diminishing returns. The random moving, random boundary, and static mobility models differ in these respective

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RI

k

US

RS

US

RS

10 20 40 50 70 100 120 150 170 200

– 910.0 125.7 22.4 43.4 36.5 17.6 11.7 13.5 9.9

– 200.0 53.3 52.2 28.6 31.1 5.1 6.5 18.2 3.8

– 200.0 3.3 54.8 31.3 17.5 13.5 1.2 4.7 2.2

– 53.8 110.0 4.8 38.6 26.2 –5.2 16.4 4.7 4.5

Table 4.2 Increase in detectability for randomly moving sensors Random Moving Sensors VI

RI

k

US

RS

US

RS

10 20 40 50 70 100 120 150 170 200

– 82.4 57.1 7.6 15.1 19.8 5.0 6.3 3.4 5.0

– 91.2 82.6 16.0 22.8 29.8 6.1 7.4 7.9 4.0

– 300.0 0.0 4.2 8.0 77.8 10.4 5.7 14.3 9.4

– 83.8 67.6 30.3 25.3 33.9 13.5 15.8 1.1 3.1

Table 4.3 Increase in detectability for randomly straight line moving sensors Random Straight Line Sensors VI

RI

k

US

RS

US

RS

10 20 40 50 70 100 120 150 170 200

– 92.0 100.5 8.1 25.2 29.0 10.0 8.4 4.0 3.4

– 76.5 88.9 26.2 16.6 31.2 9.1 11.7 2.4 4.1

– 200.0 83.3 18.2 23.1 37.5 13.6 20.0 10.0 10.6

– 112.5 64.7 7.1 20.0 44.4 21.2 1.6 9.4 2.9

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Table 4.4 Increase in detectability for sine wave (arc length) sensors Sine Wave (Arc Length) Sensors VI

RI

k

US

RS

US

RS

10 20 40 50 70 100 120 150 170 200

– 116.6 20.9 29.8 21.5 22.4 11.3 8.0 6.0 6.5

– 78.3 26.8 15.4 40.2 6.1 14.4 4.5 5.5 3.2

– 20.0 27.8 78.3 19.5 32.7 9.2 11.3 7.6 4.7

– 14.3 50.0 16.7 25.0 45.7 13.7 6.9 1.6 38.1

Table 4.5 Increase in detectability for sine-wave (x axis) sensors Sine Wave (X Axis) Sensors VI

RI

k

US

RS

US

RS

10 20 40 50 70 100 120 150 170 200

– 71.1 64.3 18.1 15.4 22.6 8.0 4.3 8.9 3.5

– 78.8 69.9 20.6 14.8 12.9 12.4 6.4 1.5 3.0

– 25.0 12.0 57.1 15.9 35.3 8.7 9.3 6.1 8.0

– 17.6 40.0 14.3 21.9 48.7 13.8 10.6 11.0 16.0

percentages. Static sensors generally experience the greatest amount of growth from one sensor quantity to the next, while sensors employing the random moving model see the lowest. Moderate to high sensor quantities see similar increases when guided by the sine wave and random boundary (straight line) models.

4.6 Concluding Remarks and Discussions In this paper we studied the detectability in incomplete sensor networks. We believe that detectability problem in incomplete sensor networks is important in many practical applications. In many circumstances there are simply not enough sensors to completely cover a region to be monitored. Therefore, the next best we can do is to utilize whatever at hand to prevent intruders from infiltrating the monitored region without being detected. Such circumstances can result from an unexpected battleground encounter or a sudden change of battleground plan. In other cases, the areas to be monitored are simply too large to deploy sufficient sensors to provide complete coverage.

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Our study shows that statically deployed sensors can perform surprisingly well against single intruders under various conditions. Constrained defending sensors do not perform as well as we originally thought. Sensors that perform sine wave movements with acceleration along the sine wave arcs (to keep the constant speed along the x-axis) perform quite well. We proposed the notion of effectiveness of sensor deployment and movement. An effective scheme should provide high detectability with a given number of sensors. It also should provide sizable gain in detectability when the number of sensors increases. The speed of mobile sensors is a clearly important factor that affects detectability. It is easy to see that if a single defending sensor can move infinitely fast, then the whole networking area cannot be infiltrated. On the other hand mobility consumes energy. This is especially a problem for those low-power sensors. Even when the area under protection is fully covered by static sensors, an effective sensor movement strategy can be used to systematically turn on/turn off group of sensors in a pattern that resembles the sensor movement. This is essentially a virtual sensor movement. By controlling the rate of sensors on/off, the virtual sensor movement can achieve better detectability while conserving energy. Currently we are studying the following related topics. The first issue is a further study of sensor movement patterns. Random movement has its advantage of unpredictability. A potential intruder cannot find regularity of randomly moving sensors. On the other hand, because the sensors are moving randomly, there is no way to allow the defending sensors to effectively communicate and cooperate. We are studying pseudorandom movement, which remedies the problem of total random movements. We are also investigating detectability in the presence of multiple intruders.

References 1. I.F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci. “Wireless sensor networks: a survey,” Computer Networks, Vol. 38, 2002, pp. 393–422. 2. J. Aslam, Z. Butler, F. Constantin, V. Crespi, G. Cybenko, and D. Rus. “Tracking a moving object with a binary sensor network,” Proc. of ACM International Conference on Embedded Networked Sensor Systems(SenSys), 2003, pp. 150–161, 3. G. Berkolaiko, S. Havlin, H. Larralde, and G.H. Weiss. “Expected number of distinct sites by N L´evy flights on a one-dimensional lattice,” Physical Review E, Vol. 53 No. 6, 1996, pp. 5774–5778. 4. G. Berkolaiko and S. Havlin. “Territory covered by N L´evy flights on d-dimensional lattice,” Physical Review E, Vol. 55, No. 2, 1997, pp. 1395–1400. 5. S. Bush, M. Steenstrup, A. Alizadeh, A. Scaglione, and J. Miller. “Future of sensor networks: new challenges and innovative approaches,” Panel Session of 13th International Conference on Computer Communications and Networks (ICCCN 2004), October 11–13, 2004. 6. M. Cardei, D. MacCallum, M.X. Cheng, M. Min, X. Jia, D. Li, and D.-Z. Ding. “Wireless sensor networks with energy efficient organization,” Journal of Interconnection Networks, Vol. 3, Nos. 3&4, 2002, pp. 213–229. 7. A. Cerpa and D. Estrin. “Ascent: Adaptive self-configuring sensor networks topologies,” Proc. of IEEE INFOCOM 2002. 8. G. Chockler, M. Demirbas, S. Gilbert, N. Lynch, C. Newport, and T. Nolte. “Reconciling the theory and tractice of (rn)reliable wireless broadcast,” Proc. of 25th IEEE International Conference on Distributed Computing Systems Workshops, 2005.

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9. V. Clouqueur, V. Phipatanasuphorn, M. Ramanathan, and K.K. Saluja. “Sensor deployment strategy for target detection,” Proc. of the 1st ACM International Workshop on Wireless Sensor networks and applications, September 2002, pp. 42–48. 10. M.D. Donsker and S.R.S. Varadhan. “On the number of distinct sites visited by a random walk,” Communication on Pure Applied Mathematics, Vol. 32, No. 6, 1979, pp. 721–747. 11. D. Estrin, R. Govindan, and J. Heidemann (eds). “Special Issue on Embedding the Internet,” Communications of the ACM, Vol. 43, 2000. 12. D. Estrin, R. Govindan, J. Heidemann, and S. Kumar. “Next century challenges: scalable coordination in sensor networks,” Proc. of ACM MobiCom’99, pp. 263–270. 13. K. Fall and K. Varadhan. “The NS manual,” May, 2005. 14. L.K. Gallos, P. Argyrakis, and K.W. Kehr. “Trapping and survival probability in two dimensions,” Physical Review E, Vol. 63 021104, 2001, pp. 1–5. 15. L.K. Gallos and P. Argyrakis. “Accurate estimation of the survival probability for trapping in two dimensions,” Physics Review E, Vol. 64, No. 5, Art. No. 051111, Part 1, November 2001. 16. C. Gui and P. Mohapatra. “Power conservation and quality of surveillance in target tracking sensor networks,” Proc. of ACM MobiCom’04, pp. 129–140. 17. J. Kahn, R. Katz, and K. Pister. “Next century challenges: mobile networking for smart dust,” Proc. of ACM MobiCom’99, pp. 271–278. 18. X. Li, P. Wan, and P. Frieder. “Coverage in wireless ad hoc sensor networks,” IEEE Transaction on Computers, Vol. 52, No. 6, June 2003, pp. 753–763. 19. B. Liu and D. Towsley. “On the coverage and detectability of large-scale wireless sensor networks,” Workshop on Modeling and Optimizationn in Mobile Ad Hoc Wireless Networks, March 2003. 20. S. Meguerdichian, F. Koushanfar, M. Potkonjak, and M.B. Srivastava. “Coverage problem in wireless ad hoc sensor networks,” Proc. of IEEE INFOCOM, 2001 pp. 1380–1387. 21. E. Nilson. “Dynamical Theories of Brownian Motion,” Princeton University Press, 1967. 2nd Ed. 2001. (Available at http://www.math.princeton.edu/nelson/books.html). 22. W. Peng, X. Zhang, and K. Makki. “Locality caching multi-root multi-generation routing algorithm in mobile ad hoc networks,” Proc. of 12th ICCCN, October 2003. Extended version submitted for journal publication. 23. W. Peng, Y. Wang, and K. Makki. “Dynamic key management for secure routing in LCMRMG MANET,” Proc. of 13th ICCCN, October 2004, pp. 227–232. Extended version submitted for journal publication. 24. W. Peng and X. Jia. “On detectability in incomplete sensor networks,” Manuscript, October 2004. 25. G.J. Pottie and W.J. Kaiser. “Wireless integrated network sensors,” Communications of the ACM, Vol. 43, May 2000, pp. 51–58. 26. P. Santi. “Topology control in wireless ad hoc and sensor networks,” ACM Computing Surveys, Vol. 37, June 2005, pp. 164–194. 27. S. Shakkottai, R. Srikant, and N. Shroff. “Unreliable sensor grids: coverage, connectivity and diameters,” Proc. of IEEE INFOCOM’2003, pp. 1073–1083. 28. S. Slijepcevic and M. Potkonjak. “Power efficient organization of wireless sensor networks,” Proc. of IEEE International Conf. on Communcations, June 2001, Helsinki, Finland. 29. R. Szewczyk, E. Osterweil, J. Polastre, M. Hamilton, A. Mainwaring, and D. Estrin. “Habitat Monitoring with Sensor Networks,” Communications of the ACM, Vol. 47, June, 2004, pp. 34–40 30. D. Tian and N.D. Georganas. “A coverage-preserving node scheduling scheme for large wireless sensor networks,” Proc. of 1st ACM International Workshop on Wireless Sensor Networks and Applications, September 2002, pp. 32–41. 31. Wikipedia: Sine waves. 32. C. Yan, X. Jia, and R. Ellis. “On random points in the unit disk,” Submitted for journal publication, 2004. 33. W. Zhang and G. Cao. “Optimizing tree reconfiguration for mobile target tracking in sensor networks,” Proc. of IEEE INFOCOM 2004.

Chapter 5

Comparative Methods of Channel Assignment in Multivariate Wireless Networks Xufei Mao, Xiang-Yang Li, and S. Kami Makki

5.1 Introduction Wireless mesh network is a network implemented over a wireless local area network (LAN), and its infrastructure type is decentralized, relatively inexpensive, reliable, and resilient since the wireless routers are often static and not powered by batteries. In addition, the access points (routers) seldom change their positions in wireless mesh networks, and some wireless nodes have gateway functions to provide the connectivity to the Internet. Therefore, such networks behave almost like wired networks with infrequent topology changes and limited node failures. Due to these good properties and potential applications such as providing commercial Internet access to residents and local businesses, wireless mesh networks have drawn a lot of attention in recent years. For example, wireless mesh networks are being used as the last mile for extending the Internet connectivity for mobile nodes. In addition, some commercial deployments of multihop wireless meshes are already in the works. For instance, a number of mesh networks have been deployed in some cities of the United States, including Medford, Oregon, and cities in Minnesota [4]. Unlike traditional wired network, close-by mesh routers share certain wireless channels and the capacity of wireless mesh network will be increased tremendously when extending from a single channel model to a multiradio, multichannel, multihop model. For example, if two nodes vi and v j could communicate with each other by channel f 1 , and both nodes have at least one more available network interface cards, which could operate on another channel f 2 , if f 2 is also available for both nodes, vi and v j could use both f 1 and f 2 to communicate simultaneously. When such cases are applied to more wireless nodes, the throughput of a wireless network will be increased tremendously.

X. Mao Department of Computer Science, Illinois Institute of Technology, Chicago, IL 60616. The work of Xufei Mao is partially supported by NSF grant CCF-0515088. e-mail: [email protected], [email protected]

S.K. Makki et al. (eds.), Sensor and Ad Hoc Networks, C Springer Science+Business Media, LLC 2008 DOI: 10.1007/978-0-387-77320-9 5,

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On the other hand, with the recent fast-growing spectrum-based services and devices, the remaining spectrum available for future wireless services is being exhausted, known as the spectrum scarcity problem. This is a serious problem in several aspects: the cell phone companies have to spend billions of dollars to bid for a 20–30 MHz 3G spectrum; it is difficult for new innovative technologies to enter the market competitively; it is difficult to provide a certain quality of service for systems operating in unlicensed spectrums. The current fixed spectrum allocation scheme leads to significant spectrum white spaces (spectrum that is not used at all for some period of time), where many allocated spectrum blocks are used only in certain geographical areas and/or in brief periods of time. As an example, the Shared Spectrum Company performed spectrum occupancy measurements, and found that the spectrum usages vary dramatically in time, geographic locations, and frequency. For example, there was at least 87% of white space measured in New York City [13]. Thus, a huge amount of precious spectrum (below 5GHz), perfect for wireless communications that is worth billions of dollars, sits there silently. It is widely agreed that opportunistic or dynamic spectrum usage will significantly mitigate the spectrum scarcity. Recently, more and more researchers have been concentrating on how to reuse the licensed spectrums for secondary users when the licensed spectrum is idle or secondary users use licensed spectrums within some special interference temperature [17] such that secondary users interfere with the primary users in the range of interference temperature. However, a series of technologies (topology of a wireless network, routing, link scheduling, and so on) become more complex and difficult due to the properties of wireless networks (nodes), such as lower power, interferences, mobility, and some other physical barriers. In addition, using multiple channels and radioscould mitigate such interference and improve the throughput to some extent, but it could not eliminate interference completely. All in all, the performance (capacity) improvement brought by multichannel and multiradio will be less effective or even degrade if we do not handle them carefully. In this chapter, we address the problem of static channel assignment in wireless networks with multiradio and multichannels under some network models and interference models. Assume that each wireless node u has a given κ(u) number of network interface cards and a subset of channels on which this node may operate. We on need to choose a channel for each Network Interface Card (NIC) of every node so that the resulting network has certain properties like being connected, that is, assigning κ(u) channels to node u. Here two nodes u and v can form a communication link (u, v) if they share a common assigned channel. We prove that it is nondeterministic polynomial-time (NP)-hard to decide whether we can assign channels to nodes such that the network is connected while the number of total assigned channels to every node does not exceed the number of NICs it has. We then propose several novel methods for assigning channels. One of our methods is based on nodes clustering: we first partition nodes into a number of clusters and connect these clusters via a backbone; we then find a channel assignment for nodes on the backbone such that the backbone is connected; finally, for each cluster, we perform a local channel assignment such that all nodes in a cluster will form a connected

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subnetwork. One of the advantages using the cluster-based channel assignment is that the method can adapt to the dynamic channel availability. When a node’s channel availability changes, we only need to update the channel assignment for one cluster if the node is not on the backbone. If it is on the backbone, we only need to additionally update the channel assignment for backbone nodes, whose amount is far less than the total number of wireless nodes in the whole network. Our extensive simulations show that our backbone-based channel assignment method induces a connected network without violating the NIC constraints for all nodes with high probability. We also study how to assign channels to get aconnected network using as few channels as possible. By using fewer channels, we leave more freedom forfuture channel assignment when new nodes join the network. We also study how to assign channels such that the resulting network supports a large number of simultaneous transmissions, thus increase the network throughput of the resulting network intuitively. As it is observed in the literature, many network properties enjoy a transition phenomenon. We also show that the network connectivity also has a transition phenomenon with respect to the number of channels available to a node when all other parameters are fixed. Assume that the total number of channels in the network is fixed and each node can only operate on s channels that are randomly chosen. Then we show that the network is connected with high probability if s is larger than a certain threshold value, depending on the number n of network nodes, the transmission radius r of every node, the number R of available radios of every node, and the deployment region (typically assumed to be a unit-area square or a disk). The rest of the chapter is organized as follows: In Section 5.2, we state our network models, interference models, and the problems to be studied. We give an overview of related work about multiradio, multichannel, multihop wireless networks in Section 5.3. In Section 5.4, we study the transition phenomena, which plays a key role for the connectivity of wireless networks.We present our detailed algorithms in Section 5.5, and Section 5.6 describes our simulation studies of proposed algorithms. Finally, Section 5.7 concludes the chapter.

5.2 Problem Formulation In this chapter, we will study static channel assignment for a multiradio, multichannel, multihop wireless network. Our objective is either to minimize the used channels while preserving a connected network, or to maximize a certain network throughput using given radio and channel availability of all nodes.

5.2.1 Network System Models We first present the network model used throughout this chapter. Consider a set V = {v1 , v2 , · · · , vn } of n wireless nodes distributed in a plane. We first assume that each

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node vi has a transmission range RT (i) that allows only those nodes within distance RT (i) from vi to receive the signal from vi correctly. Here we emphasize that v j − vi ≤ RT (i) is a necessary but not sufficient condition for two nodes vi and v j to compose a physical communication link, for example, such link may not exist due to physical barriers. We assume that each terminal vi also has an interference range R I (i) such that every unintended receiver would be interfered by the signal from vi when it is using the same channel as vi does simultaneously. Typically, RT (i) ≤ R I (i) ≤ β · RT (i), where β is a constant factor and 2 ≤ β ≤ 4 in practice. We use G 0 = (V, E) to denote the complete communication graph, where E is the set of all communication links. In addition, every wireless terminal (node) vi has one or more NICs and each of them could operate on one or more spectrum radios. Here we use I (vi ) to denote the number of NICs of a node vi . Let F = { f 1 , f 2 , · · · , f k } denote the set of K orthogonal (could be nonorthogonal in certain situations) channels, which could be used by all nodes V . We generally assume that each NIC could only operate on a subset of F channels due to the hardware constraints, and let F(v, i) be the set of channels that can be operated by ith NIC for node v, where 1 ≤ i ≤ I (v). Let F(v) be the #set of channels that can be used by node v via any of its NICs, denotes i.e., F(v) = 1≤i≤I (v) F(v, i). For each link e = (u, v) ∈ E, F(e) $ the set of channels, which could be used by e, that is, F(e) = F(u) F(v). When F(e) is empty, it means that the two end-nodes of e cannot communicate directly over e under the radio and channel constraints. For simplicity, we abuse the notation a little bit, we use G = (V, E) to denote the communication graph, where E now denotes all the links e = (u, v), such that u and v can communicate directly with each other under the radio and channel constraints of these two nodes.

5.2.2 Problem Formulation Transition Phenomena of Network Connectivity on Channel Availability: The first question we want to investigate is the effect of channel availability on the connectivity of network G. Assume that due to designing or environmental constraints, a wireless NIC can only operate on a randomly selected c channels out of total maximum |F| = k channels. It is not difficult to see that when c is sufficiently smaller than k, the network is more likely to be disconnected, and when c is sufficiently close to k, the network is more likely to be connected (when the graph G 0 is connected). We thus would like to study the asymptotical transition behavior of the network connectivity in terms of the relation of c and k and other parameters such as the number n of nodes, the normalized transmission range RT . The remaining main challenge we will address here is to statically assign channels to the NICs of each node such that the resulting wireless network has certain properties, e.g., being connected while using the least number of channels. At a

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first glance, the problem of assigning channels to wireless nodes appears to be a graph-coloring problem. However, a standard node-coloring problem fails to assign channels correctly because it does not capture the constraint where two adjacent communicating nodes of one link need to be assigned a common color (channel). In addition, an edge-coloring formulation also fails to capture the constraint that only a limited number of colors can be incident onto a node due to the limited number of NICs for each node. Furthermore, both formulations fail to capture the property that the resulting network must be connected. For simplicity, we first assume that we have fixed channels. Notice that, in practice, we may have flexible channels. Furthermore, a node can merge several consecutive channels into one big channel and thus saves the NICs it needs. Actually, we can prove that an available flexible channel assignment only increases the throughput of the network, but it will not determine whether there is a channel assignment that results in a connected network. Channel Assignment for Connectivity: We first formally define the channel assignment problem when only network connectivity is required. Remember that throughout in this chapter, we only consider static channel assignment, i.e., each NIC will select one and only one channel from its operable channels to operate on. We notice that, in practice, dynamic channel switching is possible for some networking cards. Dynamic channel switching clearly can potentially improve the network throughput performance. However, this is not without a price: the hardware needs to be specially designed, and the channel switching does have some overhead such as delay and synchronization between transmitting nodes and receiving nodes where they need to switch to the same channel almost at the same time period. In light of these possible overheads, we mainly consider the static channel assignment where each radio of every wireless node will operate on a predetermined channel. The channel assignment problem is to determine which channel to operate exactly. Let A (vi , k, f j ) ∈ {0, 1} be the channel allocation function that denotes whether the kth NIC of node vi selects to operate on channel f i or not. Obviously, A (vi , k, f j ) = 0 if f j ∈ F(vi , k); A (vi , k, f j1 ) + A (vi , k, f j2 ) ≤ 1 since one NIC of a node can only operate on one channel under static channel assignment. When channel assignment is given, we use A (vi ) = { f j | A (vi , k, f j1 ) = 1 for some NIC} to denote the channels selected by some NICs of node vi . We define the communication graph G A = (V, E ) induced by the channel assignment method A as follows: E contains a link e = (u, v) only if e ∈ E and A (u) ∩ A (v) = ∅. We say that a channel assignment A is valid if the communicagraph. The total channels used by all nodes under A tion graph G A is a connected # is denoted as FA = u∈V A (u). In this chapter, we first seek a channel assignment that produces a connected network while using as few channels as possible. Channel Assignment for Throughput: Although network connectivity is an important property of a network, network throughput is a more meaningful criterion to optimize. However, a direct optimization of network throughput involves many aspects of the networking such as traffic prediction, routing, link scheduling, and so on, which has drawn significant amount of research interests recently. A full

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study of this problem in multihop multichannel multiradio is out of the scope of this chapter. Here we concentrate on assigning channels to nodes such that the resulting communication graph permits the maximum number of simultaneous transmissions, i.e., the size of the maximum independent set in the conflict graph (to be defined later). Two links can transmit at the same time if they will not cause interference with each other. Notice that there is a distinction between the network throughput and the maximum number of simultaneous transmissions permitted in a network. To study the network throughput under a certain channel assignment, we need to specify the interference model to be used. Here we will adopt several widely used interference models as follows. One of the main obstacles in designing wireless network protocols is the signal interference. A number of interference models have been proposed in literature, such as the protocol interference model [8], the Request to Send (RTS)/Clear to Send (CTS) interference model, and the signal-to-interference-and-noise ratio model, and so forth. For example, according to IEEE 802.11, a transmitter sends a RTS frame to intended receivers before sending a data frame. If the intended receiver is available to receive data frame, it will respond with a CTS frame to the sender. For every transmitter–receiver pair, all wireless nodes within the interference range of either the transmitter or the receiver will refrain from transmitting. In other words, for two simultaneous transmitting links x y and uv, x and y cannot be inside the interference region of either u or v, and vice versa. The protocol model (PrIM) was first proposed in [8]. In this model, a transmission from node vi (transmitter) to node v j (receiver) is successful if and only if the intended receiver v j is sufficiently apart from any other transmitter transmitting simultaneously, that is, vk − v j ≥ (1 + η)vi − v j ), where vk = vi and constant η > 0. Similar with PrIM, Wang et al. [22] recently proposed the fixed transmission power protocol interference model (fPrIM) where the transmission from vi to v j is successful only if v j is not within the interference range of any other transmitter vk transmitting in the same time slot using the same channel, that is, vk − v j > R I (k). Another interference model is the Transmitter Interference Model (TxIM) [23]. In this model, transmission from node vi is successful if and only if, for any other transmitter vk transmitting in the same time slot using the same channel, vi − vk > (1 + η)(RT (i) + RT (k)). Here, η is a system parameter. The physical interference model uses the signal-to-interferenceand-noise ratio (SINR) to describe the aggregate interference in the network. In this model, a transmission from node vi to node v j is successful if and only if the SINR at the receiver is at least the minimum SINR threshold required. The channel assignment and link scheduling is closely related to the graph coloring of the conflict graph modeling of the wireless networks. Conflict graph modeling has been widely used to model interference in wireless mesh network, which is defined as follows: Consider a graph G = (V, E), where V is the set of wireless devices and E is the set of communication links. The conflict graph G = (V , E ) corresponding to G has vertices V corresponding to the links in E, which means that if there is a link vi v j ∈ E, there will be a vertex vi, j in G . Conflict graph G has an edge between two vertices in G if and only if the corresponding links in E denoted by these two vertices in G conflict with each other, i.e., they

5 Comparative Methods of Channel Assignment in Multivariate Wireless Networks Fig. 5.1 A simple network represented by a graph G with four nodes

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cannot transmit at the same time slot using the same channel. Specifically, if two links vi v j and v p vq in graph G conflict with each other, there will be a link vi, j v p,q in G between two vertices vi, j and v p,q . Notice that there will be a different conflict graph G under constraints of different interference models for the same node set V , as well as a different channel assignment scheme. Take a simple example, shown in Fig. 5.1, with four wireless nodes, V = {A, B, C, D}, each of them has at least two available NICs. We assume that node A and C are not within the interference range of each other, nor are nodes B and D. Figure 5.2(a) shows the conflict graph G under the RTS/CTS model without considering the channels and the radios of all nodes. Assume node A could operate on channels {1, 2}, node B could operate on channels {2, 3}, C operates on channels {3, 4}, and D operates on channels {1, 4}. When each node has only one NIC, then clearly both A and B should use channel 2 to communicate with each other; similarly, C and D should use channel 4 to communicate with each other. In this case, links AB and AD cannot be activated at the same time. Figure 5.2 (b) shows this phenomenon of conflict when channel availability is taken into account. Figure 5.2 (c) shows that all four links can be activated at the same time if every node has two NICs.

5.3 Related Work As we know, traditional multihop wireless networks are comprised of single radio components, and using multiradio and multichannel could efficiently enhance the throughput of the whole wireless network by exploiting the multiple channels and channel reuse opportunities. However, simply using multiradio and multichannel

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without an efficient channel assignment algorithm cannot effectively exploit the increasing bandwidth available, and even decrease the network performance due to channel switching overhead and system management overhead. As noted in [2,6, 3], there are a number of common issues concerning multiradio, multichannel, multihop wireless networks including network connectivity, sharing channels, switching channels dynamically, and network topology. Concerning the subject of multichannel, multihop wireless networks, some researchers have proposed several approaches. For example, in [9,16], Jain et al. proposed a Carrier-Sense Multiple Access (CSMA) protocol based on a modification of IEEE 802.11 for multihop wireless networks that uses multiple channels and a dynamic channel selection method. Their main idea was to divide the available bandwidth into N channels and the transmitting station selects the appropriate channel to transmit packets based on the interference power measurements on all available channels. So et al. [10,12] proposed a Media Access Control (MAC) protocol requiring only one transceiver per host for ad hoc wireless networks. This MAC protocol enables hosts to utilize multiple channels by switching channels dynamically, thus increasing throughput of wireless networks. Unlike those approaches mentioned earlier, which need to modify the IEEE 802.11, Bahl et al. present a link-layer protocol called Slotted Seeded Channel Hopping (SSCH) in [18]. SSCH increases the capacity of an IEEE 802.11 network by utilizing frequency diversity and each node in the wireless network uses SSCH to decrease interference, thus improving the capacity of wireless networks. Das et al. [5] present two mixed integer linear programming models for solving the fixed channel assignment problem with multiple radios through finding fixed channel assignment strategies to maximize the number of simultaneous bidirectional links. There are other examples of research concerning using multi-NIC for each node, include [19] and [21]. The methods adopted in [19] require each node to have as many NICs as its neighbors have, and also require a sufficiently large number of available channels. In [21], authors assume there is an a priori and identical channel assignment to the NICs of each node, and the channel assignment for all wireless node is the same: binding #1 NIC with channel 1, #2 NIC with channel 2 and so on. However, as we know, such requirements are unrealistic because the number of NICs each wireless node has may be different and some NICs could only operate on a fixed subset of channels due to the hardware constraints, such as 802.11X series NICs could operate on 11 channels. In this chapter, we assume that different wireless nodes may have different number of NICs, and that the types of NICs do not need to be uniform. Furthermore, the actual available channels for different wireless node could be different, which is more general than previous studies and more close to practice. Other research such as [1], committed a joint channel assignment scheme for throughput optimization in multiradio wireless mesh networks. However, it assumes that all nodes have the same transmission range and only considered the static channel assignment situation. In other words, they assume that for each node v, the number of available channels for it is no more than the number of NICs

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I (v). However, as we know, in practice, not only could the transmission ranges of wireless nodes be different, but also nodes could adjust the channels they operate on dynamically.

5.4 Transition Phenomena Recent work [20] and [14] has shown that, when n nodes are randomly deployed in a certain region, there is a critical transmission power rn required to ensure with high probability that two wireless nodes in the network could communicate with each other through one- or multihop paths if all nodes have fixed power rn . In other words, such critical transmission power is also the threshold of keeping the whole network connected, if the area of the plane and the number of nodes in the networks are fixed. Generally, it was known that, given n nodes of set V randomly deployed in a unit area region (such as a square or a disk) and every node with transmission range rn , the unit disk graph network G(V, rn ) formed by V (which has a link uv iff u − v ≤ rn ) is connected with high probability if π nrn2 ≥ log n, otherwise it is disconnected with high probability. For multiradio, multichannel, multihop wireless networks, several networking parameters will affect the network connectivity, for example, the transmission range of wireless nodes, the number of radios available for every node, and the number of channels that can be used by each radio. Traditional results on critical transmission range for connectivity assumed that every wireless node only has one NIC and there is only one channel to choose. In a wireless network with multiradios, we assume that channels, which can be operated by a radio of a specific wireless node, are randomly chosen from a set of channels. Then we would like to study whether there is a critical density of channels for the network connectivity. Clearly, we first need the transmission range rn to satisfy the requirement π nrn2 ≥ log n. In multiradio, multichannel networks, we generally assume there are k channels F available globally and each radio will be able to operate on s channels randomly selected from F . Notice that when two end-nodes of a link uv in G(V, rn ) do not have a common operable channel, then this link uv, will not be operable by u and v although nodes u and v are physically within the transmission range of each other. We define a network G(V, rn , s, k) as the set of links uv, where u − v ≤ rn and u and v have a common channel. Clearly, if s > k2 , then it is guaranteed that two end-nodes of a link uv in G(V, rn ) will have a common channel to communicate, that is, G(V, rn , s, k) is connected as long as G(V, rn ) is connected. We want to know the critical value for s (with fixed rn and k) that will allow the network G(V, rn , s, k) to remain connected. Obviously, a link uv remains in G(V, rn , s, k) if they have a common channel, whose probability is k k−s Pk,s = 1 − sk ks , s

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if every node only has one radio. When every node has same set of R distinctive radios, the probability that two nodes will have a common channel among any of these R radios is k k−s R Pk,s,R = 1 −

k ks

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s

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Consequently, every link in G(V, rn ) will survive in G(V, rn , s, k) with a probability Pk,s,R , i.e., the network G(V, rn , s, k) can be modeled as a Bernoulli model. From [27], we know that the network G(V, rn , s, k) is connected with high probability only if π · Pk,s,R · n · rn2 ≥ log n. The simulation results of transition phenomena of network connectivity are reported in Fig. 5.3. Here, the x-coordinate indicates the number of available channels on which each node could operate during a period of time, and y-coordinate denotes the connectivity of the whole wireless network. In this simulation, we randomly generate 300 and 400, wireless nodes respectively, in a 500 × 500 unit region and the difference between these two cases is that the transmission range of the former is 75 units and 50 units of the latter. Typically, here a unit represents about one m. We assume the maximum number of available channels on which the wireless nodes could operate is 11, in practice, this number maybe different, for example, IEEE 802.11b specifies 11 channels in the 2.4 GHz spectrum, three of which are orthogonal, and IEEE 802.11a specifies 13 orthogonal channels in the 5 GHz. We vary the number of available channels for wireless nodes from 1 to 11, and the 1

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results indicate that the connectivity of a wireless network increases sharply from two to four available channels. The whole wireless network is connected almost 100% provided the available channels are equal to or greater than four.

5.5 Our Approaches In the previous section, we showed that for a network to be connected, we need at least a certain number of channels for each node if the channels are randomly available. In this section, we are ready to present our approaches for static channel assignment while achieving connected networks, and/or networks permitting largest number of simultaneous transmissions.

5.5.1 Complexity Result First of all, given a wireless network and the radio and channel availability constraints of all wireless nodes, we show that it is NP-complete to decide whether we have a channel assignment that results in a connected network without channel switching. Theorem 1 It is NP-complete to decide whether we have a channel assignment that results in a connected network without channel switching (i.e., the number of assigned channels to each node is no greater than its number of NICs). Proof Clearly the problem is NP since we can check whether a given assignment is valid in polynomial time. We then show that it is NP-hard from the induction of a NP-complete problem finding a minimum-degree spanning tree. It is known that it is NP-complete to decide whether a given graph G has a spanning tree whose maximum node degree is at most a given integer D [15]. Given the graph G = (V, E) and integer D, we construct a channel assignment problem for a network G as follows. The network G = (V , E ) is the same as G, and each wireless node of V will have D radios. There are m total channels, where each channel corresponds to an edge in the graph G. The set of channels on which a wireless node can operate is the set of channels corresponding to all incident edges of this node in G. We then show that graph G has a spanning tree T with a maximum degree D iff there is a channel assignment for G that results in a connected network without channel switching. First of all, if such a tree T does exist, then our channel assignment for the network G will work as follows: a node u is assigned a channel represented by the edge e, if e is an edge incident on u in the tree T . Clearly, the total number of channels assigned to every node u is at most D, and the network induced by the channel assignment is obviously connected since T will be a subgraph of the induced network. Second, assume there is a channel assignment that induces a connected network. Since each node has at most D radios, the number of channels assigned to every

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node is at most D and thus the induced network has the maximum degree D. Consequently, any spanning of the induced network is a spanning tree for G whose maximum degree is at most D. This finishes the proof. In the remainder of this section, we propose several novel methods to assign channels to every node in order to achieve a certain network property. Notice that given n wireless nodes randomly distributed in a region, whether those nodes could form a connected network or not has been determined when the attributes of nodes are given, such as the transmission range, interference range, available channels, and NICs of nodes.

5.5.2 Backbone Based Approach Assume there are n wireless nodes randomly distributed in a region and each node vi has I (vi ) NICs. The transmission range of vi is RT (i). Every node vi has some adjacent neighbor nodes, denoted by N (vi ). Here if v j ∈ N (vi ), then v j should be within the transmission range of vi and node vi and v j should have one or more common channels, that is F(i) ∩ F( j) = ∅. Notice that, v j ∈ N (vi ) does not mean vi also belongs to N (v j ) due to the different transmission range of vi and v j . Notice that N (vi ) could be empty in some special case, and the network G is then not connected. We always assume that the network is connected, by having enough channels, to wireless nodes. On the other hand, assume we have enough channels and we would like to minimize the number of channels needed to guarantee the whole network connected. Our first method is a Backbone Based Approach (BBA). Obviously, the centralized method will get the best channel assignment performance. However, a centralized approach, letting some node collect information of all other nodes in the network, is almost impossible due to the low memory and potentially high mobility of wireless nodes. Even if possible, it is unwise because the whole network would be full of messages regarding the information of wireless nodes, which will sharply decrease the throughput of networks. The main idea of BBA is to let every node only record some necessary information of some neighboring nodes, typically at most three hops away. Our BBA will partition the wireless nodes into clusters: a clusterhead in each cluster will be in charge of the channel assignment for all nodes in the cluster; the clusters are connected via gateway nodes, which will ensure that the resulting network is connected. The benefits of using BBA are that (1) the majority channel assignment will be restricted to a small local neighborhood, thus, it is possible to find the optimal assignment for this small local neighborhood; (2) the backbone is sparse and already connected, thus making it much easier to have a channel assignment that results in a connected network. Through the backbone, a node vi could communicate with any other node v j in the network through one or multihop communication. In BBA, we divide all nodes into three different type sets: Dominators, Dominatees, and Connectors. A typical method for building a dominating set typically works as follows: Initially all nodes are marked as white (whose status is not

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determined yet). A white node claims itself to be a dominator if it has the largest Identity (ID) (or some other ranking methods such as the number of radios or the node degree) among all of its neighbors, then it will broadcast a message IamDominator to its one-hop neighbors, and mark itself Dominator. Here we assume that each node knows the IDs of its one-hop neighbors. When a white node receives an IamDominator message, it will mark itself as a Dominatee and then broadcast IamDominatee to its one-hop neighbors. Through the aforementioned procedure, the set of dominators is actually a maximal independent set in which there are no adjacent nodes (i.e., two nodes could communicate directly in one-hop). For simplicity, a dominatee node will choose only one dominator from possibly several neighboring dominators. If the shortest path connecting a dominator vi and a dominator v j is k-hops, we say v j is a k-hop dominator-neighbor of vi , and vice versa. Typically, in this chapter, we need k to be 2 or 3. Here we also define another criterion called channel-degree for selecting dominators. Assume that a node vi has k one-hop neighbors N (vi ) and for a neighchannels between vi and v j is ci j . Then boring node v j , the number of common the channel-degree of node vi is v j ∈N (vi ) ci j . When channel-degree is used for building a maximal independent set, we select a white node to Maximal Independent Set (MIS) if it has the largest channel-degree among all its white neighbors. After getting the dominator set and dominatee set, the next step is to choose some nodes from dominatee set as gateway nodes (also called connectors) to connect all dominator nodes and thus the backbone of whole network. There are several different centralized approaches to find connectors. One way is to let the dominatees, which are dominated by most dominators, have priority to become connectors. First, all dominatees are in the candidate set of connectors. We pick the dominatee with the most dominators from the candidate set and make it a connector. Then we delete it from candidate set. Second, we find the next dominatee with the most dominators from the remaining candidates, if this dominatee could connect at least one unconnected dominator or connect two different trees composed of dominators and connectors, it claims itself to be a connector; otherwise, we delete it from candidate set. We find the next candidate node and repeat the earlier procedure until all dominators are connected completely. Here, we assume that every dominatee node knows how many and which dominators could dominate itself. Another way to connect dominators is known as Steiner tree algorithm. This straightforward approach gives the approximation ratio c · (H (Δ) + 1), where c is the approximation ratio for the unweighted Steiner tree problem. Currently, the best ratio for c is 1 + 2/ ln 3 ≈ 1.55, by Robins and Zelikovsky [7]. However, all of the previously mentioned approaches are centralized and this is not practical. We use two different approaches to elect connectors from dominatees and construct the backbone of a wireless network with dominators. Locally Selected Connectors: One efficient approach is that for each pair of dominators vi and v j that are at most three hops away from each other, we find one shortest path connecting them and add all links of this path into the backbone. It has

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Fig. 5.4 Backbone of a wireless network

been proved in [11,26] that the size of the backbone constructed as ealier is at most a small constant factor of the optimum when the network is modeled by a unit disk graph. Notice that it is possible that there may be multiple paths selected to connect two dominators u and v, thus making the backbone more robust. See Fig. 5.4 for an illustration of a wireless backbone. Minimum Spanning Tree (MST) Backbone: The aforementioned method can select a small number of gateway nodes; however, if the backbone is too dense, it may not be good for our channel assignment. Notice that we need to result in a connected network, thus, more links in the backbone means that our channel assignment should satisfy more constraints (a link in the backbone poses a constraint such that the end-nodes of this link should be assigned at least one common channel). In light of this, we propose to use the minimum spanning tree to build the backbone, which is the sparsest backbone we could get. For every pair of dominators u and v that are two or three hops away, we assume there is a virtual link connecting them with the cost defined as the Euclidean distance u − v between them, or 1/(F(u) + F(v)). The intuition behind 1/(F(u) + F(v)) is that we want to connect pairs of dominators who have more channel availability, which will make it easier to get a connected network without channel switching. For distributed implementation, we can also apply a local minimum spanning tree structure proposed in [24,25]. We then study how to assign channels to dominatees, especially all nodes dominated by one specific dominator node. One simple approach could just use the star structure: every dominatee node is connected to the dominator node and we want to assign channels to them such that these links between the dominator and the dominatee nodes will have common channels. This simple approach clearly will put a heavy burden on the dominator node since its channel assignment needs to satisfy the connections to all its dominatees, which may be impossible. We adopt another simple approach as follows. We build some sort of minimum spanning tree to connect the dominator and all its dominatees (excluding the connector nodes). The

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Algorithm 1 Spanning Tree for Local Neighborhood Input: Assume there are n wireless nodes V = {v1 , v2 , . . . , vn } in the local area Z , including one dominator and a number of dominatees, and E is the set of all possible links (edges) whose start points and end points are in V . Let E be all links formed by nodes V where vi v j ∈ E if they are within the transmission range of each other and share a common operable channel. Output: A spanning tree G = (V, E ). 1: V = ∅; E = ∅ 2: Collect all available channels, which could be used by all links in E, and save these channels into the set C = {c1 , c2 , . . . , ck } by decreasing order of usage, that is, c1 is the channel, which could be operated most by all links. Set i = 1. 3: while i ≤ k do 4: Find all links v p vq that can operate on channel ci , here v p and vq are from different connected components of graph G = (V, E ). The set of such links is denoted as E i . 5: for each link v p vq ∈ E i do 6: Add v p vq to E if v p and vq are from different connected components of G = (V, E ), and update graph G accordingly. 7: Remove link v p vq from E i . 8: end for 9: Update i = i + 1. 10: end while

selection of the link cost will clearly affect the performance. If Euclidean distance is used, we know that every node has at most five neighbors in the minimum spanning tree; therefore, it only needs to ensure that it has common channels with these neighbors. Algorithm 1 illustrates our approach of constructing local minimum spanning tree based on the channel availability of different nodes.

5.5.3 Spanning Tree Based Approach (STBA) In this subsection, we propose another minimum spanning tree method to find a structure as a base of our channel assignment. We will also compare the performances of MST-based structure and cluster-based structure. Assume there are n wireless nodes in a region Z , and C = {c1 , c2 , . . . , ck } is the set of channels, which could be operated on by all n nodes. Assume each node must have at least one NIC, which could operate on one of the channels in C. We adopt two ways to compute the weight of links. One is to use the Euclidean distance vi − v j as the weight of link vi v j . We use Prim’s algorithm to implement the Minimum Spanning Tree. The other one is to use fewest number of channels to connect all nodes, which means when we choose one link from all candidate links, we always pick up the link that will lead to a minimum increase of the number of channels already used by all selected links. Algorithm 2 presents our method that constructs a spanning tree for channel assignment.

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Algorithm 2 Minimum Incremental Spanning Tree Structure Input: G = (V, E) Output: Spanning Tree G ST = (V , E ). 1: V = ∅; E = ∅ Let c1 be the channel that could be operated by the most links. 2: Pick a random link v1 v2 with a common channel c1 . Add v1 and v2 to V . Let C be the set of channels assigned to nodes in V so far. 3: while |E | < n − 1 do 4: Pick a link vi v j such that either vi ∈ V or v j ∈ V or both, and there is a common channel between vi and v j using channels from C . If no such link exists, find a channel c that is used by the most links with at least one endnodes from V − V . Then pick a link vi v j such that either vi ∈ V or v j ∈ V or both, and it has a common channel c. Let C = C ∪ {c}. Add link vi v j to E and V = V ∪ {vi , v j }. 5: end while

5.5.4 Assign Channels After the structures have been constructed, we now are ready to show how to assign channels to radios of every node such that the resulting network will be connected. Given a structure H (typically a connected spanning tree), we propose two different approaches to assign channels to links of the structure H . The first approach will always find a channel, say c, that can be used by the greatest number of unassigned links in H and then assign c to all appropriate links in H (i.e., the end-nodes of these links); these links are called assigned. Originally, all links in H are unassigned. Notice that Algorithm 2 also produces such an assignment at the time of constructing the spanning tree. Observe that such an assignment may not always be valid: sometimes the number of assigned channels to a node may be more than the number of the NICs it has. When the structure H is a tree, we actually can perform the channel assignment as follows. Assume that the tree is rooted. Pick a leaf node v and assign v and its parent node u with a channel c that is mostly used by links incident on u. Remove node v and its incident link from the tree H . Repeat the earlier steps until H becomes empty.

5.6 Performance Evaluation In this section, we present our simulation results that evaluate our algorithms to study the performance gain of using multiradio, multichannel, and multihop for wireless mesh networks. Besides the transition phenomenon, which has been illustrated in 5.4, we demonstrate the performance of both the Backbone Based Approach and the Spanning Tree Based approach. In our simulation, we assume that each wireless node’s NIC could operate on all 11 channels, and the wireless node will not dynamically switch the channel during a certain time period. We assume

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Minimum Number of Required Channels

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Fig. 5.5 Comparison result between BBA and STBA for number of needed channels

there are 300 wireless nodes randomly distributed in a 500 × 500 units (meters) area and the transmission range for each wireless node is 75 units. We first compare the performance of two channel assignments obtained by our Backbone Based Approach and Spanning Tree Based Approach, respectively. Figure 5.5 shows the results of the minimum number of channels required by BBA and STBA to keep the whole network connected. We vary the number of available NICs from 5 to 11, and randomly bind each NIC with one of 11 channels. Through the two curves, we know that BBA needs fewer channels to make the wireless network connected under the same condition. We then study the number of simultaneous transmission links that can be supported by the resulting network from a given channel assignment method. To some extent, the more simultaneously transmission links exist, the more throughput of the whole wireless network will be obtained. As can be seen from Fig. 5.6, the maximum number of links, that could transmit data simultaneously in the resulting wireless network obtained by our two approaches have a little difference too. Clearly, the STBA performance is better than the BBA on this point. Here, we assume for each node vi , R I (i) = 1.5 × RT (i), and the interference range of a link e (vi v j ) is R I (e) = R I (i) ∪ R I ( j). We adopt the RTS/CTS interference model in our simulation and thus if a link e has any one end in the R I (e), and if e and e are assigned the same channel in channel assignment method, they will interfere with each other. We also measure the number of total interference among all links. Observe that the number of total interference directly influences other issues such as link scheduling, and thus influences the throughput of whole network. Figure 5.7 presents the result of our simulation concerning this total interference number for all links of connected wireless networ. We found that the backbone based channel assignment method produces the least amount of total link interferences.

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Number of Simultaneous Links

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Fig. 5.6 Comparison result between BBA and STBA on the number of simultaneous transmitting links 8000 7500

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Fig. 5.7 Total link interferences among all links in the network

Notice that in a channel assignment produced by some of the aforementioned approaches we cannot simultaneously guarantee that the resulting network is connected and the number of assigned channels to a node is not greater than its number of NICs. Remember that it is NP-hard to decide whether we can achieve the above for an arbitrary network. If a node has more assigned channels than the number of NICs it has, then clearly, this node needs to perform channel switching during the routing, and this causes not only delay but also some other overhead in routing. We then study the number of NIC violations the network will have—to get a connected network under a certain channel assignment method. Here the NIC violation of a node is defined as the number of assigned channels to this node minus

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Table 5.1 Number of average NIC violations for a channel assignment # of Channels

6

7

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CDS MST

2.2608 0

2.2556 0.1111

1.3622 0.0165

0.422 0.0035

0.02 0

0 0

the number of NICs this node has if assigned channels are larger than the number of NICs; otherwise, it is 0. We then conducted extensive simulations to study the expected number of violations in a channel assignment. In our simulations, we randomly generate 300 nodes, and the transmission range of each node is 75 units. The number of NICs for each node is three and every NIC could operate on three of 11 channels. We randomly generate 300 network instances and then produce data for Table 5.1. Notice that when the number of available channels is 6 or 7, the connectivity of the original network is very bad (about five network instances out of 300 samples are connected in our simulations). When the number of NICs comes to 8, 9, 10, the network is connected with high probability. The number reported in Table 5.1 is the average of the performances of these network instances where the original network is connected. Based on our simulations, we found that MST often will have fewer NIC violations: most times it will only have about one channel switching needed in the whole network. On the other hand, when the original network is connected, the connected dominating set (CDS) also only has an insignificant number of NIC violations. These simulations confirm that our backbone based channel assignment method indeed will give us a connected network without channel switching with high probability. We also conducted extensive simulations to study two different channel assignment methods and found that the channel assignment assigning the most widely used channels first always has the best performances compared with the method specifically designed for the tree.

5.7 Conclusion In this chapter, we studied the static channel assignment problem for Multivariate wireless networks (multiradio, multichannel, multihop wireless networks) by statically mapping a channel to each radio of the nodes through comparing different methods. We showed that it is NP-complete to find a channel assignment such that the resulting network is connected. We then gave several novel methods that only use a small number of channels while resulting in a connected network. We also presented a novel method to assign channels such that the network will support a large number of simultaneous transmissions (thus possibly increasing the network throughput). We theoretically analyzed the expected number of channels that a node needs to be able to operate so that it can result in a connected network with high probability. We conducted extensive simulations to study the performances of our

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algorithms. One important future research is to design centralized and message efficient distributed algorithms such that they have a theoretically proven worst case performance guarantee.

References 1. M. Alichery, R. Bhatia, and L.E. Li. “Joint channel assignment and routing for throughput optimization in multi-radio wireless mesh networks.” MobiCom ’05: Proceedings of the 11th annual international conference on Mobile computing and networking, vol. 40, No. 8, 2005, pp. 58–72 2. A.K. Das, H.M.K. Alazemi, R. Vijayakumar, S. Roy. “Optimization Models for Fixed Channel Assignment in Wireless Mesh Networks with Multiple Radios. Sensor and Ad Hoc Communications and Networks, 2005 3. B. Leiner, D. Nielson, and F. Tobagi. “Issues in packet radio network design.”, Proceedings of the IEEE, vol. 75, January, 1987, pp. 6–20 4. Chaska wireless solutions. http://www.chaska.net. June, 2006 5. A.K. Das, H.M.K. Alazemi, R. Vijayakumar, and A. Naguib. “Optimization models for fixed channel assignment in wireless mesh networks with multiple radios”, In Second Annual IEEE Communications Society Conference on Sensor and Ad Hoc Communications and Networks(SECON). 2005 6. F. Tobagi. “Modeling and performance analysis of multi-hop packet radio networks.” Proceedings of the IEEE, vol. 75, January, 1987, pp. 135–155 7. G. Robins and A. Zelikovsky. “Improved steiner tree approximation in graphs.”, Proceedings of ACM/SIAM Symposium on Discrete Algorithms, 2000, pp. 770–779 8. P. Gupta and P. Kumar. “Capacity of wireless networks”, IEEE Transactions on Information Theory, Vol. 46, No. 2, 2000, pp. 388–404 9. N. Jain, S. Das, and A. Nasipuri. “A Multichannel CSMA MAC protocol with Receiver-Based Channel Selection for MultiHop Wireless Networks,”, IEEE IC3N, Phoenix, October 2001, citeseer.ifi.unizh.ch/jain01multichannel.html 10. J. So and N.H. Vaidya. “Multichannel mac for ad hoc networks: Handling multichannel hidden terminals using a single transceiver.” ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc), May, 2004 11. K. Alzoubi, X.-Y. Li, Y. Wang, P.-J. Wan, and O. Frieder. “Geometric Spanners for Wireless Ad Hoc Networks.” IEEE Transactions on Parallel and Distributed Processing, 2003 12. J. So and N.H. Vaidya. “A routing protocol for utilizing multiple channels in multi-hop wireless networks with a single trasceiver.” Tech. Report University of Illinois at UrbanaChampaign, Ocotober, 2004 13. M.A. McHenry, D. McCloskey, and G. Lane-Roberts. Shared Spectrum Company. “Spectrum Occupany Measurements, Location 4 of 6: Republican National Convention, New York City, New York August 30, 2004 – September 3, 2004, Revision 2.” 14. M. Sanchez, P. Manzoni, and Z.J. Haas. “Determination of Critical Transmission Range in Ad-Hoc Networks.”, Multiaccess Mobility and Teletraffic for Wireless Communications Workshop (MMT’99), 1999 15. M.R. Garey and D.S. Johnson. “Computers and Intractability.”, W.H. Freeman and Co., NY, 1979 16. N. Jain, S. Das, and A. Nasipuri. “Multichannel csma with signal power-based channel selection for multihop wireless networks.”, Proceedings of the IEEE Vehicular Technology Conference (VTC), September, 2000, pp. 6–20 17. P.J. Kolodzy. “Interference temperature: a metric for dynamic spectrum utilization.” International Journal of Network Management, 2006, pp. 103–113 18. P. Bahl, R. Chandra, and J. Dunagan. SSCH: Slotted Seeded Channel Hopping for Capacity Improvement in IEEE 802.11 Ad-Hoc Wireless Networks”, ACM Mobicom, 2004

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19. P.H. Hsiao, A. Hwang, H.T. Kung, and D. Vlah. “Load-Balancing Routing for Wireless Access Networks”, Proceedings of the IEEE INFOCOM, 2001 20. P. Gupta and P.R. Kumar. “Critical Power for Asymptotic Connectivity in Wireless Networks”, Stochastic Analysis, Control, Optimization and Applications, 1998, pp. 547–566 21. V. Bahl, A. Adya, J. Padhye, and A. Wolman. ‘‘Reconsidering the Wireless LAN Platform with Multiple Radios.”, Workshop on Future Directions in Network Architecture, 2003 22. W. Wang, Y. Wang, X.-Y. Li, and W.-Z. Song, and O. Frieder. “Efficient Interference Aware TDMA Link Scheduling for Static Wireless Mesh Networks.”, ACM MobiCom, 2006 23. S. Yi, Y. Pei, and S. Kalyanaraman. “Localized Construction of Low Weighted Structure and Its Applications in Wireless Ad Hoc Networks”, ACM/Kluwer Wireless Networks (WINET), 2003 24. X.-Y. Li. “https://apstwo.st.ewi.tudelft.nl/koen/MACsoup/taxonomy.php” April, 2006 25. X.-Y. Li, Y. Wang, and W.-Z. Song. “Application of k-local MST for topology control and broadcasting in Wireless Ad Hoc Networks” IEEE TPDS, 2004 26. Y. Wang and X.-Y. Li. “Geometric Spanners for Wireless Ad Hoc Networks” Proceedings of the 22nd IEEE International Conference on Distributed Computing Systems (ICDCS), 2002 27. C.-W. Yi. “Probabilistic Aspects of Wireless Ad Hoc Networks”, 2005

Chapter 6

Heterogeneous Wireless Networks: QoS-Aware Integration Architecture Ashraf Nusairat, Xiang-Yang Li, and S. Kami Makki

6.1 Introduction With the development of new wireless network technologies (e.g., WiFi and WiMAX), it becomes more important now that we need to provide seamless connectivity, richer services, and better quality for wireless data users while supporting heterogeneity in communication technologies, network architectures, and applications. The integrated wireless network, which is a network of networks achieved after convergence of different heterogeneous wireless networks and communication technologies, is a viable tool to achieve this and attracts lots of research attention recently. The integrated wireless network is expected to be capable to provide high speed data rates in indoor and outdoor environments, with end-to-end QoS, offering any kind of services at anytime, anywhere, always on with seamless interoperability and affordable cost. The integration of 3G wireless wide area (WWAN) technology with wireless local area network (WLAN) technology was triggered by the wide spread of WLANs and the high data rate that WLANs provide to its users. The WLAN can be used to complement the WWAN services by providing high speed data rates to users in areas where WWAN fails to offer the required data rates. Various levels of interaction between WLAN and 3G networks have generated six different interworking architecture scenarios as specified by 3GPP TR 22.934 [1]. The proposed scenarios gradually bring the two systems from noncoupled to very tightly coupled systems where the end user will be seamlessly roaming between the two systems and will be able to use both circuit-switched and packet-switched services. Several approaches for combining cellular and ad hoc networks have been proposed by researchers [2–7]. Some of these focus on higher total throughput through cell load balancing [2, 5], some focus on enhancing call blocking/dropping probability [2,4,6], some focus on increasing the individual user’s downlink rate [3,7], while others attempt to increase the range of high bandwidth channels [3,4]. Some assume the user equipment supports one radio interface and reserves some of the available channel

A. Nusairat Department of Computer Science, Illinois Institute of Technology, Chicago, IL 60616 e-mail: [email protected], [email protected]

S.K. Makki et al. (eds.), Sensor and Ad Hoc Networks, C Springer Science+Business Media, LLC 2008 DOI: 10.1007/978-0-387-77320-9 6,

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bandwidth for ad hoc connectivity [2,3,5], while others assume the user equipment can support multiple radio interfaces—one for cellular and the other for ad hoc—and concurrently can be connected to both systems [4,6,7]. One common approach used by all previous researchers is the use of the noncoupled integrated system model. We propose a new architecture for the integrated wireless system that will increase overall WWAN cellular system capacity and enhance the endusers experience by providing the expected QoS. In our architecture, we propose connecting the WLAN to the 3G UMTS radio access network (UTRAN) through fast and secure direct communication media. The WWAN cellular traffic will be transparently routed through the WLAN between the UTRAN system and mobiles. When a user is in the coverage of both UTRAN and WLAN and its cellular data rate degrades to a value not acceptable for the current QoS traffic class, the integrated wireless system will use the availability of the WLAN to bring back the data rate of the user to a rate acceptable by the current QoS traffic class parameters. Our approach is different from other previous approaches[3–7] as follows: (1) We propose that the WLAN access point (AP) be connected to two systems: the Internet service provider (ISP) for Internet/Intranet connectivity (current connection), and the UTRAN for cellular connectivity (new connection). This is different than the tightly coupled approach where the AP is connected to the packet-switched domain rather than to the RAN. (2) We propose that the UTRAN will need to handle two types of cellular connections with the user equipment: one direct and the other through a WLAN AP. (3) We dynamically adjust (shuffle) the user connections in the integrated system to admit new connections or to enhance the rate of a specific user. Our main contributions in this chapter are (1) we proposed a new architecture for integrating the cellular system with the ad hoc WLAN system that will increase the cellular system capacity and maintain the user’s data rate within the acceptable range for the QoS traffic class, (2) we dynamically adjust the connections of existing mobile users to provide a certain QoS performance guarantee to all users and to minimize the number of dropped calls, and we proved that the total supported rate of all users is at least half of the optimum, (3) we developed a simulation environment to evaluate the proposed architecture, and (4) the simulation results show that the new proposed architecture greatly increases the overall system performances and maintains the user’s data rate in an acceptable range for the user’s QoS traffic class. The rest of the chapter is organized as follows. In Section 6.2, we give brief introduction of convergence networks and describe the questions to be studied. In Section 6.3, we propose our approaches to dynamically adjust user connections. Our simulation studies are reported in Section 6.4. In Section 6.5, we briefly review related researches in the literature. We then conclude our chapter in Section 6.6.

6.2 Networking Architecture and Problem Description Here we briefly review WWAN with emphasis on 3G UMTS networks and WLAN with emphasis on 802.11 networks. More details about UMTS,WiFi can be found at [8–11].

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WWANs are intended to provide a global mobility with wide range of services including telephony, paging, messaging, Internet, and broadband data. It is possible to negotiate and renegotiate the characteristics of a bearer service at session or connection establishment and during ongoing session or connection. Bearer services have different QoS parameters for maximum transfer delay, delay variation, and bit error rate. One of the dominant WWANs is UMTS. UMTS system automatically adjusts the data rate [12–14] of the users depending on the changes in the cellular radio environment due to mobility, or the current user activity, or the load on the system. Scheduling of users in the UMTS system is done using wideband code division multiple access (WCDMA). The radio frame is 10 ms and the user can send/receive at the beginning of a radio frame. Multiple users can send and receive at the same time without collision. A IEEE 802.11 network provides the user with high data rates and is used in hot-spots, campuses, and personally owned to provide wireless connectivity to the Intranet/Internet. It has a limited coverage range of less than 200 m. The WLAN network works in two modes, infrastructure and ad hoc. In infrastructure mode, mobile nodes will be associated with AP and all nodes communicate through the AP. In ad hoc mode, all nodes communicate with each other directly or through multihop forwarding using ad hoc routing algorithms.

6.2.1 Problem Description In cellular networks, base stations and wireless links have capacity constraints that limit cell throughput. Those constraints can be node physical resources constraints or geographical constraints. Geographical constraints includes, but not limited to, radio frequency environment, and base station position. If a base station is positioned in bad radiofrequency (RF) environment, its cell throughput will be less compared to a cell in a better RF environment. In UMTS systems, mobiles have different downlink (DL) data rates depending on their radio environment. Mobiles with good radio environment will be assigned the maximum requested DL data rate, while mobiles with bad radio environment will be assigned a lower DL data rate. In this dynamic RF environment, the base station’s cell throughput will be less than the supported peak throughput because more radio resources are needed to support the mobiles in bad radio environments. The coexistence of cellular networks and WLANs can be utilized to increase the mobile’s DL data rates and increase the capacity of base station by freeing radio resources that can be used to serve new mobiles or increase the DL data rate of existing users. The available bandwidth of a WLAN can be utilized to create better routes between the mobiles and the base station and hence increase the DL data rate of the mobiles. In this chapter, we propose a new architecture for the integrated system that will increase overall cellular system capacity and enhance the endusers experience by providing the expected QoS. In our architecture, we propose connecting the WLAN to UTRAN through fast and secure direct communication media. The cellular traffic will be transparently routed through the WLAN between the UTRAN system and mobiles.

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TALK/DATA TALK

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RS CS TR RD TD CD

RS CS TR RD TD CD

TALK/DATA TALK

RS CS TR RD TD CD

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RS CS TR T R RD TD CD

Fig. 6.1 Integrated/hetrougenous wireless network

When a mobile1 has a low data rate, less than a threshold for a period of time, the integrated system decides to use available WLAN bandwidth to increase the mobile’s DL data rate. It will discover an ad hoc path from the NodeB (i.e., base station in cellular networks) to the mobile through the WLAN. This path will relay the traffic between the mobile and the NodeB. If the WLAN is configured to operate in the point coordinating function (PCF) mode, the ad hoc path will be a single hop. If configured to operate in distributed coordinating function (DCF) mode, the ad hoc path may be multiple hops. Figure 6.1 shows both configurations. We will call the WLAN node in the ad hoc path, relaying the traffic to/from the UTRAN, a proxy AP. This chapter will study two issues related to integrating WWAN and WLAN technologies. The first issue is the use of the WLAN network to increase the DL data rate of a single mobile to maintain its QoS characteristics. The second issue is the use of the WLAN network to increase the overall cellular system performance. Both issues require the discovery of a proxy AP. We will present an algorithm to find the proxy AP with the required proxy DL data rate and an ad hoc path with the required bandwidth.

1 The

words node and mobile will be used interchangeably in the rest of the chapter to mean the same thing.

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6.2.2 Basic Architecture In our architecture we propose connecting the WLAN to UTRAN through fast and secure direct communication media. The media can be Ethernet with secure virtual private network (VPN) connection between the UTRAN and the WLAN or can be 802.16 or some other media that can perform the required task, the type of the UTRAN-to-WLAN communication media is out of the scope of this chapter. The cellular traffic will be transparently routed through the WLAN between the UTRAN system and mobiles. This architecture requires modifications to both systems to route the traffic correctly. The WLAN needs to distinguish between two types of WLAN connections, the original 802.11 connections that are destined to the ISP and a new type of cellular connections (will call it proxyed connections), which should be routed to the UTRAN. Also, the UTRAN system should distinguish between two types of connections, current cellular connections and the new proxyed connections (between the UTRAN system and mobiles through ad hoc path). The distinction between the two types of connections is needed in order to adjust the radio link parameters at both UTRAN and WLAN to take into account the nature of the communication media between the two systems. For example, if the communication is through IP, the radio link control (RLC) and media access control (MAC) parameters at the UTRAN should be changed when the call is proxyed through an AP to accommodate the nature of IP traffic. Also the WLAN should treat the proxyed traffic with higher priority and should reserve the required resources to guarantee minimum delay in processing and transmitting the proxyed traffic.

6.2.3 Network Model We assume that each wireless device (called node hereafter) is capable of communicating with ad Hoc network and cellular network simultaneously by either having separate wireless interfaces or one integrated interface. We assume that all APs in the coverage of a NodeB are configured to operate in infrastructure (contention free) mode. Furthermore, we concentrate on single hop integrated network model in which there is no mobile-to-mobile ad hoc connection in the proxyed cellular path. Figure 6.2 illustrates the single hop integrated wireless network. In this model, the NodeB, each AP Ai , and each node Ni is characterized by the attributes listed in Table 6.1. A single hop mode integrated wireless network is then modeled as a directed2 graph G = (V, E), where V is the set of all n + a = |V | wireless nodes and APs, and E is the set m = |E| of direct links. Figure 6.2 illustrates the integrated wireless network and the corresponding graph G. A direct link (u, v) belongs to E if and

2 We concentrate on DL rate because most of applications will have asymmetric data rate with U Lrate ≤ DLrate

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TALK/DATA TALK

RS CS TR RD TD CD

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RS CS TR RD TD CD

(a) Integrated Network

(b) Corresponding Graph

Fig. 6.2 Single Hop Integrated Network and the corresponding graph

only if node v can have a direct connection with node u with DL rate ≥ DL T hr eshold . The weight of each directed link (u, v) is the DL rate of node v through node u. We assume the root of G is the NodeB, the leaves are the n mobile nodes. Also, we assume that any mobile node with 802.11 connection only is not part of G. The effective proxy bandwidth at APs is dependent on the available NodeB’s proxy bandwidth c Pbw(C), the 802.11 available bandwidth apbw(Ai ), and the AP’s available proxy bandwidth ap Pbw(Ai ) and is bounded by: apE f f Pbw(Ai ) = min(ap Pbw(Ai ), apbw(Ai ), c Pbw(C)).

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Table 6.1 NodeB, APs, and mobiles characteristics Attribute

Description

NodeB CBW(C) cbw(C) PCBW(C) cPbw(C) a APs n mobiles

Maximum Cellular DL bandwidth (kbps) Available Cellular DL bandwidth (kbps) Maximum Proxy DL bandwidth (kbps) Available Proxy DL bandwidth (kbps) APs A = {A1 , A2 , A3 , ..., Aa } in its coverage area Nodes N = {N1 , N2 , N3 , ..., Nn } in network

AP Ai APBW(Ai )

apbw(Ai ) K (Ai ) k(Ai ) APPBW(Ai ) apU sdPbw(Ai ) apPbw(Ai ) ap E f f Pbw(Ai ) T U S(Ai ) PU S(Ai ) apN um P(Ai )

Maximum bandwidth (kbps) Available bandwidth (kbps) Maximum number of 802.11 connections Current 802.11 connections, k(Ai ) ≤ K (Ai ) Maximum Proxy bandwidth (kbps) Used Proxy bandwidth, apU sdPbw(Ai ) ≤ APPBW(Ai ) Available Proxy bandwidth (kbps), apPbw(Ai ) ≤ APPBW(Ai ) Effective Available Proxy bandwidth (kbps), ap E f f Pbw(Ai ) ≤ APPBW(Ai ) Target User Set. List of nodes with direct cellular connection in the coverage of Ai but does not have an active 802.11 connection with Ai List of nodes proxyed through Ai . PU S(Ai ) ⊆ N Number of proxyed connection, apN um P(Ai ) ≤ k(Ai )

Mobile Ni R(Ni )

R(Ni ) Rmax (Ni ) DL T hr eshold AR(Ni )

r A j (Ni ) rc (Ni ) T AS(Ni ) Ria

DL rate requested to support current QoS class (kbps) Current cellular DL rate (kbps) Maximum supported downlink rate (kbps) Lower bound downlink data rate acceptable for the current QoS class after which the NodeB will try to find another path to the node to increase the DL rate. The new downlink rate after proxying cell connection through an AP. Available 802.11 DL rate (kbps),for 1 ≤ j ≤ a Current 802.11 DL rate (kbps) Target Active Set. List of neighbor APs, not including the associated AP, with estimated DL rate greater than DL T hr eshold Target Expected DL Rate, a ∈ T AS(Ni )

In G a leaf node will not have a direct connection with both AP and root simultaneously. A leaf node will have either a direct connection with the root or a proxyed cellular connection through A Pi . If the mobile has an active 802.11 connection and an active cellular connection, the 802.11 bandwidth allocated for the mobile will be reflected in the available bandwidth of the AP apbw(Ai ) and this connection will not be included in G.

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6.3 Proposed Approach In this chapter, we propose a new architecture for the integrated system that will increase overall cellular system capacity and enhance the endusers’ experience by providing the expected QoS.

6.3.1 Downlink Rate Adjustment of an Existing Call In this subsection, we study how to accommodate a sequence of downlink rate adjustment requests. For a given new request, we will find whether we can accommodate it without changing the configuration of existing ongoing traffics. If the request cannot be accommodated, we will explore different methods to try to accommodate the request by trying to free resources at the NodeB and neighbor APs. 6.3.1.1 DL Rate Adjustment without Changing Existing Traffic A node Ni with a cellular DL rate greater than DL T hr eshold will have a direct connection with the NodeB. When the cellular rate drops below DL T hr eshold , the NodeB will try to find a proxy AP in an attempt to increase the DL rate of the node. To find a proxy AP Ai for a node Ni , the following conditions must be satisfied: k(Ai ) < K (Ai ), apbw(Ai ) ≥ AR(Ni ), and apE f f Pbw(Ai ) ≥ AR(Ni ). Here the adjusted rate AR(Ni ) should be at least DL T hr eshold and can be defined as: x · R(Ni ), or y · DL T hr eshold , or Rmax (Ni2)+R(Ni ) , where x, y are rate adjustment factors and x > 1, y > 1. When R(Ni ) < DL T hr eshold , the NodeB will start the proxy discovery procedure as described in Algorithm 6.1. 6.3.1.2 Downlink Rate Adjustment by Changing Existing Traffic We then study the scenario when the NodeB decides to increase the DL rate of node Ni , but the NodeB does not have the available cellular bandwidth to accommodate this request and all APs covering the node do not have enough resources to accommodate the request. The NodeB might attempt to accommodate the request by one of the following two methods: 1) decrease the rate of some proxyed connections to

Algorithm 6.1 Proxy AP Discovery Input: A network G rooted at NodeB, a node Ni to adjust its DL rate and the new DL rate AR(Ni ). Output: A proxy path from root to node Ni through the discovered proxy AP. 1: Remove edge (r oot, Ni ) from G. 2: Add edges (u, Ni ) to G, where u ∈ {A j | r A j (Ni ) ≥ AR(Ni ), ap E f f Pbw(A j ) ≥ AR(Ni ), 1 ≤ j ≤ a}. 3: Find a path from root to Ni . 4: The AP in the path is the proxy AP.

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free proxy bandwidth at APs and NodeB, or 2) shuffle proxyed connections between different APs to free proxy bandwidth at one of the APs. In the first method of decreasing the rate of some proxyed users to free proxy bandwidth to accommodate the request, we select an AP from the list of target APs of user Ni and reduce the rate of one or more proxyed users of that AP by α (rate reduction factor) until the required proxy bandwidth is available to accommodate the request. The AP selection can be done in one of following heuristics: 1) Assuming all existing proxyed connection will be reduced by factor of α, select the AP with the maximum freed proxy bandwidth, i.e., select AP that satisfies: max(apE f f Pbw(A j ) + α × apU sd Pbw(A j )), ∀A j ∈ T AS(Ni ) 2) Select the AP with the maximum average proxyed bandwidth per connection apU sd Pbw(A ) i.e., select AP with the value max( apN um P(A j )j ), ∀A j ∈ T AS(Ni ). Once an AP is selected, the rate of one or more proxyed users will be reduced by α. The users can be selected randomly or start with the users with the highest proxyed bandwidth. The second method, shuffling proxyed connections between different APs to free proxy bandwidth at one of the APs in the mobile’s target active set, is similar to GAP (Generalized Assignment Problem) [15] but with the restriction that nodes can be assigned to subset of the APs. In our problem, the node is in the coverage of multiple APs and the expected data rate from each AP is different, i.e., the weight of item varies depending on the assigned knapsack. We will simplify our problem by fixing the expected data rate from all APs covering a node and only include APs in target active set that can provide data rate higher than a threshold rate. This will simplify our problem and it will be equivalent to MKAR (Multiple Knapsack Problem with Assignment Restrictions) studied in [16]. In MKAR, a set of items need to be assigned to a set of knapsacks with the restriction that an item can be assigned to a subset of the knapsacks and only assigned to one knapsack of the subset. Each item has a predefined weight and each knapsack has predefined capacity. The simplification of our original problem to MKAR can be done in one of the following heuristics: 1) The Threshold rate will be the current data rate of the user. Every AP in T AS(Ni ) with expected data rate less than the current user’s data rate will be removed from T AS(Ni ). 2) The Threshold rate will be derived from the minimum threshold for the current user’s QoS, i.e., Threshold rate = β × DL T hr eshold , β ∈ [1, 2]. Every AP in T AS(Ni ) with expected data rate less than Threshold rate will be removed from T AS(Ni ). We will call β MKAR Simplification Factor. In MKAR Dawande et al. [16] proposed several algorithms to solve the problem with the goal of maximizing the assigned weight. They provided a successive knapsack algorithm with 12 −approximation. We will use this algorithm to solve our assignment problem. The successive knapsack algorithm runs through the set of APs

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Algorithm 6.2 Mobile Assignment by Successive Knapsack Input: N users and m APs. Output: Some or all N users are assigned to APs. 1: Initialize: S = N , for i = 1, ..., m. 2: for each AP i do $ 3: Solve a single knapsack problem for AP i with item set S T U S(Ai ) to maximize assigned weight. 4: Let Si be the set of items assigned. Update S by removing Si from it, i.e., S = S − Si . 5: end for

in any order and solves a single knapsack problem for each AP to find the maximum bandwidth of admissible users. The generic successive knapsack algorithm for N users/nodes and m APs is shown in Algorithm 6.2. For Algorithm 6.2, we have the following theorem: Theorem 6.1 The supported data rate to all mobiles by Algorithm 6.2 is at least of the optimum.

1 2

The successive knapsack algorithm selects an AP and solves the single knapsack problem. In our study, we propose following different ordering of APs: 1) 2) 3) 4)

Select an AP randomly, Sort APs in ascending order of covered users, Sort APs in descending order of capacity, y . Sort APs in descending order of number ocapacit f cover ed user s

Not all APs in the network will be considered for solving our problem, only a subset will be considered depending on number of hops we use in discovering the set of target APs (knapsacks) and the set of nodes (items) that will be used as an input to the successive knapsack algorithm. We will solve our problem in two phases: 1) The preparation phase, which will prepare the input required by the successive knapsack algorithm. It will discover the set of APs and the set of users that will be used in solving the assignment problem. 2) Run the successive knapsack algorithm on the sets found in the preparation phase. If all users are assigned to APs, then the request will be accepted, otherwise it will be rejected. The steps of the preparation phase are: 1) For all APs covering the requesting mobile, add the APs with an expected data rate greater than the fixed Threshold rate to the set of knapsacks. 2) For all APs found in step 1, add all associated mobiles with proxyed connection to the set of items. 3) For all APs covering each new mobile found in step 2, add the APs with an expected data rate greater than the fixed Threshold rate to the set of knapsacks.

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The aforementioned preparation phase uses three-hop information levels to build the set of APs and the set of users/nodes. A generalized approach will be to use k-hop information levels (where k is an odd number greater than 1) to cover a larger subset of the network. k should be odd number, if k is even then we only consider nodes covered by the discovered APs and we do not include all APs covering newly added users in the (k − 1)-hop, in this case, a knapsack is missing, which can be the target for assigning an item. When k is odd we consider all possible target APs that a user can be assigned to and the proxy bandwidth used by nodes that are not included will be reflected as an initial assigned bandwidth. In our simulation study, we will use three-hop information levels.

6.3.2 New Call Request When a node Ni is requesting a new cellular connection with a DL rate of R(Ni ) and the NodeB does not have enough cellular bandwidth to accommodate it, the NodeB might attempt to accommodate the request by one of the following methods: 1) decrease the cellular downlink rate of some users to free cellular bandwidth. 2) if the NodeB has enough proxy bandwidth and the user is in the coverage of any AP, then attempt to proxy the new request through an AP. The NodeB can proxy the new request through an AP in different ways similar to the ones explained in Section 6.3.1 with a difference that the current user DL data rate is 0. We can use the same methods in Section 6.3.1 to find the proxy AP by assuming the current user DL data rate is 0 kbps and the NodeB is trying to increase the DL rate to R(Ni ). If an AP is found, the request is accommodated, otherwise it will be rejected. 3) if the NodeB has enough proxy bandwidth, then existing users with direct cellular connections and in the coverage of APs can be proxyed to free cellular resources at the NodeB. We will call the mechanism to free cellular resources at the NodeB “load shuffling.” The NodeB can perform load shuffling by proxying cellular connections based on DL rate, or call elapsed time, or random selection. Load shuffling will have a local impact if only cellular connections are proxyed through APs and the existing proxyed-traffic through the APs do not change. Load shuffling will have a global impact if, after proxying the cellular connections, the existing proxyed-traffic through the APs changes. In this case, the NodeB can perform load shuffling by freeing as much cellular bandwidth as possible.

6.3.2.1 Proxy Cellular Connection Based on DL Rate In this method, the users with direct cellular connections are sorted based on their data rate. The users not covered by APs (| T AS(N j ) |= 0) will not be considered. In this method, we will try to proxy as many users needed to free the required cellular

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bandwidth to accommodate the new request. If the required resources were freed then the request is accepted. If a cellular connection can be proxyed to more than one AP, we will use the following AP selection heuristics: • • • •

random, AP with minimum number of connections, AP with maximum free proxy bandwidth, the AP that can provide the highest expected bandwidth.

6.3.2.2 Proxy Cellular Connection Based on Call Elapsed Time This method is similar to Section 6.3.2.1 except the users are sorted in nonincreasing order based on the call elapsed time. Callers with long call time will be the targets for proxying. 6.3.2.3 Proxy Cellular Connection Randomly This is similar to Section 6.3.2.1 except the users are randomly selected for proxying. 6.3.2.4 Free as Much Cellular Bandwidth as Possible (Greedy Method) In this method, NodeB will try to proxy all cellular users to free as much cellular bandwidth as possible. Cellular users with T AS(N j ) = φ are targeted to be proxyed. Freeing cellular bandwidth can be done in one of the following ways: • proxy as many cellular connections as possible without changing the existing proxyed traffic on the APs. • proxy as many cellular connections as possible by changing the existing proxyed traffic on the APs. This problem is similar to the shuffling proxyed connections between different APs problem addressed in Section 6.3.1.2 with a difference that we are not only shuffling the existing proxyed connections and adding one proxy connection, but we are trying to add as many new proxyed connections as we can. In this new problem, we have two types of users, existing proxyed users and new users(users with direct cellular connections). During shuffling, existing users should take precedence over new users when assigned to a target AP. This problem can be solved by using the successive knapsack algorithm with slight modification when solving the single knapsack problem for an AP. The modification will be to solve the knapsack problem for an AP twice. First, solve it with existing proxyed users as the target users and update the AP capacity to reflect the assigned users. Second, solve it with new users as the target users. Then if all existing proxyed users are assigned to APs and the free cellular bandwidth at the NodeB is greater than the new call request data rate, accept the call otherwise reject it. Algorithm 6.3 is the modified algorithm where Nold is the set of existing proxyed connections through all APs, Nnew is the set of cellular connections, m is the set of APs.

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Algorithm 6.3 Mobile Assignment with New Users Input: Nold : the set of existing proxyed connections, Nnew : the set of existing cellular connections, R: new call request rate, and m: APs. Output: New Request is#either accepted or rejected. 1: Initialize: S = Nold Nnew , for i = 1, ..., m. 2: for each AP i do $ $ 3: Solve a single knapsack problem for AP i with item set S T U S(Ai ) Nold to maximize assigned weight. $ $ 4: Solve a single knapsack problem for AP i with item set S T U S(Ai ) Nnew to maximize assigned weight. 5: Let Si be the set of items assigned. Update S by removing Si from it, i.e., S = S − Si . 6: end $ for 7: if S Nold = φ then 8: Reject the new call request. 9: end if 10: if cbw(C) > R then 11: Accept the new call request. 12: else 13: Reject the new call request. 14: end if

For Algorithm 6.3, we also have the following theorem: Theorem 6.2 The supported data rate to all mobiles by Algorithm 6.3 is at least of the optimum.

1 2

6.4 Performance Evaluation In order to study the proposed rate adjustment mechanism and the proposed dynamic adjustment of user connections (connection shuffling) mechanisms in a more general setting, we conducted extensive simulations of a full integrated network written in C++ language. In this section, we describe our simulation model and the results we obtained.

6.4.1 Simulation Environment Our simulation model is composed of 100 mobiles that are placed randomly on a 700 m × 700 m square area, 20 AP nodes that are placed randomly on the same area and, a NodeB with one cell placed at the center of the area. We model the signal propagation using a combination of both free-space propagation model and two-ray ground reflection model. When a transmitter is within the reference distance of the receiver, we use the free-space model where the signal attenuates as 1/r 2 . Otherwise, we use the ground reflection model where the signal falls off as 1/r 4 . The MAC layer was modeled by introducing packet transmission error with certain small probability (e.g., 0.1) and by choosing packet transmission time of 10 msec. If an error occurs, the packet is retransmitted after a 0.5 s timeout.

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The 10 msec value is inline with the UMTS radio frame length. We use a UDP-like transport protocol in all our simulations. No ad hoc routing algorithms are needed because the nodes communicate directly with the associated AP. We model the mobiles traffic by using traffic profile scheme. In this scheme, each traffic profile simulates the traffic load generated by the mobile in the UL and the traffic sent to the mobile in the DL for the duration of the call. Each traffic profile has profile steps, each step simulates the generation of traffic with the following parameters: DL duration, UL duration, DL packet size, UL packet size, DL packet interarrival time, UL packet interarrival time, and the step duration. Using the traffic profile approach, different services can be simulated such as voice, hypertext transfer protocol (HTTP), file transfer protocol (FTP), and others. In our mobility model, the mobile nodes move according to the random waypoint mobility model as in [17]. In our simulation, the node’s speed is classified into three categories: stable nodes, slow nodes moving at speed of 1.5 m/s, and moderate nodes moving at speed of 5.5 m/s. The nodes choose their speed between the three categories uniformly. The pause time is generated according to the exponential distribution. The average pause time is 60 s. Each node keeps a list of neighboring APs sorted according to the received signal power. If a node has a WLAN connection and moves out of the coverage of its associated AP, it will try to connect to another neighboring AP if one exists. If the node’s WLAN connection is a cellular-proxyed connection and the associated AP is out of reach, the node will try to proxy the connection through a neighbor AP or establish direct cellular connection with the NodeB or drop the call. We simulate the changes in the cellular and WLAN RF environment according to the randomly generated events Decrease DL rate and Increase DL rate described in Table 6.2. In our simulation, the nodes randomly choose an event and try to execute

Table 6.2 Simulation Events Event

Description

Decrease DL rate

This simulates the scenario when current RF conditions become worse.Under the new conditions, the current data rate cannot be supported and must be decreased. This simulates an improving of current RF conditions. Under the new conditions, the current data rate can be increased in steps up to the maximum requested QoS rate. Add a new 802.11 connection between a mobile node and an AP if 802.11 resources are available. The connection duration is generated randomly with a configurable average duration (360 s in all the simulations reported). The call is terminated after the duration is over or the node moves out of the coverage of any APs. Add a cellular connection with certain QoS data rate between a mobile node and the NodeB if cellular resources are available. The connection duration is generated randomly with a configurable average duration (180 s in all the results reported later). The call is terminated after the duration is over. If the node is not a stable-node, it will execute a moving event as explained in the mobility Section 6.4.1.

Increase DL rate Add 802.11 connection

Add cellular connection Move

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it if possible. The events supported in our simulation are listed in Table 6.2. Here each mobile is assumed to have a minimum and a maximum downlink rate it can support. When increasing or decreasing the downlink rate, the new rate will be within the supported range. In our simulations, we also fix the following parameters. The NodeB has cellular bandwidth 2 Mbps and it has proxy bandwidth 3 Mbps. Each AP has 802.11 bandwidth 10 Mbps and proxy bandwidth 1 Mbps. The coverage range of each AP is 100 m. The rate reduction factors of cellular calls and proxyed calls are 0.3. The MKAR simplification factor is chosen as 1.5. Furthermore, AR(Ni ) is set as Rmax (Ni )+R(Ni ) . 2

6.4.2 Performance Results In our simulation study, we are interested in the following performance metrics: 1) 2) 3) 4)

User and integrated system’s throughput. Concurrent and average number of users. Number of accepted/dropped/blocked calls. Available bandwidth at the NodeB.

We ran the simulation with different configurations as listed in Table 6.3. For each configuration, we ran our simulation five times for a duration of 1 h with

Table 6.3 Different Simulation Configurations #

Description 0 1 2 3 4 5 6 7 8 9

10 11 12

No Rate Adjustment. The standalone cellular system. No interaction with APs Rate adjustment without changing existing traffic Rate adjustment and decrease rate of proxyed users to accommodate new rate Rate adjustment and shuffle proxyed users between APs to accommodate new rate. AP selection methods = Min. no. of covered users Rate adjustment and decrease cellular users rate to accommodate new call request Rate adjustment and proxy new call request if no NodeB cellular resources are available Same as Config 5 and if not enough proxy BW at the NodeB then try decreasing AP’s proxyed users BW to proxy the new call Same as Config 5 and if not enough proxy BW at the NodeB then try shuffling proxyed users to free proxy BW and proxy the new call. AP selection methods = Min. no. of covered users Rate adjustment and proxy cellular users (based on DL rate) for new call request. AP selection methods is Random. Rate adjustment and proxy cellular users (based on call elapsed time) during new call request. AP selection methods = Random Rate adjustment and proxy cellular users (Random) during new call request. AP selection methods is Random Rate adjustment and proxy cellular users (greedy without changing existing traffic) for new call request. AP selection methods is Random. Rate adjustment and proxy cellular users (greedy with shuffling) for new call request. AP selection methods = Min. no. of covered users

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different mobile’s and AP’s random positions in every run. We averaged, over all the runs, the performance metrics. We studied the impact of rate adjustment on all the aforementioned performance metrics. The impact of dynamically adjusting the system connections (by shuffling users, proxying users, or decreasing rate) on the system performance metrics was studied. We also studied the impact of AP selection methods on the system performance in the cases of shuffling users to accommodate a new request.

6.4.2.1 User and Integrated System’s Throughput Figures 6.3 and 6.4 illustrate the cellular user’s connection throughput with and without proxy connection. We randomly selected a mobile and monitored its downlink rate during a random call with no proxy and a random call with a proxyedconnection. In the case of no proxy (Fig. 6.3), the connection downlink rate dropped to 0 kbps after 388 s before finishing the call (the call duration was 797 s). While in the case with proxyed-connection (Fig. 6.4), when the call rate dropped to a rate less than the minimum acceptable rate (32 kbps in this example) for the connection’s QoS, the downlink rate adjustment algorithm kicked in and found a proxy AP and increased the downlink rate. The connection downlink rate was acceptable for the

44 13 3 13 6 15 8 16 2 23 7 25 5 26 3 35 4 38 8 50 0 79 7

22

0

15

DL Rate (Kbps)

DL Data Rate Without Proxy 120 100 80 60 40 20 0

Call Time (Sec.)

Fig. 6.3 DL Rate (Cellular system (No Proxy AP))

DL Rate (Kbps)

DL Data Rate With Proxy 140 120 100 80 60 40 20 0 0

32

32

64

79 85 110 116 Call Time (Sec.)

Fig. 6.4 DL Rate (Integrated System (With Proxy AP))

153

172

174

181

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Table 6.4 Simulation average statistics at NodeB Simulation configuration #

Average system throughput

Average available BW

Average available proxy BW

Average # users

0 1 2 3 4 5 6 7 8 9 10 11 12

1921 3299 3299 3299 4435 4575 4578 4525 4515 4435 4543 4460 4023

78 81 81 81 41 86 87 85 124 141 120 242 464

3000 1533 1533 1533 202 367 293 385 336 408 324 318 184

26 40 40 40 50 50 50 52 54 52 54 54 55

whole duration of the call and the call was not released compared with the case without proxy. Table 6.4 shows that the average integrated system’s throughput with proxyedconnections increased by 172% (in the cases without dynamically adjusting the system connections) and increased by 233% (in the case with dynamically adjusting the system connections) compared with the case without proxy, and this aligns with our expectations. 6.4.2.2 Concurrent and Average Number of Users Tables 6.5 and 6.4 show that number of concurrent users and number of average users increased when using proxyed-connections because extra cellular resources are freed and can be used to accept new calls. Also, the results show that configurations Config 8–Config 12 have the highest average/concurrent number of users, Table 6.5 Call attempts statistics Simulation configuration #

Attempted calls

Accepted calls

Blocked calls

Dropped calls

Concurrent calls

0 1 2 3 4 5 6 7 8 9 10 11 12 Average

2590 2676 2767 2767 2293 2155 2116 2083 2927 3031 3006 3064 3319 2684

36% 43% 43% 43% 90% 67% 68% 73% 91% 93% 91% 92% 90% 71%

64% 57% 57% 57% 10% 33% 32% 27% 9% 7% 9% 8% 10% 29%

40% 16% 16% 16% 23% 23% 23% 21% 9% 7% 9% 9% 5% 14%

34 59 59 59 60 62 60 63 65 63 65 65 73 61

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which is inline with our expectations. Configuration 12 showed the maximum number of concurrent and average users, because of greedy shuffling, which results in freeing more cellular resources than other configurations(as can be seen from the average available BW in Table 6.4). 6.4.2.3 Number of Accepted/Dropped/Blocked Calls Table 6.5 illustrates the percentage of accepted calls (both direct and proxyed) and percentage of blocked calls and the percentage of dropped calls. The results show that more calls are accepted in the proxy configurations (Config 1–Config 12) compared to the nonproxy configuration (Config 0). Call blocking and dropping ratios are higher in the nonproxy case than in the proxy cases. In the proxy configurations, more combined resources are available at the integrated system to serve users, which results in higher call acceptance ratio and less call blocking/dropping ratios. In the case of no proxy (Config 0), the calls are dropped because the downlink rate is decreased to a rate less than the minimum required for the current QoS. In the proxy cases (Config 8–Config 12), the connections are dropped because the downlink rate is decreased to a rate less than the minimum required for the current QoS, and no AP is available to proxy the connection or the mobile’s cellular proxyed-connection is dropped because of mobility (moved out of the coverage of its associated AP and there is no neighbor AP to handoff to) and the mobile could not handoff to the cellular network (no available cellular resources). To find out the best proxy configuration(s) that provide higher acceptance and low blocking/dropping ratios, we averaged the results of Table 6.5 for each category. Any configuration that has acceptance ratio greater than the average and blocking ratio less than the average and dropping ratio less than the average is a target for the best acceptable configuration. Our results shows that configurations (Config 8–Config 12) are best acceptable configurations. 6.4.2.4 Available NodeB Bandwidth Table 6.4 illustrates the average available cellular and proxy bandwidth at the NodeB for all simulation configurations. Config 8–Config 12 have the best average cellular and proxy bandwidth, and the average available cellular bandwidth. This is due to the extensive use of the proxy bandwidth to serve users. Config 8–Config 11 are based on proxying cellular connections one at a time when a new cellular call cannot be admitted, which increases the available NodeB bandwidth and utilizes the available proxy bandwidth. Config 12 provides the best utilization of the proxy resources because it tries to proxy as many cellular users as possible when a new cellular call cannot be admitted. 6.4.2.5 Impact of Shuffling on System Performance Metrics Shuffling users was simulated in Config 3, Config 7, and Config 12. In Config 3, shuffling was intended for dynamically reassigning proxyed users to different APs

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Table 6.6 Success rate of shuffling proxyed users to accept new request with diff AP selection methods AP Selection method Simulation User’s new Min. # Max. average configuration # proxyed rate Random covered users Max. Free proxy BW free proxy BW β*Min. QoS Curr. Rate β*Min. QoS Curr. Rate

7 12

49% 25% 17% 51%

48% 29% 14% 56%

44% 28% 20% 40%

46% 28% 22% 40%

to free proxy resources at the APs to accommodate new downlink rate adjustment attempt. Table 6.6 shows the results of shuffling users for the applicable configurations. As can be seen in the table, our simulation results show that this method was not of help at all in improving any of the system performance metrics. As can be seen in Tables (6.4, 6.5, and 6.8), Config 3 performance metrics exactly match the performance metrics of Config 1 and Config 2. The three configurations (Config 1–Config 3) have the same performance metrics because the new arrived calls are rejected because there are not enough cellular resources at the NodeB and at the same time, the new rate adjustment attempts fail because there is no AP to proxy the connections (as can be seen in Table 6.8 where 97% of rate adjustment failed due to no AP availability). Configurations (Config 1–Config 3) concentrate on different methods to improve rate adjustment through proxying calls, but if there are no available APs (the user is not in the coverage of any AP) the methods will not have any impact on enhancing the rate adjustment success rate. Table 6.7 illustrates the impact of shuffling on accepting new calls by proxying the new call requests through available APs. In Config 5, if no cellular resources are available at the NodeB, an attempt will be made to proxy the new call. The attempt will be successful if proxy resources are available at the NodeB and the mobile’s associated AP, no further action is taken. If there are no proxy calls, the call is rejected. Configuration Config 6 is similar to Config 5 with the extra step of trying to free proxy resources by decreasing proxyed connections rate. This method increases the successful proxy attempts by 2%, not a substantial improvement. Configuration Config 7 is similar to Config 5 with the extra step of trying to free proxy resources by shuffling proxyed users between APs in an attempt to free proxy resources, which increases the successful proxy attempts by 10%. The last configuration where shuffling was applied is Config 12, the impact of shuffling in Config 12 on system performance metrics can be seen by comparing it with other configurations trying to achieve the same task of proxying existing Table 6.7 Impact of shuffling when proxying new call requests Configuration #

Proxy new call attempts

% Successful attempts

5 6 7

1476 1473 1466

52% 54% 62%

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% Failed due To

Simulation configuration #

Total

%Pass

Failed

No NodeB proxy BW

No AP

No proxy AP BW

1 2 3 4 5 6 7 8 9 10 11 12

376 376 376 968 357 345 352 445 401 405 400 156

81% 81% 81% 55% 45% 45% 49% 47% 51% 45% 40% 37%

73 73 73 432 198 189 178 237 197 221 241 98

3% 3% 3% 61% 68% 67% 63% 61% 57% 60% 63% 15%

97% 97% 97% 38% 32% 32% 37% 39% 43% 40% 37% 84%

0% 0% 0% 1% 0% 1% 0% 0% 0% 0% 0% 1%

cellular calls to accept new cellular call, those configurations are Config 8–Config 12. As shown in Tables 6.5 and 6.4, in Config 12 the maximum concurrent calls, the percentage of dropped call, the average number of users, and the average available NodeB bandwidth in the system were the best among all other configurations, while the other performance metrics are almost the same as the other configurations (Config 8–Config 11). Shuffling kept the average available NodeB bandwidth high, which in turn increase number of accepted calls in the system and reduces the call blocking rate. 6.4.2.6 Impact of AP Selection Methods on System Performance Metrics In this subsection we analyze the impact of AP selection method, where applicable, on system performance metrics. Tables 6.6 and 6.9 illustrate the impact. Our simulation results show that the AP selection method does not have noticeable impact and the performance difference between the methods: 1% in the nonshuffling configurations (Config 8–Config 11) and 4% in the shuffling configurations (Config 7 and Config 12). Hence, any method can be used without drastically impacting the performance. Table 6.9 Success rate of proxying cellular connections to accept new calls with different AP selection methods AP Selection method Simulation configuration #

Random

Min. connections

Max. free proxy BW

Best expected rate

Max average proxyed BW

8 9 10 11 Avg.

77% 78% 75% 63% 73%

74% 78% 75% 62% 72%

76% 78% 76% 61% 73%

74% 78% 76% 61% 72%

75% 77% 76% 62% 72%

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To decide on the preferred method, we analyzed the shuffling algorithm execution success rates for the two configurations, Table 6.6 shows the success rate of the shuffling algorithm for the different AP selection methods, if we average the success rate of the different methods, the AP selection method “Min. # Covered Users” will be the best among all other selection methods. Hence, in the shuffling configurations (Config 7 and Config 12), we chose Min. # Covered Users as the AP selection criterion. For the nonshuffling configurations (Config 8–Config 11), we averaged the success rate of executing the algorithm of each AP selection method and we found that Random and Max. Free Proxy BW have the maximum average execution success rate as shown in Table 6.9, so we picked the Random method and used it in all simulations studies of configurations (Config 8–Config 11). 6.4.2.7 Impact of MKAR Simplification Method on System Performance Metrics To use MKAR algorithm for shuffling users between APs, we made an assumption to simplify our problem and reduce it to MKAR. We assumed that a target user that can be assigned to multiple APs have only one expected rate from all APs and we proposed two values for that rate: current user rate or β · R(Ni ). Table 6.6 illustrates the results of our simulations for both simplification methods. In Config 7, where we shuffle existing proxyed calls between APs, the use of β · R(Ni ) method provides the best results because when a call is proxyed through an AP, the downlink rate is set to Rmax (Ni2)+R(Ni ) , which is in most cases higher than β · R(Ni ). When shuffling a proxyed user, the lower the new data rate the higher the probability of finding an AP with available proxy BW and hence increasing the success rate of shuffling algorithm. In Config 12, where we shuffle existing cellular and proxyed calls, the method of using the current data rate as the new rate provides the best results, because when the cellular calls are proxyed during the shuffling procedure the probability of the current cellular rate less than Rmax (Ni2)+R(Ni ) is higher. Hence, less proxy bandwidth is used and more calls can be proxyed. Besides, shuffling only occurs if a new call cannot be admitted and at that time old cellular calls’ data rate would have been dropped because of the random generated Decrease DL Rate event during the lifetime of the call. 6.4.2.8 Rate Adjustment Analysis The success rate of rate adjustment through proxying connections varies from one configuration to another as shown in Table 6.8. Configurations (Config 1–Config 3) that concentrate on enhancing the rate adjustment success rate show higher success rates than all other configurations, but those configurations have the same success rate, which indicates that basic rate adjustment attempt should be enough to proxy the user and if adjustment fails, no further action should be taken to free resources to attempt to proxy the connection. The rest of the configurations (Config 4–Config 12) shows lower rate adjustment success rate because those configurations concentrate

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on proxying connections and fully utilizing the NodeB proxy interface, as can be seen in Table 6.4, the average available proxy bandwidth at the NodeB is very small compared with configurations (Config 1–Config 3) and this is why the rate adjustment success rate is lower.

6.5 Literature Review Recent years saw a great amount of research in heterogeneous wireless networks, especially the integration of 3G wireless networks and IEEE 802.11 networks, due to the need to provide users with the best quality of service. Several approaches for a combined cellular and ad hoc network model have been proposed. Some of these focus on higher total throughput, some focus on enhancing call blocking/dropping probability, some focus on increasing the individual user’s downlink rate, while others attempt to increase the range of high bandwidth channels. To support the architecture, a few proposals require only one single radio technology, and the rest require two different radio interfaces—one for the cellular channel and the other for the multihop ad hoc path. In opportunity-driven multiple access (ODMA) [3], 3GPP proposed a method to increase the data rate at the cell border by reserving UMTS frequency/channels for node-to-node communication (in-band communication) and create a multihop path between a mobile with low data rate and the NodeB through a gateway mobile. Mobiles need to support both frequency division duplex (FDD) and time division duplex (TDD) to benefit from the method. In ODMA, relaying is done using the same WCDMA TDD carrier frequency by allocating a relaying frequency range within the TDD frequency range. Therefore, it is different than our approach in which we use different technology (WLAN) as the relaying route. In multihop cellular network (MCN) [4], Lin and Hsu studied decreasing the number of base stations while keeping the same coverage area and decrease the call block/drop ratio by introducing mobile-to-BTS multihop routes. By decreasing number of BTSs, MCN can no longer guarantee a full coverage of the area and the multihop approach will neither increase the system capacity nor decrease the call blocking/dropping probability, unless a large percentage of the calls are intracell calls, which usually is not the case in practice. In MADF [5], Yu et al. proposed allocating static channels called forwarding channels for relaying traffic between users of different cells in order to increase system capacity and achieve load balancing among cells. This approach is similar to MCN [4] but does not use WLAN technology for the ad hoc routing path, it reserves channels in the same frequency band for forwarding purposes only. Therefore, it is different than our approach in which we use different technology (WLAN) as the relaying route. In MACA [2], Yu et al. proposed a new channel allocation scheme to achieve load balancing in a cellular network. An ad hoc overlay network is added on the fixed-infrastructure cellular network. Channels assigned to this ad hoc network can be used to help the fixedinfrastructure to achieve load balancing. Specifically, a user in a congested cell may set up a multihop relaying route through other users, using the ad hoc channels, to nearby noncongested cell. This approach does not guarantee increase of the user’s

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bandwidth and will not guarantee the user’s required QoS and introduces a lot of overhead control messages to establish/release/maintain the ad hoc routes specially during mobility because the ad hoc channels have lower power and can only reach a short distance. In our approach, we relay the traffic through WLAN to the same cell, we do not try to find an unloaded neighboring cell and redirect the traffic to it. In iCAR [6], Wu et al. focus was on improving the cellular system’s circuit-switched and emergency calls traffic call blocking/dropping probability by diverting traffic from congested cells to neighboring noncongested cells using dedicated stationary ad hoc relay stations for relaying the traffic. In our approach, we relay the traffic through WLAN to the same cell not to an unloaded neighboring cell and we try to maximize the cell throughput by maintaining the user’s QoS. In UCAN [7], Luo et al. proposed new architecture to enhance user/cell throughput through opportunistic use of the IEEE 802.11 interface. The BTS forwards packets for clients with poor channel quality to proxy clients with better cellular channel quality. Breadth-first search (flooding) is used for proxy path discovery, which disadvantages such as traffic generated by the routing protocol can cause severe congestion, and when multiple hosts try to find a path to the base station, hosts that have a good downlink rate will be congested as they will be on many paths. Also, the maximum bandwidth is limited by the cellular link capacity, which generally cannot meet the requirement of high-demanding multimedia applications. This is different than our approach of having two separate links, one for cellular calls and the other for proxyed traffic. Also, in our approach, we require the WLAN AP to distinguish between two types of traffic (relayed traffic and ad hoc traffic).

6.6 Conclusion In this chapter, a new architecture for integrating the cellular system with the WLAN system and an algorithm to dynamically adjust (shuffle) user’s connections were proposed. Through extensive simulations, we demonstrated the effectiveness of our proposed architecture and showed that integrating both technologies will enhance the user’s data services and provide seamless mobility, which helps in increasing user’s satisfaction. For NP-hard user rate adjustment problem (to admit as many users as possible or to admit users with maximum total supported bandwidth), we propose a shuffling algorithm that achieves one-half approximation ratio at the worst case. Our simulation results showed that the new proposed architecture and shuffling algorithm increased overall system’s call success rate, decreased call blocking and dropping rates, increased system throughput, and maintained the user’s data rate in an acceptable range for the user’s QoS traffic class. Although we have studied the performance impacts of the new proposed architecture and shuffling algorithm on the integrated system, there are still several interesting problems left for further study. As a future work, we will expand our architecture to include proxying users’ connections through multihop routes and compare the system performance with the single-hop route approach studied in this chapter. Also, studying the impact of the proposed architecture on delay-sensitive

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traffic is also a future work. Finding the optimal number of APs in the coverage of a cell is another interesting future problem worthy of studying.

References 1. 3GPP, “Feasibility study on 3gpp system to wireless local area network (wlan) interworking,” “http://www.3gpp.org/ftp/Specs/html-info/22934.htm”, 2003, TR 22.934. 2. X.-X. Wu, B. Mukerjee, and S.-H. G. Chan, “Maca – an efficient channel allocation scheme in cellular networks,” IEEE Global Telecommunications Conference (Globecom’00), 2000, vol. 3, pp. 1385–1389. 3. 3GPP, “Opportunity driven multiple access (odma),” “http://www.3gpp.org/ftp/Specs/htmlinfo/25924.htm”, 1999, TR 25.924. 4. Y.D. Lin and Y.C. Hsu, “Multihop cellular: A new architecture for wireless communication,” in IEEE INFOCOM, 2000, pp. 1273–1282. 5. X. Wu, S.-H.G. Chan, and B. Mukherjee, “Madf: A novel approach to add an ad hoc overlay on a fixed cellular infrastructure,” in IEEE WCNC, 2000. 6. H. Wu, C. Qiao, S. De, and O. Tonguz, “An integrated cellular and ad hoc relaying system: icar,” IEEE Journal on Selected Areas in Communications, vol. 19, no. 10, pp. 2105–2115, Oct 2001. 7. H. Luo, R. Ramjee, P. Sinha, Li (Erran) Li, , and S. Lu, “Ucan: A unified cellular and ad hoc network architecture,” in ACM Mobicom, Sept. 2003. 8. H. Holma and A. Toskala, WCDMA For UMTS Radio Access For Third Generation Mobile Communications, John Wiley and Sons Ltd, third edition, 2004. 9. T. Ojanpera and R. Prasad, WIDEBAND CDMA For Third Generation Mobile Communications, Artech House, 1998. 10. C. Smith and J. Meyer, 3G Wireless with WiMAX and Wi-Fi, McGraw-Hill, 2004. 11. C. Siva Ram Murthy and B.S. Manoj, Ad Hoc Wireless Networks Architectures and Protocols, Prentice Hall, 2004. 12. 3GPP, “Utra high speed downlink packet access (hsdpa); overall description,” “http://www. 3gpp.org/ftp/Specs/html-info/25308.htm”, Dec. 2004, TS 25.308. 13. 3GPP, “Fdd enhanced uplink; overall description,” “http://www.3gpp.org/ftp/Specs/html-info/ 25309.htm”, June 2005, TS 25.309. 14. 3GPP, “Multiple input multiple output (mimo) antennae in utra,” “http:// www.3gpp.org/ ftp/Specs/html-info/25876.htm”, August 2004, TS 25.876. 15. I.H. Osman, “Heuristics for the generalised assignment problem: simulated annealing and tabu search approaches,” OR Spectrum, vol. 17, no. 4, pp. 211–225, December 1995. 16. M. Dawande, J. Kalagnanam, P. Keskinocak, R. Ravi, and F. S. Salman, “Approximation algorithms for the multiple knapsack problem with assignment restrictions,” Journal of Combinatorial Optimization, vol. 4, no. 2, pp. 171–186, June 2000. 17. D.B. Johnson and D.A. Maltz, “Dynamic source routing in ad hoc wireless networks,” Kluwer Academic Publishers, 1996.

Chapter 7

Distributed Energy-Aware Topology Control Algorithm for Wireless Sensor Networks Zijian Wang and Jun Zhang

7.1 Introduction Wireless sensor networks have been used in various areas, such as environment monitoring, target or object tracking, and industry automation and control. Topology control has been effectively applied in sensor networks to prolong network lifetime, supplement routing protocols, and mitigate communication interference. There are two approaches for topology control in sensor networks: hierarchical topology organization and power control. The connected dominating set-based virtual backbone construction is a typical technique falling into the first approach and the computational geometry-based power control is a typical strategy belonging to the second approach. A dominating set (DS) is a subset of nodes in a graph such that each node not in the subset has at least one neighbor in the subset. If the nodes in the dominating set form a connected graph, the set is called connected dominating set (CDS). A CDS is a good candidate of a virtual backbone. Only the dominator nodes are responsible for relaying messages for the network. The nondominator nodes can thus turn off their communication module to save energy when they have no data to be transmitted. The searching space for a route is reduced to the nodes in the CDS. As long as changes in network topology do not affect this subnetwork, there is no need to recalculate routing tables. Constructing minimum CDS (MCDS) for an arbitrary graph is known to be NP-hard [5]. Current MCDS algorithms contain two types. One type is to find a CDS first, then prune some redundant nodes to attain MCDS [4,16]. The other type is to form a maximal independent set (MIS) at first, and then find some connectors to make the independent nodes connect together [14]. The algorithms mentioned earlier failed to put energy at each node into consideration when constructing the CDS. Actually, energy is a limited resource for nodes, and dominator nodes have heavy communication load for relaying messages for Z. Wang School of Electronics and Information Engineering, Beihang University, Beijing, 100083, China e-mail: wang [email protected]

S.K. Makki et al. (eds.), Sensor and Ad Hoc Networks, C Springer Science+Business Media, LLC 2008 DOI: 10.1007/978-0-387-77320-9 7,

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the network. Thus, the energy of nodes in the CDS determines the lifespan of the network. Wu et al. in [15] proposed a new algorithm for power-aware CDS based on [16]. Acharya et al. in [1] present a power-aware MCDS construction through introducing a concept of threshold energy level for dominating nodes based on [4]. A novel energy-efficient distributed approximation algorithm that computes a suboptimal MCDS in polynomial time based on coordinated reconstruction mechanism is proposed in [17]. Kim et al. in [8] present two versions of the timerbased energy-aware CDS protocol based on [18]. However, none of the protocols takes energy-efficiency of paths into consideration and the dominator nodes will transmit with maximum power, which leads to unnecessary energy consumption and redundant links. The resulting topology may be nonplanar and cannot be used for geographic routing protocols [7]. Power control mechanisms adjust the power on a per-node basis, so that onehop neighbor connectivity is balanced and overall network connectivity is ensured. Previous proposals of computational geometry-based power control took advantage of some original research topics in computational geometry, such as the Gabriel graph, the relative neighborhood graph, the Yao graph [10], and the Delaunay triangulation [9]. The relative neighborhood graph and the Gabriel graph are planar graphs, but the paths in relative neighborhood graph are not energy-efficient and Gabriel graph is not a spanner. Paths in Yao graph are energy-efficient, but Yao graph is not guaranteed to be planar. The Delaunay triangulation proposed by Li et al. is a planar spanner graph with energy-efficient paths. However, none of these algorithms takes energy of node into consideration. Furthermore, the resulting flat structure encounters scalability problems with increased network size. There are algorithms that combine the hierarchical topology organization and power control. The method proposed in [6] combines the node clustering algorithm with a new routing graph, called Restricted Delaunay Graph. Similarly, this algorithm does not take energy of node into consideration. Alzoubi et al. integrate the CDS and the local Delaunay graph to form a backbone of the wireless network in [2], in which the remaining battery power of node is mentioned as alternative criteria to construct the CDS. In this chapter, we propose a distributed energy-aware topology control algorithm that integrates an energy-aware MCDS (EAMCDS) and the local Delaunay graph. Our EAMCDS algorithm is related with [1] based on [4]. Our work significantly differs from [1] in the following aspects. 1. We use energy life as the energy measurement of node instead of energy level. 2. We use a new leader election algorithm, which is more practical to select the starting node of the algorithm. 3. Our algorithm will form a CDS for any connected graph without the assumption that removal of a node with less energy will not make the graph disconnected. 4. We propose a feasible reconstruction procedure once the energy lives of some nodes of the initial CDS fall below certain threshold. 5. We perform extensive simulations with more accurate energy model for communications.

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The remainder of the chapter is organized as follows. Section 7.2 describes the network model and preliminaries used in this chapter. In Section 7.3, we propose our novel distributed energy-aware topology control algorithm. Section 7.4 presents the simulation results. Finally, we conclude this chapter in Section 7.5.

7.2 Network Model and Preliminaries 7.2.1 Network Model The sensor network comprises a sink node and a set of sensor nodes, and all sensor nodes except for the sink node are static and power constrained. All sensor nodes are homogeneous, that is, their maximum transmission ranges and battery powers are the same. Each node has one unique identifier and all transmissions are omnidirectional with adjustable transmission range. We assume that each sensor node knows its position and remaining power. In this chapter, like many existing approaches, we do not deal with the issue on how messages use a shared channel to avoid contention and collision. It is assumed that this issue is taken care of at the media access control (MAC) layer.

7.2.2 Election Factor We introduce the election factor concept and select the node with maximal election factor as the starting node of the algorithm. Election factor Vi of node i is defined as Vi = (Di , L i , I Di ), where Di is the degree of node i, L i is the energy life of node i defined as follows, and I Di is the unique identifier of node i. The election factors of two nodes are sorted based on the following rule: Vi > V j if (1)Di < D j or (2)Di = D j and L i < L j or (3)Di = D j , L i = L j and I Di < I D j

7.2.3 Energy Life of Node Energy life L of node is the function of the node’s remaining energy E and energy draining rate R, that is, L = f (E, R). The draining rate Ri (t) of node i at moment t is defined as follows: Ri (t) = (E i (0) − E i (t))/t,

(7.1)

where E i (0) is the initial energy of node i and E i (t) is the remaining energy of node i at moment t.

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The energy life L i (t) of node i at moment t is defined as follows: L i (t) = E i (t)/Ri (t)

(7.2)

7.2.4 Energy Model for Communications The energy cost for communications of node is composed of the transmitting energy cost E t x and the receiving energy cost Er x defined as follows: E t x = a + td n

(7.3)

Er x = c,

(7.4)

where a is the energy consumed by the transmitter electronics, t accounts for energy dissipated in the transmit op-amp, d is the distance between the transmitting node and the receiving node, n ≥ 2 is the path-loss exponent of outdoor radio propagation models and c is the energy consumed by the receiver electronics.

7.3 Energy-Aware Topology Control Algorithm Our energy-aware topology control algorithm has three phases: EAMCDS construction, local Delaunay triangulation construction, and topology reconstruction. In the first phase, an EAMCDS is constructed rooted from a leader node. In the second phase, we build the local Delaunay triangulation on top of the EAMCDS. In the third phase, we look for alternative EAMCDS once the energy lives of some nodes of the initial CDS fall below certain threshold to reconstruct the topology.

7.3.1 EAMCDS Construction The idea of EAMCDS is to form CDS with nodes that have large degree and longer energy life. Thus, size of the resulting CDS will be small and nodes in the CDS will have enough energy to serve as dominator nodes. In the algorithm, we consider two types of nodes: dominator nodes and nondominator nodes. A dominator node is a node that cannot be removed from the CDS, since its removal would result in an infeasible solution. A nondominator node is a node whose energy life is not above threshold energy life or its removal does not disconnect the subgraph induced by the current solution. It is assumed that initially all the nodes in the network form a CDS and all the nodes are in uncertain status. At each step of the algorithm, at least one node’s status will become dominator or nondominator. At the end of the algorithm, these dominator nodes will form the EAMCDS.

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As usual, we elect a leader node as the starting node of the algorithm. Leader election algorithm [11] used in [4] and [1] is designed to perform random node election and cannot be modified to perform extrema-finding [13]. Thus, here we use an extrema-finding election algorithm [13] to elect a leader node with the maximal election factor. The execution starts from the leader node with the maximal election factor, which runs the self-identification procedure. At first, the leader node will check its degree. If the degree is one, the node will execute leave-dominating-set procedure described as follows. If the degree is greater than one, the node will verify whether removing itself from the graph would disconnect the subgraph induced by the resulting set of nodes through running distributed breadth first search (BFS) algorithm [3] from this node. If this is the case, the node will run the join-dominating-set procedure. Otherwise, the leave-dominating-set procedure is executed. The join-dominating-set procedure will fix the current node in the resulting EAMCDS. First, the node changes its own status to dominator node and sends a message “NEW DOM” to its neighbors to announce that it has become a dominator. Neighbors receiving this message will set the nearest sender of the message as its dominator. Then, it sends a message “ASK INF” to ask for the degree and energy life of its neighbors whose status has not been determined. Neighbors receiving this message will send back a message “INF REP” to inform its degree and energy life. Neighbors of the dominator will be classified into two groups: neighbors with energy lives less than threshold energy life, and neighbors with energy lives greater than threshold energy life. First, the neighbors with energy lives less than threshold energy life will be considered to be removed out of the EAMCDS. This is done based on the degree of the neighbor. Neighbor with the smallest degree in this group will be chosen first and will receive a message “SEL IDE” from the dominator. After receiving this message, the chosen node will run the self-identification procedure. The dominator node will wait for a response message (“DIS CON”/“NEW DOM”) from the self-identification procedure, receiving which it will send “SEL IDE” message to the next candidate. This will continue according to increasing order of degrees of neighbors unless all the neighbors with energy lives less than threshold energy life receive the “SEL IDE” message. Then, neighbors with energy lives greater than threshold energy life will be considered to be removed out of the EAMCDS just in the same way as above until all the eligible neighbors receive the “SEL IDE” message. The leave-dominating-set procedure is executed only when it is known that the current node can be removed. The first step is to change its own status to nondominator node and send the message “DIS CON” to all neighbors to announce that it has left the dominating set. Then the dominator for this node will be selected. If there are some dominator nodes in the neighborhood, the nearest one will be used. Otherwise, a new dominator will be chosen as follows. A message “ASK INF” will be sent to ask for the degree and energy life of its neighbors whose status is dominator or uncertain. Neighbors receiving this message will send back a message “INF REP” to inform its degree and energy life. The node that has energy life greater than the threshold energy life and has the highest degree among all the eligible neighbors will

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Waiting for identifying reply DIS_CON/C4/A6 DOM_MEM/C4/A6

DOM_MEM/!C5/A6 DIS_CON/!C5/A6

Fig. 7.1 State transition of EAMCDS construction

Table 7.1 State transition conditions of nodes Identifier

State transition conditions

C0 C1 C2 C3 C4

Node degree is one or the network is connected without this node The node is a dominator node All of the neighbors received ASK INF message have replied INF REP message The energy lives of all the neighbors are above the threshold All of the neighbors whose energy lives are below the threshold have received SEL IDE message All of the neighbors whose energy lives are above the threshold have received SEL IDE message The node has a dominator node

C5 C6

be chosen. Finally, the message “SET DOM” will be sent to the chosen node. If the status of the chosen node is uncertain, it will run the join-dominating-set procedure. The construction of EAMCDS is the procedure of controlling the state of node. If the state transition condition is satisfied, the state of the node will be changed according to the receiving message and current state and the corresponding action will be executed. The state transition diagram of EAMCDS construction is given in Fig. 7.1. The state transitions are denoted in the form of “receiving message/transition condition/action,” where “—” indicates there is no transition condition need to be satisfied or no action to be executed. The state transition conditions are listed in Table 7.1 and the actions executed by the node are listed in Table 7.2.

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Table 7.2 Actions executed by nodes Identifier

Actions

A0 A1 A2 A3 A4 A5

Set the node to nondominator node Set the node to dominator node Send DIS CON message to all the neighbors Send DOM MEM message to all the neighbors Send ASK INF message to all the neighbors Send SEL IDE message to the node with the smallest degree and undetermined status whose energy life is below the threshold Send SEL IDE message to the node with the smallest degree and undetermined status whose energy life is above the threshold Send SET DOM message to the node with the largest degree whose energy life is above the threshold

A6 A7

7.3.2 Local Delaunay Triangulation Construction Several routing algorithms require that the underlying topology be planar. Although the EAMCDS constructed earlier will select nodes with longer energy lives to serve as dominators, the dominator nodes will transmit with maximum power, which will result in unnecessary energy cost and redundant links between nodes. Thus, the EAMCDS can be a nonplanar graph. The Local Delaunay Triangulation (LDT) algorithm [9] introduces the concept of k-localized Delaunay triangle L Del (k) (V ) and adjusts the transmission power using the position information of the nodes. The algorithm first constructs a graph of L Del (1) (V ) and then makes it planar efficiently. Thus, we apply the localized Delaunay triangulation on top of the EAMCDS to reduce the energy cost and planarize the topology.

7.3.3 Topology Reconstruction The energy lives of dominator nodes decrease as energy is consumed. If the energy lives of some nodes of the initial CDS fall below certain threshold, these nodes will start the leader election procedure to reconstruct the topology. The leader election algorithm we used ensures that the unique new leader node with the maximal election factor will be elected at last even multiple nodes start the leader election procedure concurrently [13]. Thus, a new EAMCDS will be constructed, rooting from the new leader node. Then, the local Delaunay triangulation will be built on top of the new EAMCDS. In such procedure, some original nondominator nodes with energy lives greater than threshold energy life will be chosen as alternative dominator nodes. Thus, the great difference of energy consumption between dominator nodes and nondominator nodes will be balanced.

7.4 Simulation Results and Analysis In our experiments, we randomly generate a set V of n wireless nodes on a 100 × 100 square of a two-dimensional simulation area, through randomly and uniformly choosing nodes’ x-coordinate and y-coordinate values. The number of

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Fig. 7.2 LDT(V)

Fig. 7.3 EAMCDS(V)

nodes n and the maximum transmission range of node are experimental parameters. We assume a link between two nodes only if their geometric distance is less than the maximum transmission range. Figures 7.2–7.4 give different topologies defined as earlier for the random generated example graph illustrated by Fig. 7.5.

7.4.1 Performance Metrics The performance metrics include the size of the CDS and the lifetime of the network. The size of the CDS should be small, thus unnecessary nodes can be excluded from

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Fig.7.4 LDT(EAMCDS(V))

Fig. 7.5 Example graph

the CDS and their energy consumed for serving as dominators can be saved. We estimate lifetime in terms of number of packets routed successfully until the death of the first node in the network.

7.4.2 Size of CDS In this section, we verify our algorithm (referred as EATC) by evaluating its performance on random networks in terms of CDS size. And we make comparison with Wu’s extension rules 1a, 2a (referred as ND) and 1b , 2b (referred as EL2) in [15].

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We perform two groups of simulation. In the first group, we fix the maximum transmission range at 25 and vary the number of nodes from 100 to 300. In the second group, we fix the number of nodes at 200 and vary the maximum transmission range from 20 to 40. For each case, (i.e., for a specified number of nodes and maximum transmission range), we randomly generate 100 connected networks and calculate EATC, ND, and EL2. Then, we take the average of the CDS size resulted by three algorithms respectively. Figures 7.6 and 7.7 give the results of the two groups of simulation. It is clear that EATC consistently generates the smallest CDS among all the algorithms for both groups of simulation. ND and EL2 show almost the same results and the size of CDS generated by EATC is just about 65% of the CDS generated by EL2 on average. Especially with the increasing network size, the CDS size of EATC is much smaller. Thus, we can exclude more unnecessary nodes from the CDS and save their energy consumed for serving as dominators.

Fig. 7.6 Size of CDS as network size increases

Fig. 7.7 Size of CDS as transmission range increases

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7.4.3 Lifetime of Network In this section, we compare EATC in terms of network lifetime with Wu’s extension rules EL2 in [15] and Butenko’s algorithm (referred as MCDS) in [4]. Energy of each node is initialized to 10,000 and the threshold energy life is set to 150 across the network. Without loss of generality, the sink node locates at the centre of the network. Two groups of simulation, the same as earlier, are performed. For each case, we randomly generate 50 connected networks and calculate EATC, EL2, and MCDS. Ten groups of packet with 10000 packets in each group are randomly generated for each topology. The source of each packet is randomly selected from all the nodes in the network and the destination of the packet is set to the sink node. The packets are routed according to the minimum energy consumption routing protocol proposed in [12]. The parameters of energy model are set to the following values: a = 0; n = 2; E t x = 20 for d = 25, and Er x = c = 1 [15]. Note that when a node transmits a packet, all of its neighbors that do not belong to the routing path also “hear” the packet and consume energy in receiving the packet. By assuming that nondominator nodes can enter a reduced energy consumption mode when data is being transmitted if they are not the destination of the packet, we omit this part of energy consumption. The simulation will be terminated if the first node dies and we take the average of the number of packets successfully routed resulted by three algorithms respectively. The results of the two groups of simulation are shown in Figs. 7.8 and 7.9. It is clear that the order from the best to the worst for both groups of simulation is EATC, EL2, and MCDS. The network lifetime of EATC is more than twice the lifetime of EL2. The reason is explained as follows. MCDS constructs the CDS without the consideration of node energy. Actually, dominator nodes consume remarkably more energy than nondominator nodes because they bear extra tasks including routing information update and data packet relay. Thus, the dominator nodes die quickly. EL2 takes energy level into consideration and deletes nodes with less residual energy from the CDS when possible, which makes it outperform MCDS. However, it still cannot balance the great difference of energy consumption between

Fig. 7.8 Network lifetime as network size increases

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Fig. 7.9 Network lifetime as transmission range increases

dominating nodes and nondominating nodes because the main objective in [15] is to minimize the size of CDS rather than to balance the energy consumption among all nodes. Hence, the dominator nodes will soon be out of energy. EATC constructs CDS with nodes whose energy lives are above threshold energy life and applies the localized Delaunay triangulation on top of the CDS through adjusting node’s transmission power to reduce energy cost. Furthermore, EATC looks for alternative CDS once the energy lives of some nodes of the initial CDS fall below certain threshold to balance the energy consumption among all nodes. Thus, the network lifetime is prolonged. We varied the threshold energy life and study the variation of the network lifetime resulted by EATC. Figure 7.10 shows the network lifetime as the threshold energy life increases from 100 to 450 when the network size is 200. The maximum transmission range is set to 25 and the initial energy is set to 10,000. We can see that the network lifetime increases as the threshold energy life increases and falls back if we continuously raise the threshold energy life. The reason is explained as follows. Dominator nodes in the EAMCDS will forward packets of other nodes as well as their own until their energy lives become less than threshold energy life. Then they will become nondominator nodes and only consume energy to transmit packets for which they are the source. If the threshold

Fig. 7.10 Network lifetime as threshold energy life increases

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energy life is low, these nodes with their residual energy lives will be able to transmit only a small number of packets for which they are the source. As we raise the threshold energy life, dominator nodes that become nondominator nodes will still have sufficient energy to transmit their packets. So number of packets successfully routed will increase. But if we continuously raise the threshold energy life, dominator nodes will become nondominator nodes with relatively long energy lives. The energy of each node will be consumed in the frequent topology reconstruction. Thus, the network lifetime will decrease.

7.5 Conclusion A distributed energy-aware topology control algorithm for wireless sensor networks is proposed, which integrates the minimum connected dominating set and the computational geometry. An energy-aware minimum connected dominating set (EAMCDS) with nodes whose energy lives are above threshold energy life is constructed first. Then, we apply the localized Delaunay triangulation on top of the EAMCDS to reduce energy cost and planarize the topology. We look for alternative EAMCDS once the energy lives of some nodes of the initial dominating set fall below certain threshold to reconstruct the topology. The algorithm is fully distributed using simple local node information. Extensive simulations have been performed to compare size of the CDS with other selection schemes and also to compare lifespan of the network in terms of number of packets successfully routed. The simulation results show that the algorithm can efficiently prolong network lifetime and balance node energy consumption with a smaller CDS size, comparing with existing classic algorithms.

References 1. Acharya, T. and Roy, R. (2005) Distributed algorithm for power aware minimum connected dominating set for routing in wireless ad hoc networks. In: Proceedings of 34th International Conference on Parallel Processing Workshops, Oslo, Norway, pp 387–394 2. Alzoubi, K., Li, X.Y., Wang, Y., Wan, P.J., and Frieder, O. (2003) Geometric spanners for wireless ad hoc networks. IEEE Trans. Parallel Distrib. Sys. 14: 408–421 3. Awerbuch, B. and Peleg, D. (1990) Network synchronization with polylogarithmic overhead. In: Proceedings of Foundations of Computer Science, St. Louis, MO, USA, pp 514–522 4. Butenko, S., Cheng, X., Oliveira, C.A.S., and Pardalos, P.M. (2004) A new heuristic for the minimum connected dominating set problem on ad hoc wireless networks. Cooperative Control and Optimization, Kluwer Academic Publisher, Norwell, MA, USA, pp 61–73 5. Garey, M.R. and Johnson, D.S. (1979) Computers and Interactability – A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, San Francisco 6. Gao, J., Guibas, L.J., Hershburger, J., Zhang, L., and Zhu, A. (2001) Geometric spanner for routing in mobile networks. In: Proceedings of 2nd ACM Symposium Mobile Ad Hoc Networking and Computing, California, pp 45–55 7. Karp, B. and Kung, H.T. (2000) GPSR: greedy perimeter stateless routing for wireless networks. In: Proceedings of the 6th Annual ACM/IEEE International Conference on Mobile Computing and Networking, Boston, pp 243–254

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8. Kim, B., Yang, J., Zhou, D., and Sun, M.T. (2005) Energy-aware connected dominating set construction in mobile ad hoc networks. In: Proceedings of 14th International Conference on Computer Communications and Networks, San Diego, California, pp 229–234 9. Li, X.Y., Calinescu, G., and Wan, P.J. (2002) Distributed construction of planar spanner and routing for ad hoc wireless networks. In: Proceedings of 21st Annual Joint Conference of the IEEE Computer and Communications Societies, Piscataway, New Jersey, pp 148–157 10. Li, X.Y., Wan, P.J., Wang, Y., and Frieder, O. (2002) Sparse power efficient topology for wireless networks. In: Proceedings of 35th Annual Hawaii International Conference on System Sciences, Hawaii, pp 3839–3848 11. Malpani, N., Welch, J., and Vaidya, N. (2000) Leader election algorithms for mobile ad hoc networks. In: Proceedings of 4th International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, Boston, Michigan, pp 96–103 12. Stojmenovic, I. and Lin, X. (2001) Power aware localized routing in wirelessnetworks. IEEE Trans. Parallel Distrib. Sys. 12: 1122–33 13. Vasudevan, S., Kurose, J., and Towsley, D. (2004) Design and analysis of a leader election algorithm for mobile ad hoc networks. In: Proceedings of 12th IEEE International Conference on Network Protocols, Washington, pp 350–360 14. Wan, P.J., Alzoubi, K., and Frieder, O. (2002) Distributed construction of connected dominating set in wireless ad hoc networks. In: Proceedings of 21st Annual Joint Conference of the IEEE Computer and Communications Societies, New York, pp 1597–1604 15. Wu, J., Dai, F., Gao, M, and Stojmenovic, I. (2002) On calculating power-aware connected dominating sets for efficient routing in ad hoc Wireless networks. J. Comm. Netw. 4: 59–70 16. Wu, J. and Li, H. (1999) On calculating connected dominating set for efficient routing in ad hoc wireless networks. In: Proceedings of 3rd Intl Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, Seattle, pp 7–14 17. Zeng, Y.Y., Jia, X.H., and H, Y.X (2006) Energy efficient distributed connected dominating sets construction in wireless sensor networks. In: Proceedings of International Wireless Conference on Communications and Mobile Computing, Vancouver, Canada, pp 797–802 18. Zhou, D., Sun, M., and Lai, T. (2005) A timer-based protocol for connected dominating set construction in IEEE 802.11 multihop mobile ad hoc networks,” In: Proceedings of the 2005 Symposium on Applications and the Internet, Trento, Italy, pp 2–8

Chapter 8

MFACE: A Multicast Backbone-Assisted Face Traversal Algorithm for Arbitrary Planar Ad Hoc and Sensor Network Topologies Hannes Frey and Franc¸ois Ingelrest

8.1 Introduction Ad hoc networks consist of independent wireless devices, which are communicating without a predefined network infrastructure. Such technology may be useful, for instance, in order to rapidly setup a communication infrastructure in disaster recovery scenarios. Moreover, ad hoc networking may provide electronic data exchange at conferences, universities, companies, or any public area such as train stations or airports. It may also be used in order to extend the coverage of wireless access points providing a link to the Internet. Sensor networks are a special class of ad hoc networks, which received significant attention in recent years. The idea is to combine small sensing, computation, and wireless communication capabilities in small low-powered devices. Once deployed, a sensor network should last many years providing measurements on some physical phenomenon such as vibration, temperature, or humidity. In this chapter, we are interested in multicast routing, where a source host decides to send a message to a set of several destination nodes. In wireless ad hoc and sensor networks, communication ranges are limited due to the path loss of radio communications, and thus many other intermediate nodes must participate in the multicasting, enabling the message to reach all destination nodes. The simplest algorithm to achieve this may be to use the well-known blind flooding method, where each node that receives the packet for the first time forwards it to its neighborhood. This method obviously ensures a total coverage of the network, provided that the latter is connected, and thus a coverage of all destination nodes. Unfortunately, it requires every node to participate, leading to a lot of duplicated packets and wasted energy: as nodes rely on limited onboard power supply, other energy-aware protocols must be designed.

H. Frey University of Paderborn, D-33098 Paderborn, Germany e-mail: [email protected]

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Routing algorithms may be classified into localized and centralized ones. The latter require information about the global network structure to be acquired and maintained. Such schemes are obviously not scalable, since the control overhead increases with the number of network nodes. Moreover, the energy consumption needed for that gathering is generally higher than the savings obtained, thanks to the centralized knowledge. Localized algorithms are a promising approach to provide networks of any size. In these schemes, a global objective is achieved by using only local neighborhood information. A special class of localized routing schemes, referred to as localized geographic routing, requires nodes to be able to determine their own location. Incorporating geographic information in routing decisions enables novel communication paradigms: in geocasting communication, for instance, rather than delivering a message to a specific network address, all nodes in a specific geographic area are addressed. All localized multicast routing algorithms described so far employ a greedy heuristic in order to forward a message using information about the destinations and the 1-hop neighbors of the current forwarding node. The next hop nodes are selected according to a local objective function, which has to be maximized or minimized. In order to provide loop-free operation, greedy routing requires a premature stopping criterion, which prevents a message from visiting a node twice. As a consequence, a message might get dropped although there exists a path from the source node to the destinations. Face traversal is a recovery mechanism, which maintains the localized nature of greedy routing schemes. However, such a scheme cannot be applied on the underlying network graph directly. The latter must be planarized to be able to use Face routing on it. Face routing, which is well-studied for the unicast case, has recently been used in combination with multicast greedy schemes as well. Some multicast algorithms described employ traditional unicast face recovery in order to recover from a greedy routing failure for each destination node individually. Thus, multicast forwarding “degenerates” to individual unicast tasks as soon as a greedy routing failure occurs. Multicast extensions to face routing are addressing this problem by handling several destinations in a single planar graph traversal. All existing multicast extensions to face recovery are either limited by the fact that they sacrifice the delivery guarantees of the unicast case, or they are limited to a specific planar graph construction method. In this chapter, we describe for the first time, MFACE, a multicast extension that both guarantees delivery and works on any planar network topology. Our generic framework does not suffer from the limitation encountered in existing solutions, and is able to use any given underlying multicast backbone to decide how face traversal should be done, and when a message should be split into multiple packets in an efficient way. The remainder of this chapter is organized as follows. In the next section, we give the needed preliminaries, while Section 8.3 proposes a literature review of the related work. In Section 8.4, we describe MFACE, our generic face multicast routing framework. This section is followed by Section 8.5, which provides a proof of correctness of MFACE in terms of loopfree operation and delivery guarantees. In Section 8.6, we provide some simulation results that demonstrate the effectiveness

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of MFACE as opposed to applying individual FACE traversals in the multicast case. We finally conclude and discuss open research issues in Section 8.7.

8.2 Preliminaries The common representation of a wireless network is a graph G = (V, E), where V is the set of vertices (the hosts, or nodes) and E ⊆ V 2 , the set of edges giving the available communications: if a node v is a physical neighbor of a node u (v lies within the communication range of u and thus receives its messages), then there exists (u, v) ∈ E. If we assume circular communication ranges and that all nodes have the same communication radius R, then the set E is defined by: E = {(u, v) ∈ V 2 | |uv| ≤ R},

(8.1)

|uv| being the Euclidean distance between nodes u and v. This model is known as the unit disk graph model and is illustrated by Fig. 8.1. A generalization of this model, the quasi unit disk graph model, allows a slight variation in each node’s √ communication range in the magnitude of 2 between a minimum and maximum √ communication radius rmin and rmax . More precisely, for rmax /rmin = 2, any edge set E complies with the quasi unit disk assumption if the following holds: (u, v) ∈ E ⇒ |uv| ≤ rmax |uv| ≤ rmin ⇒ (u, v) ∈ E .

(8.2)

The density d of the network is the average value of neighbors per node. For a given multicast task, the set of destination nodes is denoted as T = {t1 , . . . , tk }. We assume that nodes are able to retrieve their absolute or relative location, by any hardware or software means, and maintain 1-hop neighborhood information,

Fig. 8.1 A example of a unit disk graph: all nodes have the same communication range and all links are symmetric

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thanks to regular beacon messages. For instance, absolute locations may be available, due to a GPS, while relative ones may be obtained by setting up a relative coordinate system based on signal strength measurements [1]. As for any other geographic routing scheme, the location of destination nodes is needed. Whenever such a scheme is used as a replacement for nongeographic routing, the position for a given node address is required. This information may be acquired due to a location database running as a separate network service [2]. A planar graph is a graph in which no edges intersect. The known localized planar graph construction methods are Gabriel graph (GG), relative neighborhood graph (RNG), and localized Delaunay triangulation (LDT). Without any additional provision, planar graph construction according to these schemes requires the unit disk graph assumption. For Gabriel graph construction, however, a localized extension has been described in [3,4], which works also under quasi unit disk graphs. The Gabriel graph (see Fig. 8.2(a)), described in [5], is constructed as follows. Starting from a unit disk graph G = (V, E), each edge (u, v) ∈ E is considered and removed if there exists a vertex w located inside the circle U (u, v) of diameter |uv| centered at the midpoint of the segment [uv]. The relative neighborhood graph (see Fig. 8.2(b)), described in [6], uses a similar removal strategy. An edge (u, v) is removed if there exists a node w such that (u, w), (w, v) ∈ E and |uw|, |wv| < |uv|. A simpler definition would be “for any triangle in the graph, remove the longest edge”. In the localized Delaunay triangulation (see Fig. 8.2(c)), each node u applies the Delaunay triangulation on its 1-hop neighborhood set. In the Delaunay triangulation, a triangle exists if there is no other vertex inside the circle passing through all the endpoints of this triangle. This locally constructed Delaunay triangulation has to be exchanged with all 1-hop neighbor nodes in order to remove Delaunay triangulation edges, which have not been preserved by other neighbor nodes. Different variants of localized Delaunay triangulation have been described in [7,8,9]. Both of these constructions are very interesting for decentralized networks since the removal strategies may be applied independently by each node, and do not require any message exchange.

w

u

v

u

v

u

v (a) Gabriel graph.

(b) Relative neighborhood graph.

(c) Delaunay triangulation.

Fig. 8.2 Edges removal strategies for constructing planar graphs: if a node exists in the grey area, the corresponding edges are removed

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8.3 Related Work A class of multicasting protocols relies on a backbone to achieve delivery of the message in an effective way. The idea is to construct a geometric overlay multicast tree, and then to use the edges of this tree to route the message in a unicast fashion between each of its vertices. Such a backbone may be, for instance, an Euclidean minimum spanning tree or a Steiner tree constructed over the source node and the set of destinations. It may actually be any tree spanning all destination nodes. In [10], the construction of such backbones is proposed in order to minimize miscellaneous metrics (e.g., bandwidth, energy consumption). Another example of a backboneassisted multicast protocol is MSTEAM [11], which uses a minimum spanning tree to decide when the message should be split into multiple packets and which next hop to choose toward a set of destination nodes. In this chapter, we apply this idea to extend face routing to the multicast case.

8.3.1 Face Traversal in Unicast Communication A unicast face routing algorithm for ad hoc and sensor networks was originally described in [12]. The algorithm makes use of an overlay planar graph to achieve the message delivery by routing packets in a localized way along the face edges of this graph. The faces used to route the message are the ones which are intersected by the straight line joining the source node s to the destination t. Face traversal is repeatedly done by using the left/right hand rule: a receiver node sends the message along the edge, which is lying next in counterclockwise/clockwise direction of the edge it was received from. For instance, when starting at node s in Fig. 8.3, the face F1 will be traversed along the path sv1 v2 when using right hand rule and along the path sv4 v3 when using the left hand rule. When the message is going to cross the edge v2 v3 , a face switch occurs, so that the packet will next be routed inside face F2 . It can be observed that face traversal might produce long detours from the shortest

v10

v9

v4 v7

v3

F3 t

F1 s Fig. 8.3 Face unicast routing: the message travels along the faces intersected by the source-destination line st

F2 v2 v1

v6 v5

v8

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possible path, in particular when the network is sparse. Greedy routing in contrast, if successful, often achieves a path length close to the shortest one. Thus, face routing is generally used as a recovery mechanism in case of a greedy routing failure. When greedy routing can be applied again, face traversal is stopped and greedy routing is resumed again. It has been observed when face routing is used as a recovery mechanism only, under the GG and RNG topology, a specific rule for switching between faces is not required [13]. Under these graph models, returning into greedy mode is always possible when traversing the very first face only. However, this holds not in general. For instance, when applying combined greedy and face routing on a LDT, switching between adjacent face might be necessary before greedy routing can be started again [13].

8.3.2 Face Traversal in Multicast Communication Similar to the unicast case, multicast greedy routing schemes might end up at a node where no better neighbor with respect to the multicast destination set exists. In order to provide delivery guarantees, a recovery scheme has to be employed in this case in order to route the message around the network such that either the destination nodes are reached or greedy routing can be resumed again. In the multicast schemes GMR [14] and GMREE [15], face traversal is employed for each of the destination nodes as a separate instance. More precisely, whenever a node s decides that a set of destination {t1 , . . . , tk } can no longer be handled in greedy forwarding mode, a unicast face traversal according to the source-destination line sti is started for each of these destination nodes ti . Each of these individual face traversals are accomplished until encountering a node which enables greedy forwarding again. In order to reduce bandwidth requirements, the routing scheme merges packets visiting the same next hop node in a single transmission. However, despite this optimization, conceptually the algorithm performs face traversal for each destination node individually. This leads to disjoint routes and thus to a higher energy consumption. Since face recovery is handled by individual unicast face traversals, correctness of the scheme in terms of loop-free operation and guaranteed delivery is ensured by the well-known results for the unicast greedy-face-greedy schemes [13]. A face recovery approach, which can handle several destination nodes in a single face traversal, was described in [16] for the first time. In the described multicast scheme Position-based multicast (PBM), face recovery is used as well in order to recover from greedy routing failures. When a node s has no neighbor node, which provides positive progress for a given set of destination nodes {t1 , . . . , tk }, multicast face recovery is started. The destinations are handled in a single traversal of the face, which contains s on its boundary and which is intersected by sp, p being the center of gravity (t1 + . . . + tk )/k of all destination nodes. In each face recovery step, however, it is tested for each destination if the current node is closer to ti than the node where the message entered face recovery mode. For all destinations which

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Fig. 8.4 A message drop in PBM: the message will traverse face F and will never find a node closer to a destination node ti than u

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satisfy this condition, greedy forwarding is started again. The remaining destinations are kept in face recovery mode. A proof on correctness of this scheme was still missing by now, and in fact, it turns out that the described variant is merely a good heuristic in order to recover from greedy routing failures. A simple example which shows that delivery guarantees are not provided by this scheme is depicted in Fig. 8.4. Node u is located closer to t1 and t2 as it is v and w. Since none of the neighbors are providing some progress toward t1 and t2 , multicast face recovery is started for the destination set {t1 , t2 }. The center of gravity p of t1 and t2 is located within the face F. However, during face traversal of F no node is encountered, which is located closer to t1 or t2 than |ut1 | = |ut2 |. Thus, the message will traverse the entire face and will be dropped after passing the first traversal edge uv for the second time. This happens independently of the existence or nonexistence of a path connecting u with t1 or t2 . The first scheme implementing a multicast extension of face routing, which provides delivery guarantees, is presented in [11]. The described multicast algorithm MSTEAM applies face traversal in order to handle a message to a set of destinations by using one of these destinations, t, as the gateway to all others. The recovery scheme is designed to run over a planar topology resulting from Gabriel Graph construction. In this case, planar graph recovery with respect to a source destination line st can be simplified to traversal of the very first face which contains s on its boundary and which is intersected by st. Correctness of the scheme is proved in [11] for Gabriel Graphs. More precisely, the Gabriel Graph property is required to prove Case 1 of Lemma 1. The proof of this case requires that for an edge uv intersecting st, at least one of the nodes u and v is lying closer to t than the Euclidean distance between s and t. Thanks to Corollary 1 in [13], this property also holds for Relative Neighborhood Graphs. It follows that the face recovery mechanism of MSTEAM provides delivery guarantees and loop-free operation as well in Relative Neighborhood Graphs. Table 8.1 provides a summary of all known face routing variants applied in multicast schemes. As we shall see in the next section, the proposed MFACE scheme is the first generic variant that provides delivery guarantees while assuming any planar topology and any underlying multicast backbone. All schemes given in this table are loop-free.

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separate unicasts average over destination points multicast overlay multicast overlay

8.4 A Generic Multicast Face Algorithm In the following section, we describe an extension of the face routing mechanism for the multicast case, referred as MFACE, which is intended to be used under any planar topology. We assume a message addressed from a source node s to a set of destination nodes T = {t1 , . . . , tk }. Furthermore, we assume that any construction mechanism was applied on S = {s} ∪ T in order to calculate a multicast backbone being a spanning tree Δ, which includes at least all nodes in S. We first consider the source node s, which initiates the multicasting task. Let Δ be the multicast backbone, which is to be used to reach all destination nodes in T . The message thus has to be routed along the edges of Δ, and must be split at node s if multiple paths start from this node. Actually, each of these paths is represented by an edge, which originates at node s and spans a subset of destination nodes. These are forming exactly a destination subset to which s has to send an individual message copy. The algorithm thus instantiates a separate multicast task for each edge st from the multicast backbone, which originates at s. More precisely, for each such edge st, the algorithm initiates a multicast task, which only considers the subtree of Δ which is reachable by the edge st. A special case occurs, when the subtree contains no destination nodes. In this case the subtree can simply be ignored. For any other subtree originating from st, which contains at least one destination node, face traversal for this multicast task is started by selecting the face adjacent to s, which is intersected by the open line segment (st]. When s has only one neighbor node v, face traversal start is done via the edge sv. When s has at least two neighbors, the selection of the first traversed edge is done according to the best angle heuristic [17]: from the possible face edges originating at s, the edge sv is selected,

Algorithm 1 Starting multicast face traversal s ← current node t1 , . . . , tk ← multicast destinations Δ ← multicast backbone over {s, t1 , . . . , tk } for all edges st in Δ do Δ ← subtree of Δ reachable via st if Δ contains at least one destination node then su ← edge minimizing ∠ust r ule ← determine traversal rule for s, u, and t begin traversal along su according to r ule and subtree Δ end if end for

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Algorithm 2 Determining the traversal rule s ← current node u ← next node t ← destination node if u is located right of st then r ule ← clockwise else r ule ← counterclockwise end if

which minimizes the angle between st and sv. This procedure is summarized by Algorithms 1 and 2 Refer to Fig. 8.5 for an example. The multicast backbone edges originating at s are st1 , st2 , and st3 . Thus, s initiates three multicast tasks, one for each edge sti . The multicast task created for st1 will traverse the face F1 , while the two multicast tasks created for the edges st2 and st3 will both traverse the face F2 . According to the best angle heuristic, the start edge for traversal of F1 will be sv since ∠vst1 < ∠wst1 is satisfied. The remaining multicast backbone considered in this case is Δ1 . Traversal of face F2 will be done in two directions, along sw for t2 since ∠wst2 is minimum, and along start edge su for st3 since ∠ust3 is minimum. In this example, Δ2 will be the remaining multicast backbone considered in the first case, while Δ3 will be the remaining multicast backbone in the latter case. We now describe how faces are switched whenever the current multicast message arrives at a face edge, which is intersected by any of the edges of the remaining multicast backbone handled by that message. Let st be the backbone tree edge where traversal of the face was started at (for instance, edge st1 in the traversal of face F1 in Fig. 8.5), let u be the current forwarding node, and let uv be the next face edge to be traversed. We consider two different cases of uv intersecting with any of the edges from the multicast backbone

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8.4.1 Intersection with the Starting Edge st Two cases arise, when uv intersects with st in a point p. When face traversal has already visited an intersection with st, which is located closer to t than it is p, then this intersection is simply ignored. If the intersection p is the one closest to t compared to all other intersections visited so far, then the multicast face routing mechanism restarts traversal of the face, which has the current node on its boundary and intersects with the open line segment (pt]. Traversal start of this face is done according to the best angle method, i.e., the current forwarding node u selects the outgoing edge which minimizes the angle with respect to the line segment ut. This rule is illustrated by Fig. 8.6, where we assume that the current multicast subtree handling was started at node s. The message is traveling along the edges of face F1 since this face is intersected by the edge st1 . When it arrives at node u, a face switch occurs. Edge uv is intersecting with the backbone edge st1 , the edge which was used in order to determine face traversal start. Thus, one single instance of the multicast message is kept and the face intersected by the remaining line segment of st1 is traversed. According to the best angle variant, traversal is started along edge uv since ∠vut1 < ∠wut1 is satisfied.

8.4.2 Intersection with Any Other Edge of the Backbone When uv intersects with any other multicast backbone edge ti t j different from st, then the edge st is removed from the multicast backbone and the remaining tree is split into two subtrees Δ1 and Δ2 . Tree Δ1 denotes the subtree, which is reachable over the directed edge ti t j , while tree Δ2 denotes the subtree, which is reachable over the directed edge t j ti . The multicast message is split into two copies in order to address each of both subtrees in a different multicast task. Selecting the face which is to be traversed next is done in the same way as it is done for the case uv intersecting with st. Let p be the point of intersection between uv and ti t j . For handling the

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remaining subtree Δ1 , the face which is intersected by the open line segment ( pt j ] is selected. For subtree Δ2 , the face which is intersected by the opposite open line segment ( pti ] is selected. Face traversal start is done according to the best angle variant, i.e., the edge which minimizes the angle with respect to the edges ut j and uti is selected, respectively. A special case occurs, when the remaining multicast backbone Δi consists only of nodes which are no message destinations. In this case the multicast task for Δi can simply be ignored. Finally, we have to consider the case that the current visited node v is equal to one of the multicast destinations. In this case, the multicast message is passed to the upper protocols layer, then node v is removed from the set of destinations, Algorithm 3 Continuing multicast face traversal r ule ← traversal rule Δ ← remaining multicast backbone e ← traversal start edge xt ← edge multicast backbone is originating from p ← last intersection point with xt u ← previous node v ← current node w ← next node according to r ule if v is a multicast destination then remove v from multicast destinations start face traversal at v else if vw does not intersect with an edge of Δ then if vw = e then send message along vw else drop message end if else if vw intersects with pt then vw ← edge minimizing ∠wvt r ule ← determine traveral rule for v, w, and t begin traversal along vw according to r ule and subtree Δ else remove xt from Δ t1 t2 ← edge in Δ intersecting with vw p ← intersection point of vw and t1 t2 Δ1 ← subtree of Δ reachable via t2 t1 Δ2 ← subtree of Δ reachable via t1 t2 for k = 1, 2 do remove t3−k from multicast destinations for message instance k if Δk contains at least one destination node of message instance k then vw ← edge minimizing ∠wvtk r ule ← determine traveral rule for v, w, and tk begin traversal along vw according to r ule and subtree Δk end if end for end if end if

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and multicast face traversal is restarted at node v using Algorithm 1. Refer to Algorithm 3 for a summary of the whole described procedure. For an illustration of the described strategy, refer to Fig. 8.6. When traveling along the face F2 , the message arrives at the intersection point p of backbone edge t1 t3 and F2 . Thus, the message is split into two multicast subtasks. One instance is handled in face F2 in order to address the subtree originating from the directed edge t3 t1 . The other instance is handled in face F3 addressing the subtree originating from the edge t1 t3 .

8.5 Correctness of MFACE In the following section, we proof correctness of MFACE in terms of loopfree operation and delivery guarantees. The proof is organized as follows. We first show in Lemma 1, when at least one destination node is reachable, face exploration from an edge intersected by the multicast backbone will always arrive at an additional intersection point. Then we show in Lemma 2 that after a message split, each message instance is addressing a disjoint multicast destination set and that no destination is erased in this step. These two algorithm invariants are finally used in order to prove the proposition of Theorem 1 and Theorem 2. Lemma 1 Let Δ be a connected backbone, which originates from xt. Let vw be an edge which intersects with xt at a point p. Let F be the face which has vw as a boundary edge and which intersects with pt. If v can reach at least one destination node in Δ then F also intersects with Δ in a point q different from p. Proof If t is a boundary node of F or if t is located outside of F then pt is also intersecting the boundary of F in a point q with |qt| < | pt| (see Fig. 8.7(a)). Since pt is a segment of the backbone edge xt it follows that Δ intersects with F in a point different from p. Assume that t is located within face F (see Fig. 8.7(b)). By assumption, v can reach at least one destination node ti . It follows from Lemma 3 in [13] that desti-

F

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(b) Node t is located inside of F.

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nation node ti is either a node of the boundary of F or is located outside of F. By assumption, Δ is connected and xt is the edge Δ originates from. Thus, there exists at least one edge in Δ which is different from xt and which intersects with the face boundary of F, i.e., we have again an intersection point q = p. Lemma 2 Let T be the set of destinations handled by a multicast message instance. Whenever the message is split into several instances, each instance is addressing a disjoint nonempty set of destination subsets. The union over those destination subsets is T . Proof When multicast face exploration is started in a node s, the destination set is split into the subsets, which are reachable over exactly one of the backbone edges originating from s (see st1 , st2 , and st3 in Fig. 8.5 for an example). For each subtree, a multicast message is created only if it contains at least one destination node. When a message is split into two instances due to an intersection with a backbone edge t1 t2 , the edge st the backbone Δ originates from is removed from Δ. The resulting tree Δ is still spanning all destinations addressed by this multicast instance, since s is not a destination node in this case. In fact, either traversal of Δ was started in s or traversal of Δ was started due to a visited edge intersecting with the multicast backbone. In the first case, s was already visited and is thus, no longer a destination node. In the latter case, s was removed from the destination nodes when traversal of Δ started. The remaining multicast backbone Δ is split into the subtree Δ1 reachable via t2 t1 and the subtree Δ2 reachable via t1 t2 . Let Ti be the destination nodes, which are connected by Δi . The destination nodes addressed by the first message instance are T1 \ {t2 }. The destination set addressed by the second message is T2 \ {t1 }. In both cases an instance of a multicast message is created only if it addresses at least one multicast destination. Finally, it holds T1 \ {t2 } and T2 \ {t1 } are disjoint and satisfy T1 \ {t2 } ∪ T2 \ {t1 } = T . Theorem 1 The described MFACE routing algorithm is loop free, independently of the underlying multicast backbone. Proof Whenever a message is split, it addresses a subset S of the destinations T , which were handled before that message split, while S = T is satisfied by Lemma 2. Moreover, two multicast messages are never merged. It follows that for each possible subset of T , at most one instance of a message may exist during a multicast task. It is thus sufficient to show that each potential message instance is forwarded only a finite number of steps. Let m be a message instance for a given destination subset and let xt be the originating edge of the multicast backbone Δ handled by m. As soon as the message arrives at an edge intersecting an edge of Δ, which is different from xt, the message instance disappears. It is split into several multicast subtasks. Two cases arise when the message arrives at an edge uv intersecting with xt. When the intersection point q satisfies |qt| < | pt| compared to the previous encountered intersection p with xt ( p = x if no previous intersection was encountered so

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far), it will begin traversal of the face having uv as a boundary node and which intersects the open line segment (qt]. When the intersection point q satisfies |qt| ≥ | pt|, the intersection is simply ignored. Since the number of edges are finite, it follows that the message can only visit a finite sequence of edges e1 , . . . , ek intersecting with xt while after ek no closer intersection to t exists (see Fig. 8.8). If the message arrives at ek without being split so far, the face F containing t is traversed. The message will either be split during this face traversal or visit the first face traversal edge twice in the same direction. In the latter case the message will be dropped. Theorem 2 Let s be the multicast start node and Δ be any connected backbone that connects s with a given set of destinations T = {t1 , . . . , tk }. The described MFACE routing algorithm provides guaranteed delivery for each ti , which is reachable from s. Proof Let ti be a destination node, which is reachable from s. Due to Lemma 2, node ti appears in a sequence of message instances, all addressing a destination subset of the previous one, until either the message is delivered to ti or dropped without delivery. Assume for the sake of contradiction that the message is dropped. A message is dropped only if it traverses a face F without finding an edge intersecting with the handled remaining multicast backbone Δ. Traversal of face F is either started due to Algorithm 1 or Algorithm 3. Let xt be the edge, which was used in order to define the multicast backbone on face traversal start. By Algorithm 1, the start node s selects the face which has s on its boundary and which intersects with xt. By Algorithm 3 face traversal is started due to an intersection of xt with a face edge e. Let p be the intersection point. The algorithm starts traversal of the face, which has e as a boundary edge and which intersect with pt. In both cases the precondition of Lemma 1 is satisfied. The face traversal start node v has received a message from the multicast start node s. Since ti is reachable from s, it follows, that v is able to reach node ti as well. Due to Lemma 1, F intersects also with Δ in a point which is different from p and s, respectively. Thus, face traversal will encounter an intersection with Δ, a contradiction.

F s

Fig. 8.8 A sequence of intersections leading toward t

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8.6 The Performance of MFACE and FACE The following demonstrates that addressing multiple destination nodes in a single face traversal can significantly improve the protocol performance in terms of hop count or energy consumption. The experimental results we provide in this section were obtained due to a home-made simulation tool. All the networks are always generated randomly by using the unit disk graph model presented in Section 8.2. The communication range of the nodes is set to R = 250 as defined in IEEE 802.11. Network nodes are always randomly placed on a square area of size 2500 × 2500. The number of network nodes depends on the required network density, which is indicated on the figures. Each measurement point is the average over 1000 independent simulation runs. In each simulation run we randomly select 10 multicast destinations, which are addressed by one multicast start node. If successful, the majority of greedy routing mechanisms achieve a performance close to the shortest path. Face traversal in contrast might produce large detours from the shortest path. Thus, face traversal is generally not applied on its own but as a recovery mechanism for greedy routing failures. Thus, in the following we studied the impact of face traversal as a recovery mechanism only. For greedy routing, we utilize the multicast greedy mechanism from [11]. Whenever at a current forwarding node v this mechanism fails for a destination set D = {d1 , . . . , dk }, we start a face recovery mechanism. Here, we compare two possible variants, the introduced MFACE mechanism and an individual face traversal — denoted as FACE in the following — for each destination node. More precisely, at node v we either start MFACE addressing D or we start a single face traversal for each node di . For the latter, however, several messages traveling the same face will be kept together as long as possible. When using MFACE recovery we resume greedy routing whenever the destination set D can be handled in greedy mode again. Under FACE recovery a destination di is handled in greedy mode again as soon as possible. In the following, as a planar graph structure for face traversal we apply Gabriel graph construction. As a backbone for MFACE and the utilized multicast greedy routing from [11] we apply Euclidean minimum spanning tree construction. Figure 8.9 depicts the performance of MFACE vs. FACE in terms of average hop count. ‘FACE total’ and ‘MFACE total’ refers to the total number of hop count produced by both greedy and face recovery. A clear reduction of hop count when using MFACE can be seen, in particular for sparse networks. Clearly, in sparse networks, greedy routing failures are more frequent and thus the effectiveness of the face recovery mechanism will have a greater impact. Under both FACE and MFACE recovery, the greedy routing part shows almost the same performance in terms of hop count (see ‘FACE in greedy mode’ and ‘MFACE in greedy mode’). However, as depicted by ‘FACE in face mode’ and ‘MFACE in face mode,’ MFACE shows a clear advantage over FACE. Although under FACE several messages traversing the same face are kept together as long as possible (and thus account for a single

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transmission per forwarding step), the average hop count is clearly increased. This is due to the fact that if resuming to greedy routing is possible for a single destination, this destination will individually be handled in greedy mode again. Thus, under FACE, several unicast transmissions might originate from a face traversal. These unicast transmissions increase the total number of message transmissions. Finally, since greedy routing failures are becoming less frequent in denser networks and the performance of greedy routing is almost unaffected by the use of either FACE or MFACE, the performance under FACE and MFACE are approaching the same performance value when network density is increased. Reducing hop count is a reasonable strategy whenever each transmission produces the same amount of cost; for instance, when considering the protocols energy consumption and when each transmission produces the same energy expenditure. However, when nodes are able to adjust signal strength, communication between two close nodes will consume less energy than communication between two nodes lying far away from each other. This fact can formally be expressed by the wellestablished exponential path loss model f (u, v) = |uv|α + c, while α ≥ 2 and c > 0. Figure 8.10 compares energy consumption produced by FACE and MFACE under the exponential path loss model. We utilized the parameter setting α = 4 and c = 108 , which often found in the literature. The greedy routing part in this case utilized a localized energy-aware metric whose details can be found in [11]. The fact that under FACE a multicast packet often degenerates to individual unicast transmissions clearly results in an increase of energy consumption. This can

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in particular be observed again under sparse networks. For instance, under a network density of five significant energy savings in the order of factor 25 are obtained when MFACE is applied instead.

8.7 Conclusion and Open Research Topics Under a localized protocol, changes in the network graph due to appearing and disappearing links require message exchange only among those nodes which are immediately affected by that change. Consequently, localized routing does not suffer from control message overhead of their centralized counterparts. They scale well with any network size, making such schemes attractive in particular for large scale sensor network scenarios consisting of thousands of nodes. In this chapter, we presented MFACE, which is the very first multicast extension of localized face routing which is able to work with any multicast backbone on any given planar topology. For instance, the variant used in MSTEAM is restricted to two planar graphs (Gabriel graph and relative neighborhood graph) and to a specific class of multicast backbones (no additional points, like Steiner points, are allowed). MFACE does not have these limitations and may be used in combination with any multicast backbone assisted greedy multicast scheme. Moreover, we have shown that MFACE is loop free and guarantees delivery as long as a path exists between the source node and the destinations. The performance evaluations show that MFACE as a recovery scheme from greedy routing failures can significantly improve protocol performance in terms of

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hop count and energy consumption. The performance studies evaluate the impact of the main difference between MFACE and multicast greedy recovery based on individual unicast face traversals. The studies were limited to a single planar graph and a single multicast backbone construction. The generic protocol design of MFACE, however, can be combined with any underlying planar graph and multicast backbone construction. Investigating the impact of different such schemes on protocol performance of MFACE is scheduled as a future research direction. The multicast face algorithm described in this work performs an individual unicast message forwarding task for each multicast backbone edge. As it can be observed in Fig. 8.5, the case of several backbone edges intersecting the same face might result in traversal of the face in two different directions. As future work, we plan to investigate how in this situation a message can be aggregated into one copy traversing the face in one direction only while maintaining loop-free operation and delivery guarantees. We expect that traversing face sequences intersected by the multicast backbone instead of traversing individual multicast backbone edges will result in energy and communication bandwidth savings. Moreover, for the unicast case, it has been observed that each localized routing algorithm might produce a routing path of length O(l 2 ), while l is the length of the shortest path [18]. A sophisticated improvement of unicast face traversal has been proposed in [19,20], which provably produces path lengths which are limited by the bound O(l 2 ). Such a scheme can thus be denoted as an asymptotically optimal localized unicast routing algorithm. Multicast routing opens a new field to the question of asymptotical optimality of localized algorithms. In future research we plan to investigate this bound in the light of the multicast problem and how the face routing improvement from [19,20] can be applied in the case of multicast routing in order to achieve asymptotical optimal routing path lengths. There are some fundamental questions which arise with respect to both localized unicast and localized multicast routing. By now, planar graph traversal is the only known solution which achieves delivery guarantees in a pure localized manner. An unresolved problem, however, remains how far one can go beyond the required unit disk or quasi unit disk graph network models. It has been shown that under a centralized topology control mechanism referred as CLDP [21] planar graph routing works well even if there might exist intersections among some of the remaining network edges. CLDP works under any undirected network topology. However, the scheme sacrifices the localized nature of planar graph routing. The protocols utilize probing messages which might travel any distance which cannot be bound by a constant k. A fundamental question remains if in arbitrary networks it is possible at all to locally construct a topology, possibly with intersecting edges, which supports delivery guarantees of a face traversal–based routing algorithm. Moreover, in three-dimensional networks, even for the unit disk graph model no localized routing algorithm has been described so far which provides delivery guarantees. A question remains if localized routing and guaranteed delivery is possible at all in the three-dimensional case. Finally, all localized routing algorithms require that nodes are able to determine their physical location (either relative to others or absolute). A fundamental question remains if geographic information is a necessary condition to enable the definition

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of localized unicast or multicast schemes which provide delivery guarantees. In other words, it remains open if it is possible at all to explore a network graph in a depth first search manner without memorizing state in the messages and the network nodes. Acknowledgments This work was partially financed by the European Commission under the Framework 6 IST Project “Wirelessly Accessible Sensor Populations (WASP)” and by the Danish Agency for Science, Technology, and Innovation, grant number 272-06-0581.

References 1. S. Capkun, M. Hamdi, J. Hubaux, in Proceedings of Hawaii International Conference on System Sciences (2001) 2. I. Stojmenovic, in Handbook of Wireless Networks and Mobile Computing, ed. by I. Stojmenovic (Wiley, 2002), Chapter 21, pp. 451–471 3. L. Barriere, P. Fraigniaud, L. Narajanan, J. Opatrny, in Proceedings of the 5th ACM International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (DIAL M 01) (2001), pp. 19–27 4. F. Kuhn, R. Wattenhofer, A. Zollinger, in ACM DIALM-POMC Joint Workshop on Foundations of Mobile Computing (San Diego, 2003), pp. 69–78 5. K. Gabriel, R. Sokal, Systemic Zoology 18 (3), 259 (1969) 6. G. Toussaint, Pattern Recognition 12 (4), 261 (1980) 7. J. Gao, L.J. Guibas, J. Hershberger, L. Zhang, A. Zhu, in Proceedings of the second ACM International Symposium on Mobile Ad Hoc Networking and Computing MobiHoc ’01 (Long Beach, CA, USA, 2001), pp. 45–55 8. X.Y. Li, G. Calinescu, P.J. Wan, in Proceedings of the 21st Annual Joint Conference of the IEEE Computer and Communications Society (INFOCOM ’02), vol. 3 (IEEE Computer Society, Piscataway, NJ, USA, 2002), vol. 3, pp. 1268–1277 9. X. Li, I. Stojmenovi´c, Y. Wang, IEEE Transactions on Parallel and Distributed Systems 15(4), 350 (2004) 10. K. Chen, K. Nahrstedt, International Journal of Wireless and Mobile Computing 3 (2005). Special issue on Group Communications in Ad Hoc Networks 11. H. Frey, F. Ingelrest, D. Simplot-Ryl, Localized minimum spanning tree based multicast routing with energy-efficient guaranteed delivery in ad hoc and sensor networks. Tech. Rep. RT-0337, INRIA (2007) 12. P. Bose, P. Morin, I. Stojmenovi´c, J. Urrutia, ACM Wireless Networks 7(6), 609 (2001) 13. H. Frey, I. Stojmenovi´c, in Proceedings of the ACM Annual International Conference on Mobile Computing and Networking (Mobicom) (Los Angeles, USA, 2006) 14. J. Sanchez, P.M. Ruiz, X. Liu, I. Stojmenovic, GMR: Geographic Multicast Routing for Wireless Sensor Networks, in Proceedings of the Third Annual IEEE Communications Society Conference on Sensor, Mesh, and Ad Hoc Communications and Networks SECON, September 25–28, (Reston, Virginia, USA, 2006) 15. J.A. Sanchez, P.M. Ruiz, I. Stojmenovic, Energy Efficient Geographic Multicast Routing for Sensor and Actuator Networks, Elsevier Computer Communications, Special Issue on Sensor-Actuator Networks (SANETs), Editors: Eltoweissy, S. Giordano, and S. Olariu, (2007) 16. M. Mauve, H. F¨uβler, J. Widmer, T. Lang, Position-based multicast routing for mobile ad-hoc networks. Tech. Rep. TR-03-004, Department of Computer Science, University of Mannheim, Germany (2003)

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17. H. Frey, I. Stojmenovi´c, On delivery guarantees of face and combined greedy face routing in ad hoc and sensor networks (2007). Journal publication in preparation 18. F. Kuhn, R. Wattenhofer, A. Zollinger, in Proceedings of the 6th International Workshop on Discrete Algorithms and Methods for Mobile Computing & Communications (DIAL M 02) (ACM Press, New York, 2002), pp. 24–33 19. F. Kuhn, R. Wattenhofer, A. Zollinger, in Proceedings of the 4th ACM International Symposium on Mobile Computing and Networking (MobiHoc 2003) (Annapolis, Maryland, USA, 2003) 20. F. Kuhn, R. Wattenhofer, Y. Zhang, A. Zollinger, in Proceedings of the 22nd ACM International Symposium on the Principles of Distributed Computing (PODC) (Boston, Massachusetts, USA, 2003), pp. 63–72 21. Y.J. Kim, R. Govindan, B. Karp, S. Shenker, in Proceedings of USENIX Symposium on Network Systems Design and Implementation (Boston, Massachusetts, USA, 2005)

Chapter 9

Service-Driven Query Routing in Sensor-Actuator Networks Abdelmounaam Rezgui and Mohamed Eltowiessy

9.1 Introduction Sensor networks have enabled a range of applications where the objective is to observe an environment and, collect information about the observed phenomena or events. In many cases, appropriate actions must be taken upon the occurrence of a given event (e.g., switching the light of a room off when it has been empty for more than five minutes or switching the light on when the presence of a human is detected). This has led to the emergence of a new generation of sensor networks, called sensor–actuator networks (SANETs), that have sensor nodes and actuator nodes.1 Sensors and actuators communicate and collaborate to perform distributed sensing and acting tasks. Sensors gather information about the physical world while actuators make decisions and perform actions that affect the environment [3]. Actuators are able to change parameters in their environment (e.g., temperature, light) as well as their intrinsic properties (e.g., location, speed, volume). Applications of SANETs include environmental applications (e.g., forest fire detection), business applications (e.g., inventory management), health applications (e.g., patient monitoring), home automation, and entertainment (e.g., interactive museums). Figure 9.1 shows the interactions among the components of a SANET. Base stations and actuators send sensing or control requests to sensors. Sensors send data or control information to base stations and actuators. Actuators may initiate actions autonomously or upon the reception of actuation requests from the base station. Actuators may send control information to the base station. Existing routing schemes for SANETs generally do not exploit the semantics of the queries. As a result, a query may be routed through several hops to end up at nodes that do not provide the sensing/actuation capability that it requests and 1

Some literature uses the term “actor” instead of “actuator”.

A. Rezgui Department of Computer Science, Virginia Tech, 2050 Torgersen Hall (0106), Blacksburg, VA 24061 e-mail: [email protected]

S.K. Makki et al. (eds.), Sensor and Ad Hoc Networks, C Springer Science+Business Media, LLC 2008 DOI: 10.1007/978-0-387-77320-9 9,

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Fig. 9.1 Interactions in SANETs

that do not have paths to nodes that provide the requested capability. This “aimless routing” obviously incurs excessive communication and processing overhead that is not strictly required to deliver the query to its recipients. In this chapter, we propose a new approach, called service-driven query routing, that reduces aimless routing. In this approach, each node: (1) determines the capability requested by each received query, and (2) maintains local information of reasonable size about the mapping between nodes and capabilities. By combining these two information, nodes are able to cooperatively build efficient paths to route query messages. Ideally, those paths would only contain nodes that provide the capability requested by the query or nodes that have paths to nodes providing the requested capability. We implemented this approach in SDRP, a service-driven routing protocol for sensor–actuator networks. Figure 9.2 depicts the intuition behind service-driven routing. It illustrates how communication may be reduced by using this principle. For example, in floodingbased routing, a copy of the query will traverse each of the links at least once (regular arrows in Fig. 9.2). Consider a node n that receives a query message m requesting some sensing/actuation capability c. In current deployments of SANETs, n will systematically forward m to (at least some of) its neighbors. In this scenario, it is likely that m traverses a large number of hops only to reach “dead ends”, i.e., nodes that do not provide the capability requested by m. If service-driven routing was used, nodes would be able to reduce the number of messages they forward by determining the capability requested by the received query. A node would forward a query only if it determined that it is on a path to nodes providing the requested capability. In Fig. 9.2, this is illustrated through the arrows with a circle in their end. If n is able to

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Fig. 9.2 Service-driven query routing: The intuition

determine whether it is on the path to one or more nodes providing the capability c, it will be able to decide whether to forward the message m or to discard it. The chapter is organized as follows. We first start with a brief literature review of research in the area of routing protocols for sensor networks. In Section 9.3, we present SDRP, a routing protocol that implements the proposed service-driven query routing approach. In Section 9.4, we present the implementation of SDRP with in our TinySOA system. In Section 9.5, we present the results of our evaluation of SDRP. In Section 9.6, we overview existing literature that considered the concept of “service” in the context of sensor networks. In Section 9.7, we discuss TinySOA as it compares to the research presented in Section 9.6. Section 9.8 concludes the chapter.

9.2 Routing Protocols in SANETs A routing protocol determines the appropriate path to transmit messages. It also specifies how routing information is shared and updated. A fundamental requirement in designing routing protocols for sensor networks is power efficiency, i.e., computing energy-efficient routes. Basic algorithms for finding energy-efficient routes use either the available power in the nodes or the energy required for transmission in the links of the routes [2]. Four approaches exist: • Maximum Power Available (PA) route: In this approach, the route that has the maximum total PA is selected. A route’s total PA is the sum of the PA of all the nodes along that route. • Minimum Energy (ME) route: In this approach, the cost of transmitting data along each link is a factor. The route that consumes the minimum energy to transmit the data is selected. • Minimum Hop (MH) route: The best route in this approach is the one with the minimum number of hops.

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• Maximum Minimun PA node route: In this approach, the route along which the minimum PA is larger than the minimum PAs of the other routes is preferred. In a recent survey, Akkaya and Younis classify routing approaches for sensor networks into three nondisjoint classes: (1) data-centric routing, (2) hierarchical routing, and (3) location-based routing [1]:

9.2.1 Data-Centric Routing In data-centric routing, users are interested in querying an attribute of the phenomenon rather than a specific sensor node [3]. For example, a user’s query may be: “Which are the rooms that have their light on?”. In this approach, interest dissemination may be initiated by the sink node or by the sensor nodes. In the first case, the sink sends the interest to certain regions and expects sensor nodes located in those regions to answer the queries. In the second case, sensor nodes broadcast advertisements for the available data and wait for requests regarding the advertised data originating from interested nodes. One of the earliest data-centric routing protocols is SPIN (Sensor Protocols for Information via Negotiation) [13]. Nodes running a SPIN communication protocol name their data using high-level data descriptors, called meta-data. They use metadata negotiations to eliminate the transmission of redundant data. When a node receives a new data, it advertises it and other nodes may retrieve the data by sending a message to that node. Another data-centric routing protocol is Directed Diffusion [14]. In this protocol, the sink node broadcasts a task description, called an interest, to all sensors. Each sensor then adds in its cache an entry for that interest containing a timestamp and information about the route back to the sink. When a source has data that corresponds to the interest, it sends the data using the route information stored with the interest entry in its cache.

9.2.2 Hierarchical Routing Hierarchical routing aims at reducing energy consumption at the sensor nodes by decreasing the number of transmitted messages to the sink. Sensor nodes are involved in multihop communication within a particular cluster rather than in more expensive network-wide communication. Data aggregation and fusion are used to reduce the traffic sent to the sink. One of the earliest hierarchical routing approaches was LEACH (Low Energy Adaptive Clustering Hierarchy) [32]. The protocol forms clusters of sensor nodes based on the received signal strength. In each cluster, only a cluster head routes data to the sink. Data processing (e.g., data fusion and aggregation) is local to the cluster. Cluster heads change randomly over time to balance energy consumption among sensors.

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9.2.3 Location-Based Routing Location-based routing exploits information about the location of nodes. Location information helps in determining the distances between nodes and, hence, makes it possible to estimate the energy consumption associated with transmission between nodes. Two protocols illustrate this class: MECN (Minimal Energy Communication Network) [26] and SMECN (Small MECN) [21,20]. Given a communication network, MECN computes an energy-efficient subnetwork. For every node, MECN determines a relay region that consists of nodes in a surrounding area where transmitting through those nodes is more energy efficient than direct transmission. The protocol constructs a sparse graph, called enclosure graph, which consists of all the enclosures of each transmit node in the network. The enclosure of a node is the union of all relay regions that the node can reach. The protocol then uses distributed Belmann–Ford shortest path algorithm to find optimal links on the enclosure graph with power consumption as the cost metric. SMECN is an improvement on the MECN protocol. If the broadcast region is circular around the broadcaster, SMECN constructs a smaller subnetwork than MECN. SMECN considers a communication network that is represented by a graph G. The objective is to compute a subgraph G of all the nodes of G such that: (1) the number of edges in G is less than that in G, (2) if two nodes u and v are connected in G, they are also connected in G , and (3) the energy required to transmit data from a node u to all its neighbors in G is less than the energy required to transmit from node u to all its neighbors in G.

9.2.4 Actuator-Aware Routing The previous three classes of protocols target traditional sensor net works that do not contain actuators. In SANETs, two additional new types of communication exist: sensor–actuator communication, and actuator–actuator communication. In [3], the authors suggest that routing protocols developed for adhoc networks such as DSR, AODV, and OLSR [6] can be used for actuator–actuator communication. It would then be necessary to improve these protocols to meet real-time requirements and minimize the overhead at sensor nodes that result from actuator–actuator communication. This approach is investigated in [10] where the authors compare the performance of three multihop routing protocols, namely, DSDV [5], AODV [4], and DSR [8] in the context of SANETs. The DSDV (Destination Sequenced Distance Vector) protocol is a hop-by-hop distance vector routing protocol requiring each node to periodically broadcast routing updates. DSR (Dynamic Source Routing) protocol is based on source routing, which means that the originator of each packet determines an ordered list of nodes through which the packet must pass while traveling to the destination. The AODV (Ad Hoc On-Demand Distance Vector) protocol is essentially a combination of both DSR and DSDV. It borrows the basic on-demand mechanism of route discovery and route maintenance from DSR, plus the use of hop-by-hop routing, sequence numbers, and periodic beacons from DSDV [7]. The

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study concluded that, among the three adhoc routing protocols, DSR is the best solution for actuator-to-actuator communications in SANETs.

9.3 SDRP: A Service-Driven Routing Protocol for SANETs A fundamental idea in the proposed routing approach is that nodes’ sensing and actuation capabilities are exposed as services. A service is a computational component that (1) has a unique network-wide identifier, (2) may be invoked asynchronously, (3) may have one or more parameters, and (4) produces one or more values as a result of the invocation. A service may have multiple service instances, each running on a given node. Nodes may or may not provide the same set of services. We implemented the proposed routing approach in SDRP, a service-driven routing protocol for sensor–actuator networks. SDRP is responsible for query routing. SDRP exploits query semantics to determine whether disseminating a query message within a given subtree of the network would contribute in answering that query. SDRP is responsible for (1) delivering incoming queries to the query processing (QP) layer of the local node and (2) forwarding query messages received from other nodes. The key idea behind SDRP is to reduce aimless routing, that is, forwarding query messages to nodes that neither provide the requested service nor are on the path to nodes that provide the requested service. To achieve this, each node builds and maintains two data structures: a it service table and a service directory. A node n i ’s service table (noted STi )contains information about n i ’s services. In particular, each entry in STi contains the service identity (serviceID) of each service that n i provides and the service class of that service (e.g., getLight()). The second data structure that each node builds and maintains aspart of the SDR protocol is the service directory. A node use sits service directory to store information about services provided by reachable nodes. Let S Di be node n i ’s service directory. An entry in S Di corresponds to a service class (e.g., getLight()) for which the local node has determined that there is at least one reachable provider. The service directory may be thought of as the routing table of SDRP. Using their respective service directories, nodes cooperate to route query messages via paths with no deadends. The basic SDR protocol consists of two concurrent activities: path learning and query routing.

9.3.1 Path Learning The purpose of this phase is to let each node know whether it is on the path to nodes providing any given service. Path learning takes place at bootstrapping time. It takes place also when new nodes are deployed or when new services are deployed on existing nodes. After the network is deployed, all nodes enter a service dissemination phase through which each node advertises its sensing and actuation services

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to its neighbors. Service dissemination is an incremental process in which nodes that become aware of new services further advertise these services in their neighborhood. At bootstrapping time, each node n i broadcasts a message MyServices that contains the list of service classes it provides. When a node n j receives this message, it iterates through each of the service classes included in the message. For each service class, n j checks whether there is an entry for that class in S D j . If not, n j simply adds a new entry corresponding to that class to its service directory S D j . In the basic SDRP, n j then broadcasts a message ServiceUpdate to its neighbors informing them that node n i provides the given service. Each node n p (other than n i ) that receives the message ServiceUpdate from n j updates its service directory as follows: For each entry in the message ServiceUpdate that corresponds to a service not already in S D p , n p adds an entry for that service to its service directory S D p . In a more efficient version currently in development, n j waits until k new entries are added to its service directory before it broadcasts the message ServiceUpdate. k, the number of entries that each ServiceUpdate message contains, is called update threshold.

9.3.2 Query Routing The second activity that the SDR protocol performs is routing queries. Query routing in SDRP is a distributed process in which several nodes cooperate in routing queries requesting services toward nodes providing those services. Typically, a query is initiated by a base station2 and it requests the invocation of a given service by a given subset of nodes. Let Q(s) be a query that the base station issues requesting the invocation of service s. First, the base station broadcasts Q to its immediate neighbors. When a node n i receives the query Q from another node n j , the SDR protocol first determines whether the local node is included in the query’s spatial scope. If so, SDRP looks up the service s in STi to check whether n i provides the service requested by Q(s). If s is in STi , SDRP simply passes the query to the local node’s query layer. SDRP then looks up s in S Di . If an entry is found, then there is a path from the local node n i to one or more nodes that provide the service s. In this case, SDRP forwards the query Q(s) to n i ’s neighbors.

9.4 Implementation We implemented SDRP as the query routing protocol for TinySOA, a prototype service-oriented query processing system built on top of TinyOS 1.1.15. Depending on the nature of the function to be provided, services in our implementation may be coded as one of three types of TinyOS processing units: (1) asynchronous commands, (2) synchronous commands, and (3) tasks. This types derive directly 2 Note,

however, that any node may initiate queries.

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from TinyOS’s constraints. Services coded as asynchronous commands (using async) may beexecuted at any time (preempting other code). Asynchronous commands are, therefore, used for services that have time constraints on their invocation time and whose execution takes a short duration. Synchronous commands do not preempt other code. They are used for services with less string ent constraints on their invocation time and whose execution may be of longer duration. Tasks in TinyOS are used to perform long processing, such as background data processing, and can be preempted by hardware event handlers. They are, therefore, used for services thatare not very critical. However, note that in TinyOS, tasks may not take parameters and do not return results. Services coded as tasks are therefore used only when no input values are needed and no output is expected. The service-driven routing protocol was implemented as a separate nesC module, called SDRP.nc, that may coexist (within a given application) with TinyOS’s standard communication mechanisms. The purpose for providing this flexibility is to enable programmers to select the routing layer to use when routing a given class of queries. For example, for queries that must reach all or most of the nodes, TinyOS’s default communication primitives would probably be more efficient.

9.5 Evaluation In this section, we present an evaluation of the proposed routing approach. We first study the scalability of SDRP, TinySOA’s query routing mechanism, in terms of energy consumption and scalability. We then conduct comparative experiments between TinySOA and TinyDB [23].

9.5.1 Energy Consumption and Scalability To evaluate SDRP’s energy consumption, we developed an evaluation benchmark that uses the Power TOSSIM simulator [30] integrated in the TinyOS package. The benchmark enables a wide spectrum of simulation scenarios. In particular, users may specify configuration parameters such as the total number of different services, the maximum number of services per node, the update threshold, etc. The benchmark also enables users to specify executions where any number of queries is injected in the network, any values for the parameters of the queries may be selected and the time between the injection of two consecutive queries may be varied. 9.5.1.1 Scalability with Regard to the Number of Nodes In the first experiment, we considered SDRP’s scalability with regard to the number of nodes. Specifically, we measured the energy required to setup SDRP as reflected in the average energy consumed by the nodes’ radios and CPUs. We ran experiments on networks with a number of nodes varying from 4 to 961 nodes. We assumed a lossy radio model and used TinyOS’s LossyBuilder tool to generate the probabilities

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for incorrect bit reception for each considered network topology. For example, in the first iteration, we generated a probability file for a grid of 2 × 2 nodes in an area of 6 ft. ×6 ft. In the last iteration, we generated a probability file for a grid of 31 × 31 nodes in an area of 93 ft. ×93 ft. Note that we kept the same node density (1/9 node per sq. ft.) for all iterations. Each node runs a number of services selected randomly between 1 and N B Smax . N B Smax was kept constant at 5 in this experiment. The identities of the services running on each node are also selected randomly from a set of NbServices (kept at 50) services. The experiment ends when no message remains in transit, i.e., when all messages sent as part of SDRP are either received or lost. Figures 9.3 and 9.4 show the results of the experiment. The figures show that energy consumption increases almost linearly until we reach about 30 nodes. From that point until the number of nodes reaches 700, energy consumption remains

Fig. 9.3 Energy consumption and scalability of SDRP with regard to network size

Fig. 9.4 Energy consumption and scalability of SDRP with regard to network size (for less than 120 nodes)

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constant. It then increases slightly and then remains constant. The key conclusion from this experiment is that, for topologies of a given size (30 nodes or more in this experiment’s conditions), energy consumption in SDRP becomes almost independent from the number of nodes. Indeed, SDRP depends only on the number and distribution of services on the nodes. This makes SDRP particularly suitable for large networks.

9.5.1.2 Scalability with Regard to the Number of Queries In the second experiment, we kept the number of nodes constant at 100 nodes and measured TinySOA’s energy consumption when the number of queries injected in the network varies from 10 to 400. The other parameters were similar to the ones used in the first experiment. The base station submits a query that requires that each node that provides the service getLight() invokes it and then sends the result to the base station. Here again, the experiment ends when no message remains in transit. We measured the average energy consumed by the nodes’ radios and CPUs from the time the base station submits the query until the end of the experiment. The experiment shows two important results. First, the setup cost in terms of energy (i.e., running SDRP before queries may be routed) is very low. For example, Fig. 9.3 shows that, at 100 nodes, SDRP’s setup requires about 330 mJ. Figure 9.5 shows that the total cost of executing 60 queries or more is slightly less than 1500 mJ. This makes SDRP’s setup cost only about 22% of the total cost of executing 60 or more queries. A more important result is that, beyond a certain number of queries (60 in this case), the cost of query processing in SDRP increases very slowly with the number of queries. This is due to the key characteristic of SDRP that eliminates much of the unnecessary traffic that would normally occur in traditional routing protocols.

Fig. 9.5 Energy consumption and scalability of SDRP With regard to number of queries

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9.5.2 TinySOA vs. TinyDB In this section, we compare TinySOA to TinyDB. We focus on three criteria: (1) energy consumption, (2) scalability, and (3) response time. To conduct our comparison, we considered that querying for the values of attributes in TinyDB is the equivalent of invoking simple services in TinySOA. However, mapping TinySOA’s services into TinyDB’s attributes is not straightforward. TinyDB has a number of specificities and limitations that had to be considered. In TinySOA, arbitrary services may be deployed on nodes. In TinyDB, however, this is not possible. Indeed, TinyDB uses a static set of attributes, e.g., temperature, light etc. This set is specified in a file (called catalog.xml) that is loaded at bootstrapping time. TinyDB then makes all of the attributes defined in the catalog available, and hence queryable, on all nodes. The second constraint was that, in TinyDB, populating nodes with different sets of attributes may not be done programmatically. TinyDB provides a mechanism to add an attribute for a specific mote on the fly, i.e., after TinyDB starts. This mechanism, however, is only available through TinyDB’s Java-based GUI. Moreover, this is only possible for constant attributes. To reflect a similar setting, we set the number of services available on each node in our TinySOA network to 19, which is the number of attributes in TinyDB’s default catalog. We considered a scenario where the base station submits a single query and waits until it receives a given number of results. In TinyDB, we wrote a Java class that interacts directly with the TinyDBApp nesC application and injects the following query in the network: select nodeid,light from sensors sample period 30000

The equivalent TinySOA query is: action getNodeID(), getLight(); time frequency 30000 ms;

In both cases, the experiment ended when the base station received a certain number qr of query results that was varied from 10 to 110. 9.5.2.1 Energy Consumption Figure 9.6 shows the average energy consumed by the nodes’ radios and CPUs in the cases of TinySOA and TinyDB. The figure shows that, in the case of TinyDB, energy consumption increases almost exponentially with the number of query results received at the base station. Figure 9.7 is a closer view that shows energy consumption in the case of TinySOA. Energy consumption, in this case, increases almost linearly with the number of results that the network generates. The difference between TinySOA and TinyDB in terms of energy consumption may be explained by the fact that TinySOA cuts significantly the number of messages required to get a query to all nodes that must contribute in its evaluation. The length

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Fig. 9.6 Comparison between TinySOA and TinyDB – varying the number of results

Fig. 9.7 Comparison between TinySOA and TinyDB – varying the number of results (zoomed in)

of the paths between the base station and the target nodes depends almost entirely on the distribution of services in the network and not much on the size of the network. If only a few nodes of the network provide the service requested by a given query, then only a proportional number of nodes will be involved in routing the query to those nodes regardless of how many other nodes exist in the network. This is not the case in TinyDB where the number of nodes that contribute to routing a given query increases systematically with the network’s size. As a result of the difference between TinyOS’s query routing and TinyDB’s query routing and given the size of the network (100 nodes), queries get a lot sooner to their destination in TinySOA than in TinyDB. As it takes longer for TinyDB to get a query to its destination, some nodes start generating results and sending them to the base station while some other nodes have not even received the query. This seems to create a significant amount of opposite traffic. This traffic translates into a large number of collisions, which

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Fig. 9.8 Comparison between TinySOA and TinyDB – response time

in turn, results into many failed transmissions and retransmissions. This, in fact, is confirmed in the next experiment. 9.5.2.2 Response Time We also conducted experiments to compare TinySOA and TinyDB from the perspective of response-time. The purpose was to measure the time taken by both networks to route query results from the nodes where they are generated to the base station. This metric is important when assessing the suitability of both networks to support real-time applications. When conducting this experiment in TinySOA, we made each node that generates a result for a query simply broadcast it to its neighbors. Each neighbor that receives a query result forwards it until the query result reaches the base station. We set the number of nodes at 100 nodes and measured energy consumption of nodes’ radios and CPUs until the base station receives a given number of results in both TinySOA and TinyDB. Figure 9.8 shows this experiment’s results. Here again, we can see that, in TinyDB, this time increases exponentially. In contrast, in TinySOA, the increase is linear. While using simple broadcasting to route query results to the base station is certainly less efficient than TinyDB’s scheme, TinySOA outperforms TinyDB mainly because of the savings (in time) that TinySOA achieves when routing queries from the base station to the nodes using SDRP. 9.5.2.3 AdHoc Network Deployment A TinyDB network must be competely defined prior to deployment. In particular, the attribute catalog must be defined before the network is deployed. In addition, all nodes must run TinyDB’s code. This makes TinyDB unsuitable for the next generation of sensor systems where different networks from different providers and running different operating systems may need to interact. In contrast, in TinySOA,

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services are dynamically discovered and used. In addition, when new services are discovered, SDRP is able to automatically update service directories without any side effects on the normal operation of the network.

9.6 Services in Current SANETs Research on service-oriented architectures (SOAs) for sensor networks is only at its infancy. Ongoing research, however, is already demonstrating the immense potential of SOAs in supporting the development of open, reusable, evolving architectures for sensor applications [25]. SOAs allow new applications to be developed by reusing/composing existing services. We argue that service-oriented architectures are a promising paradigm that has the potential of radically changing the focus of research in the area of SANETs. In particular, service-oriented SANETs (SOSANETs) provide an efficient and elegant approach that offers two key benefits: (1) network-independent application development and (2) efficient, uniform, application-aware, cross-layer optimization. Indeed, with SOSANETs, programmers would specify sensing and actuation requests in terms of abstract service invocations instead of low-level sensor readings or actuator activations. Also, SOSANETs will provide “loose decoupling” between networks and applications that will offer SANET designers substantial flexibility in developing query engines. In particular, SOSANETs will enable both application-independent and applicationaware cross-layer optimization. Recent research has recognized the promise of service-oriented architectures in addressing many of the current limitations of SANETs. In this section, we overview recent research that has considered the concept of services in building SANETs. Service-oriented SANET architectures may provide one (or both of) two types of services: (1) middleware services and (2) in-network services:

9.6.1 Middleware Services These are high-level programming abstractions that the SOSANET exposes to applications as a middleware layer. Typically, a middleware service is implemented as a module that runs off-network and that interacts with one or several nodes to provide its functionality. Most existing SOSANETs provide only middleware services. Examples include Atlas [19], SONG [17], and Sens-ation [31]. Atlas is a service-oriented sensor and actuator platform that enables programmable pervasive spaces. This platform is focused primarily on an OSGi-based service framework [19]. Sens-ation is an open and generic service-oriented platform, that enables standardized communication within individual infrastructures, between infrastructures and their sensors, but also among distributed infrastructures. On a whole, Sens-ation facilitates the development allowing developers to concentrate on the semantics of

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their infrastructures, and to develop innovative concepts and implementations of context-aware systems [31]. In [16], the authors describe the architecture and programming model of a semantic-service–oriented sensor information system platform. They envision a hierarchical architecture for sensor infrastructures, consisting of sensors, field servers, and gateway servers. At the bottom level, various sensor nodes gather data from the physical environment and communicate among each other or with higher level nodes. The next level entities in the hierarchy are field servers that directly connect to sensor nodes. A field server converts sensor data, which are usually in platform-specific format into something that is open and directly usable, such as XML data format or standard image encoding. Users interact with the sensor infrastructure through gateway servers where user requests and sensor information flow through. A gateway server may contain a planner that converts user requests into tasks that can be executed on a set of field servers. It may employ database servers that archive history to be fused together with real-time information. The authors introduce the idea of semantic services, which are computational components that transform raw sensor data into high- level semantic information. For example, a truck detector used in a parking garage may detect the presence of a truck by estimating the length of a mobile object. In this case, the service (i.e., the truck detector) generates semantic information (i.e., presence of a truck) from a data stream regardless of how the length estimation is obtained. To enable these transformations, the authors introduce the idea of defining a sensor information ontology that captures the information about physical entities collected by sensors and their relations. The ontological abstraction allows a sensing system to optimize its resource utilization in collecting, storing, and processing data. An interesting aspect in this approach is service composition. Services are composed by connecting their input and output ports with compatible semantics. The connections between input and output ports of different services have publish– subscribe semantics. In the automatic service composition model, the users do not need to compose the services manually to create a sensor information application. They can simply issue a query that requests data streams with desired semantics to the gateway server. A query planner can search through all possible services and sensor configurations for the best service composition that can answer the user’s queries. In [9], the authors propose a Web Services approach for the design of sensor networks. The purpose was to enable a flexible architecture where sensor networks’ data can be accessed worldwide. In this approach, sensor nodes are service providers and applications are clients of those services. Sensor nodes publish their services by sending the services’ description to sink nodes. The Web Services Description Language (WSDL) is used to describe data and functionalities of sensor nodes. Sink nodes provide the service descriptions of the whole sensor network. They act primarily as service providers to the external environment. Applications submit their service requests to sink nodes, which then interact with the appropriate sensor nodes requesting their specialized services, in order to meet the user application needs.

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In [28], the author present Shaman, an extendable Java-based service gateway for networked sensor systems. Shaman integrates small network-attached sensor– actuator modules (SAMs) into heterogeneous, high-level networking communities. The system unburdens its connected SAMs by transferring functionality from the SAMs to the gateway. The services that Shaman exposes to clients are therefore off-network services. Clients submit their requests to proxies that translate these requests into SAM-specific commands. In [33], the authors propose a middleware for accessing sensor data that is based on the service-oriented architecture using Web services and Grid technologies. The purpose of the middleware is to integrate sensor networks into a networked virtual enterprise, making the physical data available to all applications in the enterprise. The middleware uses the WSRF (Web Services Resource Framework) to manage stateful (sensor) resources. The WSRF specifies how to use Web services to access stateful resources. The authors address the issue of power efficiency for sensor application services and provide a query optimization mechanism at Web services level based on the Markov Decision Process (MDP). In [22], the authors present a Data Service Middleware (DSWare) layer for sensor nodes that exists between the application layer and the network layer. DSWare provides the abstraction of data services to applications. The purpose is to enable applications to query the sensor network without having to implement the entire stack of application-specific data services including group management, query optimization, local data processing, and event detection. An example of services offered by DSWare is a real-time event detection service. In [18], the authors present WISE, a Web-Services framework for publishing, browsing, and analyzing real-time sensor data. Providers register their sensors with a UDDI registry where any user can discover them over the Internet. Once the desired sensors are located, the user can employ two new communication protocols, namely, SSCP and SSTP, to control the incoming sensor streams. As the data arrive at the user browser software, a corresponding plug-in such as a data animation module is activated to allow the user to “see” the data stream presented in an intelligible way. In [29], the authors aims at enabling programmers to develop and deploy sensor network applications while being agnostic about the actual network implementation, yet still meeting the application requirements in terms of timeliness, lifetime, etc. For this, they define a set of services and interface primitives called the Sensor Network Services Platform (SNSP). The SNSP description of an application captures the interaction between controllers, sensors, and actuators. This description is purely functional and does not prescribe how and where each of the functions will be implemented. Information such as energy, delay, cost, and memory size, is provided once the functional components of the SNSP are mapped onto actual hardware nodes. This mapping is achieved through a description of the actual hardware platform given by the Sensor Network Implementation Platform (SNIP). In [12], the authors describe EMS (Emergency Medical Services), an emergency medical response system that couples the efficient data collection of sensor networks with the flexibility and interoperability of a Web services architecture.

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The objective in architectures that provide middleware services is almost invariably to decouple the application development from the low-level hardware details of nodes and networks. The proposed middleware layers are often programming interfaces that simplify the development of sensor network applications. Efficiency is rarely part of the design objectives. Indeed, MS architectures often target one or a combination of the four following objectives: (1) abstraction, (2) interoperability, (3) decoupling between services and SANETs, and (4) cost reduction.

9.6.2 In-Network Services These are a low-level code units that run directly on nodes. Little research has investigated SANETs with in-network services. As SANETs proliferate, future sensor infrastructures with network services will likely require the interoperability among several nodes of different networks and providing different services. Two issues seem particularly important in enabling this scenario: defining standards enabling communication among nodes of various SANETs and mapping high-level application specifications into efficient executions that involve multiple services of several networks. Examples of SANET architectures with in-network services include [27] and [15]. In [27], the authors address the issue of efficient service discovery in wireless sensor networks where services run on nodes. They propose a service discovery protocol that relies on a clustering structure. This structure offers distributed storage of service descriptions. The clusterheads act as directories for the services in their clusters. In [15], the authors present RASA, a service architecture for mobile sensor networks. The main purpose in RASA is to enable postdeployment changes on the code running on sensor nodes. RASA features software changes by injecting services at runtime. RASA extracts implicit information about the network and adapts the software running on nodes based on the current conditions of the network. Services are software parts including executable code, which are injected into the network without previous knowledge and are executed at every node. Moreover, a service consists of several modules to support reusability of already written components and to reduce service size by outsourcing often used components to the node software.

9.6.3 Cross-Layer Services A third type of architecture combines the two previous approaches. Services, in these architectures, are deployed at several layers. In particular, services are deployed as a programming interface and as code units that run on nodes. An example of these architectures is OASiS [24], designed as a uniform serviceoriented programming framework for sensor networks. OASiS in that it captures

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applications as a graph of modular services that it executes in response to the detection of physical phenomena.

9.7 TinySOA vs. Other Existing Service-Oriented Systems TinySOA introduces fundamental changes in the design and implementation of sensor networks. In particular, it enables three important design features not simultaneously available in existing service-oriented systems: • On-Node Services: Almost all existing “service-oriented” architectures for sensor systems introduce services as off-network programs running on computers and not sensor nodes. Examples include: [18, 33, 29, 9,16]. TinySOA deploys onnode services that may be advertised, discovered, and invoked by entities within or outside the network. This makes TinySOA networks open environments that may readily interoperate with each other as well as with other types of client entities. For example, consider a user roaming an area where different TinySOA networks are deployed. Using a “generic” mobile device such as a laptop or a cell phone, this user may be able to discover and invoke services provided by nodes that belong to different networks. Interaction would be possible without any prior configuration of the mobile device to query any given TinySOA network. • Service-based Optimization: Both in-network and off-network optimization have already been proposed in a number of existing service-oriented sensor systems. Examples include [28, 33] and [16] for systems capable of off-network optimization and [11] for systems capable of in-network optimization. These systems, however, do not exploit services in optimization. They simply provide traditional, application-level forms of in-network optimization. None of these systems have considered the idea of exploiting services in low-level mechanisms such as routing. In TinySOA, services are both a design paradigm and an optimization means. They enable new forms of in-network and off-network optimization: – In-Network Service-Based Optimization: TinySOA enables in-network servicebased optimization both at the application level (e.g., multiquery optimization, result aggregation, etc.) as well as at lower levels. An example of the former is TinySOA’s ability to associate a single service invocation with several queries. An example of the latter is TinySOA’s SDRP protocol described in this chapter. – Off-Network Service-Based Optimization: From the perspective of TinySOA’s clients (e.g., base station, mobile user), TinySOA streams query results in ways similar to existing sensor systems. Traditional off-network optimization techniques (caching, query rewriting, reprocessing previous results to answer new queries, etc.) are also applicable in the context of TinySOA. • Application Independence and Application Awareness: Application awareness refers to the ability to exploit the specific characteristics of a given

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Table 9.1 TinySOA vs. other service-oriented systems

[11] [28] [18] [33] [29] [9] [12] [16] [19] [27] [15] [24] TinySOA

Abstraction

Type of services

Application awareness

Off-network optimization

Node services Jini Services Web services Web services Node services Node Web services Web services .NET components OSGi-based services Ad hoc Ad hoc Objects Node services

In-network Off-network Off-network Off-network In-network In-network Off-network Off-network Off-network In-network In-network In,Off-network In-network

No No No √

No √

No √

No √

No √

No No No √

No No √ √ √

No No √ √ √

In-network optimization √ No No No No No No No No √ No No √

application to improve the overall efficiency of the network. Several prior efforts have proposed application-aware solutions. However, these solutions are often too specific to the considered class of applications. In contrast, TinySOA expose “neutral” services that any application may use with the same efficiency expectations. TinySOA is therefore application independent while it is still able to exploit any specific characteristics of a given application. Table 9.1 gives a summary comparison of TinySOA with other service-oriented sensor systems. In the Abstraction column of the table, the term node services refers to a software module running on sensor nodes. Web services refer to cases where the service is Web-accessible through standards such as XML. Node Web services refer to cases where the service is both hosted on sensor nodes and Webaccessible. While existing literature has already explored some aspects of service-oriented design in sensor networks, our work is a fundamentally novel approach where services are selectively deployed on top of the bare operating system controlling sensor–actuator nodes. Another major difference is that services in our approach are not only a means for better expressivity but, more importantly, a key element in query optimization.

9.8 Conclusion We presented SDRP, a service-driven routing protocol for sensor–actuator networks. SDRP is a routing layer for service-oriented SANETs (SOSANETs). In these networks, nodes expose their sensing and actuation capabilities in the form of services that may be invoked by any application. We implemented our approach in TinySOA, a SOSANET developed on top of TinyOS. Empirical results show that our SDRP-based TinySOA system achieves significant improvements over existing architectures on many aspects including energy consumption, scalability,

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and response time. Future SANETs will require new architectures. We foresee service-oriented architectures as a highly viable candidate to support the requirements of tomorrow’s sensor–actuator networks.

References 1. K. Akkaya and M. Younis. A Survey of Routing Protocols in Wireless Sensor Networks. Elsevier Ad Hoc Network Journal, 3/3:325–349, 2005. 2. I. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci. A Survey on Sensor Networks. IEEE Communications Magazine, 40 (8):102–114, 2002. 3. I.F. Akyildiz and I.H. Kasimoglu. Wireless Sensor and Aactor Networks: Research Challenges. Ad Hoc Networks, 2 (4): 351–367, 2004. 4. C.E. Perkins and E.M. Royer. Ad-hoc On-Demand Distance Vector Routing. In Proc. of the Second IEEE Workshop on Mobile Computing Systems and Applications (WMCSA), pp. 90–100, February 1999. 5. C.E. Perkins and P. Bhagwat. Highly Dynamic Destination-Sequenced Distance-Vector Routing (DSDV) for Mobile Computers. In Proc. of the SIGCOMM Conference on Communications Architectures, Protocols and Applications , pp. 234–244, August 1994. 6. M. Conti, G. Maselli, G. Turi, and S. Giordano. Cross-Layering in Mobile Ad Hoc Network Design. IEEE Computer, Special Issue on Ad Hoc Networks, 37 (2): 48–51, 2004. 7. D.A. Maltz. On-Demand Routing in Multi-hop Wireless Ad Hoc Networks. PhD thesis, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, May 2001. 8. D.B. Johnson and D.A. Maltz. Mobile Computing, Chapter 5: Dynamic Source Routing in Ad Hoc Wireless Networks, pp. 153–181. Kluwer Academic Publishers, 1996. 9. F.C. Delicato, P.F. Pires, L. Pirmez, and L.F. Rust da Costa Carmo. A Service Approach for Architecting Application Independent Wireless Sensor Networks. Cluster Computing, 8 (2–3): 211–221, 2005. 10. D.V. Dinh, M.D. Vuong, H.P. Nguyen, and H.X. Nguyen. Wireless Sensor Actor Networks and Routing Performance Analysis. In Proc. of the Internat. Worshop on Wirless Ad-hoc Networks, 2005. 11. F. Golatowski, J. Blumenthal, M. Handy, M. Haase, H. Burchardt, and D. Timmermann. Service-Oriented Software Architecture for Sensor Networks. In Proc. of the International Workshop on Mobile Computing, pp. 93–98, 2003. 12. N. Hashmi, D. Myung, M. Gaynor, and S. Moulton. A Sensor-based, Web service-enabled Emergency Medical Response System. In Proc. of the Workshop on End-to-end, Sense-andrespond Systems, Applications and Services (EESR), pp. 25–29, Berkeley, CA, USA, USENIX Association, 2005. 13. W.R. Heinzelman, J. Kulik, and H. Balakrishnan. Adaptive protocols for information dissemination in wireless sensor networks. MobiCom ’99: Proceedings of the 5th Annual ACM/IEEE International Conference on Mobile Computing and Networking, pp. 174–185, New York, USA, ACM Press, 1999. 14. C. Intanagonwiwat, R. Govindan, D. Estrin, J. Heidemann, and F. Silva. Directed Diffusion for Wireless Sensor Networking. IEEE/ACM Transactions Networks, 11 (1): 2–16, 2003. 15. J. Blumenthal and D. Timmermann. Resource-Aware Service Architecture for Mobile Services in Wireless Sensor Networks. In Proc. of the International Conference on Wireless and Mobile Communications (ICWMC ), pp. 34–39, July 2006. 16. J. Liu and F. Zhao. Towards Semantic Services for Sensor-Rich Information Systems. In Proc. of the Second IEEE/CreateNet International Workshop on Broadband Advanced Sensor Networks (Basenets), October 3, 2005. 17. J. Liu and F. Zhao. Towards Service-Oriented Networked Embedded Computing. Technical Report MSR-TR-2005-28, Microsoft Research, February 2005.

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18. K.A. Hua, R. Peng, and G.L. Hamza-Lup. WISE: A Web-based Intelligent Sensor Explorer Framework for Publishing, Browsing, and Analyzing Sensor Data over the Internet. In Proc. of the 4th International Conference on Web Engineering (ICWE), pp. 568–572, July 2004. 19. J. King, R. Bose, Y.Hen-I, S. Pickles, and A. Helal. Atlas: A Service-Oriented Sensor Platform: Hardware and Middleware to Enable Programmable Pervasive Spaces. In Proc. of the 31st IEEE Conference on Local Computer Networks, pp. 630–638, November 2006. 20. L. Li and J. Halpern. A Minimum-Energy Path-Preserving Topology-Control Algorithm. IEEE Transactions on Wireless Communications, 3 (3): 910–921, 2004. 21. L. Li and J. Y Halpern. Minimum Energy Mobile Wireless Networks Revisited. In Proc. of the IEEE International Conference on Communications (ICC), June 2001. 22. S. Li, Y. Lin, S. Son, J. Stankovic, and Y. Wei. Event Detection Using Data Service Middleware in Distributed Sensor Networks. Special issue on Wireless Sensor Networks of Telecommunications Systems, 26 (2–4): 351–368, June–August 2004. 23. S. Madden, M.J. Franklin, J.M. Hellerstein, and W. Hong. TinyDB: An Acquisitional Query Processing System for Sensor Networks. ACM Transactions Database Systems, 30 (1): 122–173, 2005. 24. M. Kushwaha and I. Amundson, X. Koutsoukos, S. Neema, and J. Sztipanovits. OASiS: A Programming Framework for Service-Oriented Sensor Networks. In Proc. of the International Conference on COMmunication System softWAre and MiddlewaRE (COMSWARE), January 2007. 25. C. Marin and M. Desertot. Sensor Bean: A Component Platform for Sensor-based Services. In Proc. of the 3rd International Workshop on Middleware for Pervasive and Ad-Hoc Computing, November 28th – December 2nd 2005. 26. V. Rodoplu and T.H. Meng. Minimum Energy Mobile Wireless Networks. IEEE J. Select. Areas Commun., 17 (8): 1333–1344, August 1999. 27. R.S. Marin-Perianu, J. Scholten, P.J.M. Havinga, and P.H. Hartel. Energy-Efficient ClusterBased Service Discovery in Wireless Sensor Networks. In Proc. of the IEEE International Workshop on Wireless Local Networks (WLN), pp. 931–938, November 2006. 28. P. Schramm, E. Naroska, P. Resch, J. Platte, H. Linde, G. Stromberg, and T. Sturm. A Service Gateway for Networked Sensor Systems. IEEE Pervasive Computing, 3 (1): 66–74, January– March 2004. 29. M. Sgroi, A. Wolisz, A. Sangiovanni-Vincentelli, and J. Rabaey. A Service-Based Universal Application Interface for Ad Hoc Wireless Sensor and Actuator Networks. In W. Weber (Infineon), J. Rabaey (UC Berkeley), and E. Aarts (Philips), editors, Ambient intelligence. Springer Verlag, 2005. 30. V. Shnayder, M. Hempstead, B.R. Chen, G.W. Allen, and M. Welsh. Simulating the Power Consumption of Large-scale Sensor Network Applications. In John A. Stankovic and Anish Arora and Ramesh Govindan, editor, SenSys, pp. 188–200. ACM, 2004. 31. T. Gross, T. Egla, and N. Marquardt. Sens-ation: A Service-Oriented Platform for Developing Sensor-Based Infrastructures. International Journal of Internet Protocol Technology (IJIPT), 1 (3): 159–167, 2006. 32. W. Heinzelman and A. Chandrakasan, and H. Balakrishnan. Energy-efficient Communication Protocol for Wireless Sensor Networks. In Proc. of the Hawaii International Conference System Sciences, January 2000. 33. L. Zhuang, J. Zhang, Y. Zhao, M. Luo, D. Zhang, and Z. Yang. Power-aware Service-oriented Architecture for Wireless Sensor Networks. In Proc. of the 31st Annual Conf. of the IEEE Industrial Electronics Society (IECON), 2005.

Chapter 10

Multiscale Anchor-Free Distributed Positioning in Sensor Networks Bastian Katz and Dorothea Wagner

10.1 Introduction In recent years, expectations of large-scale wireless sensor networks becoming a practical solution for many tasks in monitoring and data-gathering increased notably [9). Despite the extensive research in both theory and practice, we still know the complexity of some of the most fundamental problems only with a high degree of idealization. Moreover, we also lack algorithms that could realize the vision of thousands of nodes that calibrate and process data in a distributed way, combining robustness and scalability. Reconstructing the nodes’ positions is one of those fundamental problems that arise early in sensor networks, known as the positioning or localization problem [1, 22]: On the one hand, there certainly is a need to know the nodes’ positions for basic network operations from topology control [19] to geographic routing [5, 14] as well as for the obvious demand to know where data or events are sensed in a network. On the other hand, when talking about sensor networks, we cannot hope for any powerful infrastructure like GPS due to comparably high costs and size requirements for receivers and the restriction that GPS does not work indoors. Many localization algorithms assume the presence of a fraction of nodes, which know their position, so-called anchor-nodes [8, 13, 20, 21, 24], but often, it will even be impossible to provide these beacons. Thus, anchor-free localization recently received more attention [7, 12, 16, 17, 24], i.e., positioning solely based on known characteristics of the wireless channel and information that nodes realistically can measure locally about their relative positions. For example, nodes can estimate distances using the received signal strength indicator (RSSI) or directions using multiple receivers or directional antennas [18]. Anchor-free localization turned out to be a hard problem in almost any setting; we give a short overview on results in Table 10.1. Localization is trivial if distances and directions between connected nodes are known and computationally easy if

B. Katz Universit¨at Karlsruhe, Germany e-mail: [email protected]

S.K. Makki et al. (eds.), Sensor and Ad Hoc Networks, C Springer Science+Business Media, LLC 2008 DOI: 10.1007/978-0-387-77320-9 10,

203

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Realization problem

Complexity

1-hop distances and directions (relative or absolute) 1-hop directions (relative or absolute) 1-hop distances Unit Disk Graph (UDG) only UDG approximation UDG with 1-hop distances UDG with 1-hop directions Absolute directions, distances, arbitrarily small errors Relative directions, distances, arbitrarily small errors

trivial in P (folklore, [7]) NP-hard [23] NP-hard [6] NP-hard [15] NP-hard [2] NP-hard [7] NP-hard [3] NP-hard (here)

only directions are known. Given only distances, the problem becomes NP-hard. Realizations of unit disk graphs (UDG) are even hard to approximate and remain hard if one knows either distances or directions. Recently, Basu et al. [3] have shown that the trivial case where distances and absolute directions are given becomes hard in the presence of arbitrarily small errors. This chapter closes an annoying gap with the proof that the more realistic realization problem with known relative distances and directions is also NP-hard in the presence of arbitrarily small errors. The complexity of positioning problems, however, is not the only problem we face. We identified the following important issues, which are not solved satisfactorily at the same time by any current positioning algorithm. Distributed computation: One of the most natural requirements for algorithms in sensor network localization is that an algorithm has to be performed in a distributed way. Although the parallelism of computation in wireless networks could be seen as a benefit, most algorithms either are centralized or try to break down centralized approaches to a distributed environment. Apparently, only a small class of approaches really work fully distributedly [3, 12, 17]. Energy awareness/congestion: Many algorithms that work in a distributed manner, and thus seem to be well-suited for sensor networks, in fact, demand all nodes to exchange data with all their neighbors as long as the algorithm is running. Among them are all approaches that use any local optimization, e.g. [12, 17]. Although these algorithms certainly are distributed, they ignore the fact that in sensor networks, this communication scheme is quite costly, as it causes interference and other sideeffects of congestion. Scalability and independence of deployment region: Comparing approaches for sensor network localization with the vision of large-scale networks [25], the most striking shortcoming of many proposed algorithms is that first, the issue of scalability almost never seems to be addressed at all, and second, algorithms highly rely on implicit assumptions made regarding the deployment of nodes, such as the convexity of the deployment region. Typically, algorithms are evaluated on scenarios with 200 to 1000 nodes in a rectangular area, leaving the question open whether the algorithm works in different setups, especially how much the size of the network influences quality and runtime.

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Our contribution to this facet of the localization problem is a novel algorithm scheme that overcomes these problems by combining the best centralized localization techniques with the powerful idea of multiscale optimization: The proposed algorithm distributedly reduces the positioning problem to small subproblems, which can be solved locally. Solutions are aggregated hierarchically, allowing for multiscale optimization in overlay networks without any of the disadvantages mentioned earlier. This chapter is organized as follows: In Section 10.2, we give a short description of the problem setup and some preliminaries. Section 10.3 proves the hardness of the localization problem with distances and relative directions in the presence of arbitrarily small errors. Our algorithm is presented in Section 10.4 along with simulation results in Section 10.5. Conclusions are presented in Section 10.6.

10.2 Preliminaries Throughout this chapter, we model a network as an undirected graph G = (V, E) with an embedding p : V → R2 and an orientation o : V → [0, 2π ) of the nodes. With respect to this embedding and orientation, distances dp and relative directions ωp,o between pairs of nodes u = v ∈ V are canonically denoted as dp (u, v) := |p(u) − p(v)| and ωp,o (u, v) := (p(v) − p(u)) − o(u) (mod 2π ) . Note that, unlike distances between nodes, directions are not symmetric. Thus, the input of a localization problem, i.e., local measurements on distances and directions, contains per edge one distance, but two direction measurements, one for each node incidence. We therefore model the input distances as function d : E → R+ and the input directions as function ω : E → [0, 2π )2 . To facilitate readability, we will rather use ω(u, v) and ω(v, u) as above for an edge {u, v} ∈ E instead of defining ω({u, v})1 and ω({u, v})2 . We denote a node v’s one-hop neighborhood in a graph G with N(G, v), its k-hop neighborhood with Nk (G, v) (both including v). A set of nodes V ⊂ V is called a dominating set, if for each node v, either v itself or one of v’s neighbors is in V .

10.3 Hardness Result Recently, Basu et al. [3] have shown that the localization problem is NP-hard if nodes know distances and absolute angles, i.e., nodes measure angles against a common north pole, both with an arbitrarily small error. We extend this problem to the less artificial case where nodes measure angles against their respective axis, i.e., without assuming any global knowledge:

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Problem 1 (Error-Realization) Given a graph G = (V, E), edge lengths d : E → R+ , relative edge directions ω : E → [0, 2π )2 and small , δ > 0, is there an embedding p : V → R2 and an orientation o : V → [0, 2π ), such that for all u, v with {u, v} ∈ E dp (u, v) ∈ [1 − ; 1 + ] and d(u, v) ωp,o (u, v) − ω(u, v) ∈ [−δ; δ]

mod 2π ?

In the following, we prove that it is NP-hard to find an embedding such that the measured distances and angles do not differ from the embedding by more than given, arbitrarily small factors and angles, respectively: Theorem 1 E RROR -R EALIZATION is NP-hard even for fixed, arbitrarily small error bounds , δ. Proof We prove this theorem by a reduction from Given an instance of 3S AT , we draw the corresponding instance canonically as shown in Fig. 10.1 with the building blocks, i.e., variables, wires, crossings, connectors, and clauses. From this drawing, we derive an input to our E RROR -R EALIZATION problem as follows. First, we observe how to design an input to the E RROR -R EALIZATION problem in order to force a graph to be embedded with fixed angles in any valid embedding: Let a graph G have a cycle of nodes we want to be realized as a polygon with prescribed angles. If we choose the input directions ω to all point outward (or all inward) by an angle of δ with respect to an arbitrary orientation of the nodes

C3

C3

C2

C2

C1

C1

x1

x1 x2

x2 x3

(a) 3SAT as Schematic drawing

x3

x1

x1 x2

x2 x3

x3

(b) 3SAT from building blocks

Fig. 10.1 Schematic drawing of a 3 S AT instance (a) and in a grid-like fashion with building blocks, i.e., variables, wires (horizontal/vertical), crossings, connections, and clauses (b)

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Fig. 10.2 A polygon with fixed angles. Input directions are dotted and differ all by δ from a polygon with the given angles

(see Fig. 10.2), every valid embedding of G that differs from ω by no more than δ for any edge-node incidence, embeds G as a polygon according to the given angles. We will exploit this fact in the following. Based on the aforementioned arguments, we construct variables by building a rectangle of four nodes. We then introduce an additional inner edge that can deviate from being parallel to the rectangle’s sides by δ in both directions (see Fig. 10.3). We also assign lengths to all edges, namely a, b, c ∈ R+ such that the triangle shown in Fig. 10.3 is valid. One can see that in every valid embedding of the six nodes, first, angles must comply with one of the drawings in Fig. 10.4, second, the edges AB and C D are maximally stretched, i.e., have lengths (1 + )b, while the edge X Y has its minimum length of (1 − )c, and third, either edges X A and Y C have length (1 + )a and BY and D X have lengths (1 − )a, or vice versa. We will call the former a true assignment, the latter a false. Now, the edges X A and BY correspond to the literals x and x respectively, i.e., a length (1 + )a corresponds to a true literal, length (1 − )a to false. Wiring, connecting, and crossing is comparably easy. The gadgets are shown in Fig. 10.5(a–d). Essentially, they all are rectangles with fixed angles, which therefore must have the same lengths for opposite edges. Variables and wires have all directions pointing outward, while in crossings and connectors, directions point inward by δ. These two kinds of gadgets are put together alternately (see Fig. 10.1(b)). Note that all rows have heights of ≈ a, but the width of columns is ≈ a only for columns corresponding to literals, while it is necessary for the other columns containing horizontal links to have width ≈ b like variables. The last gadget is a clause, shown in Fig. 10.5(e). If we choose x, such that (1 − )x = (3(1 + ) + 2(1 − )) · a ⇔ (5 + )a = (1 − )x ,

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i.e., even with the edges with length ≈ x having the shortest possible length (1−)x, there must be no more than two “short” edges on the right side, that is, at least one connected literal must be true, and more are always possible. On the other hand, it is easy to see how a valid assignment can be transformed into a valid embedding. Rows that correspond to an occurrence of a literal have the respective height, the other rows have height (1 + )a. Columns that correspond to a literal again have the width induced by the literal’s value, other columns have width (1 + )b.

10.4 Hierarchical Localization Although almost every anchor-free localization problem is hard – especially in the presence of errors, recent work has shown strengths and weaknesses of existing heuristic approaches. Obviously, any kind of purely incremental algorithm cannot prevent an increase in errors, but there are many other techniques that work quite

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well in some sense. The first observation is that we have many techniques at hand that could be used to localize small networks, although the best of them typically work in a centralized manner and sometimes are highly complex, e.g., use linear or semidefinite programming as in [4]. They seem to be unsuitable for larger networks, but on the other hand, they can still be used to let nodes localize some reasonably small neighborhood. For those algorithms that really work in a distributed way, a typical approach is to first find a folding free embedding, i.e., an embedding without overlappings of different parts of the network, and then perform any kind of local stress minimization. Examples are AFL [17] and EIGEN [12]. In order to embed the network folding free, the former spreads nodes between five heuristically chosen reference nodes, the latter uses a distributed version of a spectral graph layout algorithm. Both these approaches implicitly rely on the assumption that the deployment area has some regular shape, e.g., is convex ([17]). Moreover, these approaches (and more) extensively use local stress minimization to gain a good localization. This can certainly be done distributedly, but it incorporates mass pairwise communication – continuously, every node has to send its current position and receive positions from its neighbors. We do believe that this kind of mass concurrent communication has to be restricted as far as possible for any localization scheme to be applied in real networks, since this really is the worst case in terms of network congestion and energy consumption. Our approach, in contrast, tries to overcome the mentioned problems following two basic ideas: First, rather than being overly distributed, it seems reasonable for us to let a sample of nodes localize some (constant-size) neighborhood in a centralized fashion. This minimizes the communication overhead without violating the restriction that nodes only have small memory and computational power. Second, because iteratively putting those local solutions together would still lead to increasing errors in large networks, we adapt the idea of graph filtration and multiscale graph layout, which is known from graph drawing [11]. Graph filtration here denotes the process to successively restrict a graph to a fraction of nodes, i.e., starting with all nodes, a filtration is a sequence V = V0 ⊃ V1 ⊃ · · · ⊃ Vk = {ˆv }. In graph drawing, the usual way is then to find a layout top-down: Given a layout for the nodes from Vi , the nodes from Vi−1 \ Vi are placed according to some good guess based on the layout of Vi ; the resulting layout is refined by local optimization and so on. In [10], a variant has been proposed for sensor network localization, but again only in a centralized fashion. Moreover, this algorithm works only top-down, guessing initial distances and directions by dead reckoning. It thus cannot work for arbitrarily large networks, as these initial errors will become arbitrarily high. Our approach consists of both a bottom-up and a top-down stage: In the bottomup pass, we first choose a fraction of the nodes to collect and localize their neighborhood. For those pairs of chosen nodes that are close to each other, we introduce virtual edges (i.e., multihop connections), deriving distances and directions from the local solutions (see Fig. 10.6). This filtration step is done recursively on the resulting overlay network until we end up with a single node, to which we assign arbitrary coordinates.

210 Fig. 10.6 Filtering from a node’s point of view. An active node (center) collects its 3-hop neighborhood by local communication (a) Routes to close active nodes are stored. They become neighbors on the next-level overlay network (b) Distances and directions are derived from local solution

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(a) An active node’s neighborhood. Active nodes are drawn black.

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In the top-down stage, knowing local solutions and coordinates for the chosen subset of nodes is enough to assign coordinates to all nodes of one abstraction level. Optionally, local problems can be solved again to refine local solutions when the chosen subset of nodes know their final positions. This process is depicted in Fig. 10.7. Note that a main difference to other approaches is that in the top-down stage every node is assigned a position only once, without any refinement when other nodes have been placed, saving a lot of communication. A more detailed view on this technique is given in Algorithm 1: Given a connected graph G = (V, E) together with erroneous edge lengths d : E → R+ and relative edge directions ω : E → [0, 2π ), we first choose a dominating subset of nodes V ⊂ V . For the nodes in V , we use any central algorithm to localize their 3-neighborhood. For pairs of nodes that mutually lie in this neighborhood,

(a) Bottom-up stage

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Fig. 10.7 Two stages of the hierarchical localization. In the bottom-up stage (a) the input network (left) is filtered repeatedly until we reach an instance, which can be solved by a single node: On every level, a dominating set of nodes is chosen, virtual edges span between chosen nodes that lie in some neighborhood. Edge distances and directions are derived from local solutions on the current level. In the top-down stage (b) starting with the positions of the topmost level, the nodes of the next levels can be positioned successively using local solutions on the respective level

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Algorithm 1 LOCALIZE (G = (V, E), d, w) 1: if |V | = 1 then 2: return any localization 3: end if 4: choose dominating subset V ⊂ V 5: E ← ∅ 6: for all v ∈ V do 7: G v ← G[N3 (G, v)] 8: (pv , ov ) ← S OLVE C ENTRALLY(G v , d, ω) (s.t. pv (v) = 0, ov (v) = 0) 9: for all u ∈ V ∩ N3 (G, v) do 10: E ← E ∪ {{v, u}} 11: d (v, u) ← dpv (v, u) 12: ω (v, u) ← ωpu ,ou (v, u) 13: end for 14: end for 15: (p , o ) ← L OCALIZE(G = (V , E ), d , ω ) 16: for all v ∈ V do 17: for allu ∈ N3 (v) \ V do 18: (p(u), o(u)) ← (p(v), o(v)) ⊕ (pv (u), ov (u)) 19: end for 20: end for 21: return (p, o)

% V 3 | u ∈ N (G, v) , E := {u, v} ∈ 2

we derive distances d : E → R+ and directions ω : E → [0, 2π ) from the local solutions. We recursively apply the algorithm to G = (V , E ) and, given a localization for V from this recursion, localize the nodes in V \ V using the (refined) local solution of the closest node in V . Note that this scheme still has two degrees of freedom: The choice of the algorithm applied to local problems and the choice of V . We leave the choice of the centralized algorithm open, but assume that we select V in the following way: For a fixed number k of rounds, every node which neither has a neighbor in V nor is itself a member of V selects itself with a fixed probability 0 < c < 1. In an additional round, every node still fulfilling this condition selects itself with probability 1. This clearly ensures that a dominating set V is chosen after k + 1 rounds, and it further ensures that we can bound every node’s probability to be selected independently of the network’s structure by c ≤ P[v ∈ V ] ≤ 1 − c · (1 − c) , since at least in the case that a node is not chosen in the first round while one of its neighbors is, the node will not be selected at all. As an example, if c = 1/2 and k = 1, each node is chosen at least with probability 1/2 and at most with probability 3/4, as there is at least a 1/4 chance that one neighbor is chosen in the first round while the node itself is not.

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Although it is not possible to give a constant bound on the maximum node degree or on the maximum size of a three-hop neighborhood during the execution, our experiments on geometric graphs with their close interrelation between Euclidean and graph distances have shown that both node degrees and problem sizes did not increase in the overlay networks (see Section 10.5).

10.4.1 Distributed Algorithm As claimed, Algorithm 1 can completely be implemented in a distributed way; an outline is given in Algorithm 2. Starting with a setup where every node knows distance and direction measurements dN , ωN for its one-hop neighbors N, every node performs the k + 1 rounds of the selection algorithm, each including a communication with its direct neighbors. Afterward, the nodes have to share information with their three-neighborhoods to let close selected nodes know each other. If a node has chosen to be active on the next level, it applies the centralized algorithm to the current neighborhood and then knows its neighbors on the next level (with estimated

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Algorithm 2 localizedistributed (N, dN , wN ) lvl ← 0 N0 ← N, d0 ← dN , ω0 ← ωN active ← true while active do perform dominating set selection algorithm exchange 3-hop information with Nlvl neighbors if node is selected solve localization problem on N3lvl Nlvl+1 ← selected nodes from N3lvl store hops in N3lvl for neighbors Nlvl+1 derive dlvl+1 and ωlvl+1 from local solution lvl ← lvl + 1 else active ← false end if end while wait for first localization send localizations to (inactive) nodes in N30 to N3lvl−1

distances and directions) as well as the hops to route information there in the current neighborhood. This procedure is repeated until, on some level, the node either has no more neighbors or it has decided not to join the next level. In the first case, the node localizes itself to some arbitrary position, in the latter, the node waits until it receives a position from some other node. In any case, as soon as a node knows a localization, it sends localizations to its neighbors on all levels in which the node was active, based on its own position and the local solutions. Note that on each level, each node has to communicate only a constant number of times with its neighbors on that level while the number of levels is in O(log D). On the other hand, distances between communicating nodes increase with the level. However, empirically, in geometric graphs, the decreasing number of active nodes compensates the growing distances of neighbors easily and thus, the number of one-hop messages sent is in O(|V | log D). Nevertheless, routing communication between higher level neighbors is a crucial point: If we denote the overlay networks as G = G 0 , G 1 , . . . G k k ∈ O(log D), neighbors in G i can be up to 3i hops apart in G (at most D hops). Thus, it is not only impossible for a node v to store complete routes to neighbors on higher levels, but we would also need to pass this information along with the messages, which is prohibitive, too. A quite straightforward way to solve this problem would be to let the nodes on routes know how to route future messages: Given that messages can be routed between neighbors in G i , which is trivially true in G 0 , every edge in G i+1 is composed of at most three hops in G i . Thus, sending an additional message containing these three hops for every edge in G i+1 is enough to inform all nodes about this edge. By the selection of active nodes in the construction of the overlay connections, each node usually is part of at most a constant number of edges on a certain level. Hence, additional memory of O(log D) per node is sufficent for this task.

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to t in G i−1 . The node s also knows such a path to v1 in G i−2 and can add this information to the route: s − vi−2 − wi−2 − vi−1 −wi−1 − t. & '( ) path in G i−2

Repeatedly applying this scheme, s can send the messages with waypoints v0 −w0 − v1 − w1 − · · · − vi−1 − wi−1 − t. While the message is routed, passed waypoints can be removed and additional waypoints are added as earlier. The number of waypoints then never exceeds 2i + 1. An example is depicted in Fig. 10.9: The node s initially knows the target node t and adds the hops known in G 1 and G 0 to v0 w0 v1 w1 t. The message passes v0 and w0 and the next node from G 1 , v1 adds the waypoints v0 and w0 , which are necessary to reach w1 , etc. In any case, every node needs to store local solutions for every level in which it was active, and as long as local solutions do not grow larger than a constant bound, memory consumption for every node is in O(log D).

10.5 Implementation and Simulation Results We implemented the proposed algorithm in its centralized variant to run a variety of simulations on networks of different shapes, densities, sizes, and error characteristics. In our current implementation, we use a very simple force-directed layout algorithm to solve local subproblems and used k = 10 and c = 5% for the selection of a dominating set. For all tests, we evaluated a variation of the global stress RMS (GSR), i.e., the quadratic mean of the pairwise relative distance violation between the original distances between nodes in the graph di j and the distances in the reconstruction dˆi j ,

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which is very similar to the global energy ratio (GER) as defined by Priyantha et al. [17], but better suited for comparing different network sizes. However, both indices equally measure both large and small-scale errors, i.e., small values indicate that first, there is not much stress in local neighborhoods, and second, the global picture of the network is recovered correctly. Deployment Regions and Radio Range: We evaluated the implementation on six different deployment regions. Region types were squared, u-shaped, star-shaped, grid-like, donut-shaped, and one of an irregular pattern (see Fig. 10.10). In any case, the nodes were randomly distributed over the area; their radio range was then uniformly chosen to generate a specified average node degree, typically between 8 and 12. Errors: To evaluate the robustness of our algorithm, we introduced noise for both distances and directions, i.e., the input distances were normally distributed around the original values with a standard deviation of up to 30%, input directions with a standard deviation of up to 30. Note that this error model does not give a bound for possible errors. As in real-life scenarios, a big challenge for the algorithm is to deal with some measurements being almost completely wrong.

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Fig. 10.11 Exemplary localizations with standard deviation of distance error 15% and angular error 15 (average GSR values in parentheses). Both local and global structure are recovered correctly

Figure 10.11 shows exemplary localizations of (comparably small) networks of 2500 nodes with errors of standard deviations approximately 15% and 15 grad, respectively. The results show how close to reality localizations with typical GSR values (0.05 to 0.1, depending on the deployment area) are. In Fig. 10.12, results for different error characteristics are depicted for networks with 5000 nodes. For these tests, we chose an average degree of 12, matching with the simulations from [3]. For each combination, experiments were repeated until statistical significance has been attained with an α-level of 0.95 and a confidence interval of length 0.02 for GSR.1 We get very similar results for all scenarios: The algorithm is able to recover node positions very accurately for errors even with a standard deviation of 15% and 15 grad and above. For much larger errors, overall quality decreases due to failures of the local algorithm. Not surprisingly, best results are achieved for the typical benchmark scenarios of squared and star-shaped deployment regions, but our algorithm also performed very well on the deployment regions that seemed to be much harder to localize before. In addition, we ran our algorithm on different network sizes of up to 128,000 nodes. As expected, the runtime increased only linearly with the number of nodes (see Fig. 10.13(a)), while the quality is independent of the network’s size (see Figure 10.13(b)). Larger errors resulted in slightly higher runtimes only as an artifact

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of the slower convergence of the optimization algorithm. This completely complies with the demand for scalable localization algorithms. An evaluation of the algorithm with varying average node degree is depicted in Fig. 10.14. It shows how a higher average node degree allows to compensate for more severe errors while for lower errors, a less connected graph would be sufficient. During all our experiments,2 there was no subproblem, i.e., three-hop neighborhood, on any level that contained more than 140 nodes – except for tests with high average degree, where three-neighborhoods in the input graph became larger. On

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the average, subproblems contained around 60–70 nodes. For our implementation, we experienced that even for 128000 nodes, 10–12 levels were sufficient.

10.6 Conclusion and Future Work In this work, we addressed the problem of sensor network localization with both distance and relative direction measurements in the presence of errors. We have shown that the presence of arbitrarily small errors is enough to make this problem hard, generalizing the work of Basu et al. [3], waiving the assumption that nodes have global knowledge about their orientation.

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We presented a novel, distributed algorithm scheme, which combines robustness to fairly large errors with scalability and independence of the deployment region. The experimental evaluation yielded that this algorithm scheme recovered node positions very accurately for severe errors even with a quite na ”ive algorithm applied to the local subproblems. Here, next steps will be to combine the proposed scheme with more sophisticated algorithms to solve local problems, as it seems that positioning with large errors mostly fails due to the inability to reduce errors on early levels. Furthermore, different algorithms could make directional information dispensable, which is currently only needed for an initial layout of the force-directed layout algorithm.

References 1. J. Aspnes, T. Eren, D.K. Goldenberg, A.S. Morse, W. Whiteley, Y.R. Yang, B.D.O. Anderson, and P.N. Belhumeur. A Theory of Network Localization. IEEE Transaction on Mobile Computing, 5(12): 1663–1678, December 2006. 2. J. Aspnes, D.K. Goldenberg, and Y.R. Yang. On the Computational Complexity of Sensor Network Localization. In Proceedings of the 1st Intl. Workshop on Algorithmic Aspects of Wireless Sensor Networks (ALGOSENSORS’04), pages 32–44. Springer-Verlag, Heidelberg, 2004. 3. A. Basu, J. Gao, J.S.B. Mitchell, and G.Sabhnani. Distributed Localization Using Noisy Distance and Angle Information. In Proceedings of the 7th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC’06), 262–273.ACM Press, New York, 2006. 4. P. Biswas and Y. Ye. Semidefinite Programming for Ad hoc Wireless Sensor Network Localization. In Proceedings of the 3rd International Symposium on Information Processing in Sensor Networks (IPSN’04), 46–54. ACM Press, New York, 2004. 5. P. Bose, P. Morin, I. Stojmenovi ’c, and J. Urrutia. Routing with Guaranteed Delivery in Ad Hoc Wireless Networks. Wireless Networks, 7(6): 609–616, 2001.

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6. H. Breu and D.G. Kirkpatrick. Unit Disk Graph Recognition is NP-Hard. Computational Geometry: Theory and Applications, 9(1–2):3–24, 1998. 7. J. Bruck, J. Gao, and A. Jiang. Localization and Routing in Sensor Networks by Local Angle Information. In Proceedings of the 6th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC’05), 181–192. ACM Press, New York, 2005. 8. K.K. Chintalapudi, A. Dhariwal, and R.G. and Gaurav Sukhatme. Ad-Hoc Localization Using Ranging and Sectoring. In Proceedings of the 23th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM’04), IEEE Press, Piscataway, 2004. 9. D.E. Culler, D. Estrin, and M.B. Srivastava. Guest Editors’ Introduction: Overview of Sensor Networks. Computer, 37(8):41–49, 2004. 10. C. Erten, A. Efrat, D. Forrester, A. Iyer, and S.G. Kobourov. Force-Directed Approaches to Sensor Localization. In Proceedings of the 8th Workshop on Algorithm Engineering and Experiments (ALENEX’06), SIAM, Philadelphia, 2006. 11. P. Gajer, M. Goodrich, and S.G. Kobourov. A fast multidimensional algorithm for drawing large graphs. Computational Geometry: Theory and Applications, 29: 3–18, 2004. 12. C. Gotsman and Y. Koren. Distributed Graph Layout for Sensor Networks. In Proceedings of the 12th International Symposium on Graph Drawing (GD’04). Springer-Verlag, Heidelberg, 2004. 13. X. Ji and H. Zha. Sensor Positioning in Wireless Ad-hoc Sensor Networks Using Multidimensional Scaling. In Proceedings of the 23th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM’04), IEEE Press, Piscataway, 2004. 14. B. Karp and H.T. Kung GPSR: Greedy Perimeter Stateless Routing for Wireless Networks. In Proceedings of the 6th Annual International Conference on Mobile Computing and Networking (MOBICOM’00), pages 243–254, IEEE Press, Piscataway, 2000. 15. F. Kuhn, T. Moscibroda, and R. Wattenhofer. Unit Disk Graph Approximation. In Proceedings of the 8th International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (Dial-M’04), ACM Press, New York, 2004. 16. D. Moore,J. Leonard, D. Rus, andS. Teller. Robust Distributed Network Localization with Noisy Range Measurements. In Proceedings of the 2nd International Conference on Embedded Networked Sensor Systems (SENSYS’04), 50–61. ACM Press, New York, 2004. 17. N.B. Priyantha, H. Balakrishnan, E. Demaine, and S. Teller. Anchor-Free Distributed Localization in Sensor Networks. In Proceedings of the 1st International Conference on Embedded Networked Sensor Systems (SENSYS’03), 340–341, ACM Press, New York, 2003. 18. N.B. Priyantha, A. Chakraborty, and H. Balakrishnan. The Cricket Location-Support System. In Proceedings of the 6th Annual International Conference on Mobile Computing and Networking (MOBICOM’00), 32–43, IEEE Press, Piscataway, 2000. 19. P. Santi. Topology Control in Wireless Ad Hoc and Sensor Networks. Wiley, September 2005. 20. C. Savarese, J. Rabaey, and J. Beutel. Locationing in Distributed Ad-Hoc Wireless Sensor Networks. In Proceedings of the 26th International Conference on Acoustics, Speech, and Signal Processing (ICASSP’01), IEEE Press, Piscataway, 2001. 21. A. Savvides, C.-C. Han, and M.B. Srivastava. Dynamic Fine-Grained Localization in Ad-Hoc Networks of Sensors. In Proceedings of the 7th Annual International Conference on Mobile Computing and Networking (MOBICOM’01). ACM Press, New York, 2001. 22. A. Savvides, M.B. Srivastava, L. Girod, and D. Estrin. Localization in Sensor Networks. Wireless Sensor Networks, 327–349, Kluwer, Norwell, 2004. 23. J.B. Saxe. Embeddability of weighted graphs in k-space is strongly NP-hard. In Proceedings of the 17th Allerton Conference in Communications, Control and Computing, 480–489, 1979. 24. Y. Shang, W. Ruml, Y. Zhang, and M.P.J. Fromherz. Localization from Mere Connectivity. In Proceedings of the 4th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC’03). ACM Press, New York, 2003. 25. M. Tubaishat and S. Madria. Sensor Networks: An Overview. IEEE Potentials, 22(2): 20–23, 2003.

Chapter 11

Evaluation of Time Synchronization over Mobile Ad hoc Networks Xiwei Zhao, Vinayak Ganapathy, Niki Pissinou, and Kia Makki

11.1 Introduction Contiguous time is an important requirement for many applications in Mobile Ad hoc NETwork (MANET). In research on time synchronization, the seminal contribution given by Lamport on event ordering in distributed systems [12] defines the rule – to preserve event ordering and causality using logical clock. An important consequence of this has been the adoption of monotonically increasing virtual clocks in any application design concerning distributed systems, including mobile and ad hoc networks. According to the IEEE 802.11 IBSS (Independent Basic Service Set) specification [8], clocks leap to the fastest known virtual clock in their neighborhood to achieve convergence – faster clocks synchronize slower clocks time synchronization function (TSF). This principle has had the remarkable achievement of preserving the total ordering of events, yet is prone from a security perspective [20] and physical clock resets [22]. To avoid temporal and causal discrepancies, distributed systems such as MANET have the option of using two schemes. These are global time synchronization (GS) and local time synchronization (LS). The first requires clocks in all participating nodes leap to the fastest clock in the system, and the latter requires every participating node to preserve its local clock and only record the offset time to its neighbors. This research presents a comparison between global and local time synchronization schemes as applied to MANET. The evaluation has been carried out with reference to convergence of time – this time is taken by the entire MANET to reach a time-synchronized state from ab initio. This essentially translates to how fast the entire MANET can be time synchronized. Also, the influences of mobility and stochastic time-delay on convergence of time are discussed. The motivation behind X. Zhao Telecommunications and Information Technology Institute, Florida International University, Miami, FL33174 USA e-mail: [email protected]

S.K. Makki et al. (eds.), Sensor and Ad Hoc Networks, C Springer Science+Business Media, LLC 2008 DOI: 10.1007/978-0-387-77320-9 11,

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the comparison is, to investigate which time-synchronization scheme is better suited for a given MANET. As true suitability of a given scheme is highly dependent on MANET topology, the aim of the research is to determine the upper bounds for synchronization efforts for particular MANET topologies. Thus, geometries, which force slowest time synchronization for a given scheme, are the candidates for determining the upper bound for time synchronization . The outline of this chapter is as follows: Section 11.2 presents the related work; Section 11.3 presents the problem, a mathematical treatment to each scheme, and comparison of the schemes with reference to mobility and stochastic time delay; Section 11.4 demonstrates results from numerical calculations. Finally, Section 11.5 presents the concluding remarks

11.2 Related Work Research body regarding time synchronization in wireless sensor networks mainly concerns itself with synchronization of local time via remote interprocess message exchange. Issues of concern include compensation for the skewness and kurtosis of physical hardware’s clock [22]; influence of network dynamics [9] and security [11]; sensor design, application, and resource limitations [2]. For MANET, some additional issues of concern regard multihop time synchronization. A rich set of solutions exist for MANET time synchronization [17]. Solutions are available for lightweight time synchronization protocols based on message exchange. The areas of concern are limited to the extent to which nodes constituting the network can transmit and receive radio waves via their air interfaces. Fancier interfaces may be highly directional, multifrequency antennas [1,21] with abilities of time-stamping transmitted packets as far down the physical layer as possible [9,13]. Relay mechanisms for forwarding synchronization primitives beyond the reach of an air interface. This entails the use of a dominating set of nodes, which cover the entire network for effectively diffusing the synchronization primitives [6]. The solutions either assume the existence of this set or form one of their own. From a security perspective, trust is now considered as an important parameter for judging and electing intermediaries and members of dominating sets [5]. Based on assumed criteria and approach adopted for time synchronization, recent research in time synchronization has been categorized into six classes [17]: • • • • •

Whether time sources used are internal or external Whether synchronization is carried out continuously or on demand Whether domain of synchronization is flat or hierarchical Whether approach is based on determining clock’s rate or offsets Whether participating nodes use an operational clock over the actual physical clock or invasively synchronize internal time, and • Whether synchronization is carried out instantly or spread over time.

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This research adds an additional perspective – to determine whether the approach used for time-synchronization is LS [2,6,15,16,18,19,22] or GS [1,4,7,10,13,14] in nature. The approach allows classification of research into two distinct groups, one of which can be considered to provide better opportunity for synchronizing time over the other. Elson, et al. [3] combines both local and global time synchronization schemes. It uses GS when synchronizing within one broadcast area, but uses LS when references nodes corresponding to different broadcast areas to exchange timesynchronization messages. The first known research into the application of IEEE 802.11 standard [8] to MANET is provided in [14], and here, we follow [14] in adopting the use of IEEE 802.11 standard [8] to MANET.

11.3 Problem Formulation and Analysis This section compares Local Time Synchronization (LS) and Global Time Synchronization (GS) schemes. The schemes are evaluated with regard to their convergence time while maintaining robustness toward mobility and stochastic time-delay. This section is divided into four subsections. The first subsection states the assumptions that are binding to the other sections, the second subsection compares GS and LS schemes from the perspective of convergence of time, and the third subsection compares GS and LS schemes from the perspective of mobility, and the fourth subsection compares GS and LS schemes from the perspective of stochastic time-delay.

11.3.1 Assumptions Assumptions 1 A MANET has a seed node.

(A1 )

This research is based on the beacon mechanism as described in IEEE 802.11 TSF [8]. The node that happens to be the first member of a MANET is defined as a seed node. The seed node is expected to instantiate a beacon period as part of its routine. The interval time between these beacons is known as target beacon transmission time (TBTT). Other nodes willing to participate in the MANET are required to conform to the beacon period as defined by the seed node. At each TBTT, all participating nodes contend for a beacon broadcast. This can result in collision – a performance factor that has been disregarded in this research because it affects both GS and LS schemes. At the end of contention, only one node manages to beacon in a broadcast area, and this is typically defined by its radio range. Additionally, due to “hidden terminal phenomenon” [8], some node may receive two or more beacons at the same TBTT. Such cases have also been treated as collisions.

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Assumption 2 MANET Nodes distribute homogeneously.

(A2 )

It is assumed that each participating node experiences the presence of equal numbers of neighbors regardless of its spatial position within the MANET. Thus, any node i has n − 1 neighbors, where n is the unit size within a broadcast area. Furthermore, it is assumed that the MANET consists of N nodes, and N = |MANET| = m · n, m ∈ I + ,

(R1 )

where | | denotes the size (numbers of participating nodes) of the network. Notwithstanding the scheme of time synchronization, the only known method for a node to exchange data regarding time synchronization is by periodically broadcasting a beacon. Assumption LS1 In a given topology, LS time-synchronization is considered complete when each participating node has broadcasted a beacon at least once. (ALS1 ) Participating nodes maintain a noninvasive local clock – one whose value is not changed by knowledge of external, and perhaps more precise and accurate clocks. Instead, the nodes maintain a vector containing time differences between their local clocks and all participating node clocks within the radio range of their air interface. This vector, henceforth called dT-vector, facilitates time interconversion between transacting node-pairs. (A2 ) simplifies the problem formulation by allowing the dTvector to maintain a fixed size of (n − 1) entries, and therefore imposes a constant working-memory cost on the node. Some LS schemes may violate (A2 ) by implementing on-demand services to gain energy-efficient performance. Such violations are omitted from this research for normalizing service comparisons with GS schemes. Assumption GS1 In a given topology, GS time-synchronization is considered complete when each participating node has attained the fastest MANET clock. (AGS1 ) In GS scheme, a MANET is considered time synchronized when the fastest time is dispersed throughout the MANET. Although an arbitrary clock can be chosen as a predefined standard clock, the IEEE 802.11 specification [8] suggests the selection of the fastest clock available among all participating nodes within an Independent Basic Service Set (IBSS) in ad hoc mode. For a MANET, this implies the selection of the fastest available clock among all participating nodes within a broadcast area, or, within the radio range of an air interface. Participating nodes maintain an invasive local clock – one whose value is changed every time a faster clock is detected within the broadcast area. The change can be carried out instantaneously, or spread over a period of time.

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11.3.2 Comparison of Time Convergence Due to beacon contention, GS and LS schemes involve a fair degree of randomness, and an exact figure regarding time-convergence cannot be guaranteed. Instead, it is intended to determine the probability that the entire MANET has been synchronized by a particular time interval. This time interval is expressed in terms of TBTTs. Let k denote the number of elapsed TBTTs. Then, the LS’s probability (i.e., the entire MANET has been synchronized by k) shall be compared with the GS’s probability (i.e., the entire MANET has been synchronized by k). A higher probability of one scheme (that the MANET has been completely time-synchronized after k TBTTs) will lead to the conclusion that the scheme performs better than the other in terms of time-convergence. Furthermore, (A2 ) implies that each node has to contend with its n − 1 neighbors to beacon at each TBTT interval: 1, 2, . . . , k. 11.3.2.1 Local Time Synchronization (LS) Scheme Given (A1 ), (A2 ), and (ALS1 ), the entire MANET can be substituted by m IBSSs, each IBSS consisting of n nodes. Then, synchronization of the entire MANET implies that each of the m IBSSs are also synchronized and, in turn, this implies that each participating node within each IBSS has beaconed at least once. Let P(i, k) denote the probability that i nodes of an IBSS have beaconed in k TBTTs. Since only one node can beacon at each TBTT, P(i, k) = 0, whenever k < i.

(RLS1 )

The argument behind (RLS1 ) is that, the n nodes of an IBSS need at least n TBTTs for each node to successfully beacon, and consequently satisfy ALS1 . Trivially, P(1, 1) = 1, and P(1, k) =

1 , k > 0. n k−1

(RLS2 )

The argument behind (RLS2 ) is there is always a node beacon at each TBTT within an IBSS. Moreover, it is rare that the same node beacons at each of k TBTTs. As shown in Appendix I, lemma 1, we have P(i, i) =

i! . (n − i)!n i

(RLS3 )

In addition, when i > 1 P(i, k) = P(i, k − 1) ·

i n−i +1 + P(n − 1, k − 1) · n n

(RLS4 )

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The argument behind (RLS4 ) is that the ith node can beacon in k TBTTs in only two ways: • when i nodes have already beaconed in k − 1 TBTTs and no new node will beacon at the next TBTT, or • when i − 1 nodes have beaconed in k − 1 TBTTs. After that, only one of the n−i +1 nodes (a new node) will beacon after failing to do so in the previous k − 1 TBTTs. Using (RLS1 ) through (RLS4 ), individual probabilities P(n, k) can be generated for all k. Then, the probability P(N, k) that the entire MANET is synchronized after k TBTTs is obtained as follows: P(N , K ) = [P(n, k)]m .

(RLS5 )

The argument behind (RLS5 ) is that, time synchronization of each IBSS is independent of others. 11.3.2.2 Global Time Synchronization (GS) Scheme The assumption (AGS1 ) implies that, the fastest time has been delivered through to the farthest participating node in a MANET. This is because the probability of the farthest node in a MANET to be time synchronized will be lower than any of the intermediate participating nodes. Given a typical MANET, many message delivery routes may exist, and therefore, the fastest time may be diffused along any of these routes. Moreover, due to inherent nature of MANET, time diffused along one route may influence and accelerate diffusion along other routes. To simplify the analysis of such a scenario, we consider two geometries. • Case I: Participating nodes lie along a line (1 dimension), and • Case II: Participating nodes lie along a circle (2 dimensions). The following notational conveniences hold for both cases I and II: let d denote the Cartesian distance between any pair of neighboring nodes; let L denote the Cartesian distance between the node possessing the fastest time and the node farthest from it; and hop distance h is defined as h = 1/2(n − 1)·d, so that using (A2 ), a given hop will essentially cover 1/2(n − 1) nodes on either side of the beacon node (by symmetry, n − 1 should be even). Case I Given (A2 ), consider a MANET with all participating nodes along a straight line (Fig. 11.1). For this geometry, L = l · d, where, l ∈ I + .

(RGS2 )

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h|n=2 d …

A

B

L

Fig. 11.1 Describing relation between d, h, and L for case I. This illustration assumes that node A possesses the fastest time and node B is the farthest node in the given MANET

We can partition the nodes in two – those nodes lying within the single-hop range h of the beacon node, and the outliers. Using (AGS1 ), the probability at which the node farthest from the node with fastest clock is synchronized can be determined. We denote this probability P(L, k) for l nodes dispersed homogeneously with internode distance d and successful in synchronizing time within k TBTTs. In order that P(L, k) be determined, we consider the following: By (A1 ), (A2 ), any node will contend with n − 1 neighbors to broadcast its beacon in a TBTT. P(i · d, 1) =

1 , for i = 1, 2, . . . , (n − 1)/2, n

(RGS3 )

and P(i · d, 1) = 0, for i = (n + 1)/2, (n + 3)/2, . . . , ∞

(RGS4 )

Also the probability for all nodes i, which are lying within a single hop of range h can be determined from Appendix II: j P(i · d, j) = 1 − n−1 i ≤ (n − 1)/2 and j = 1, 2, . . . and, from Appendix II, n lemma 2, we have P(i · d, j) = P(i·, j − 1) + {P((i −

1 n−1 ) · d, j − 1) − P(i · d, j − 1)} · , (RGS5 ) 2 n

in which i > (n − 1)/2 and j = 2, 3, . . . . In fact, any two-dimension MANET topology should include at least two independent routes toward the farthest node. Case II Extending the MANET geometry with all participating nodes to lie along a circle (Fig. 11.2), the distance L shall correspond to the circumferential distance between two nodes lying along the diameter. Thus, (RGS2 ) holds when the total number of nodes in this geometry is 2l. Circular geometry facilitates analysis by presenting only two routes along which the fastest time can be disseminated from one node to another. As a conservative simplification to calculate the probability that the farthest node is time synchronized, the coupling effect of those two routes is only considered at the farthest node.

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Fig. 11.2 Describing relation between d and L for case II. This illustration assumes that node A possesses the fastest time and node B is the farthest node in the given MANET

d

A

B

L

Since two independent, symmetric routes exist for achieving time synchronization , the probability Pθ (L, k) for successfully synchronizing time within k TBTTs will be obtained as Pθ (L , k) = 2P(L , k) − P(L , k)2 .

(RGS6 )

As mentioned earlier, due to symmetric routes, (RGS6 ) is grossly simplified; however, it suggests that as the number of routes between a pair of nodes increases, the rate of time synchronization actually increases. It is claimed that, a circle represents the worst case MANET topology for GS time synchronization possible in two dimensions. Thus, the probability for any two- or three-dimensional MANET to be time-synchronized within k TBTTs will be higher due to increased numbers of alternative routes available for diffusing the fastest time.

11.3.3 Comparison with Reference to Mobility 11.3.3.1 Mobility and LS Scheme In LS scheme, whenever a node receives the beacon from a neighbor, it measures the time difference between itself and the neighbor, populating one element in the dTvector. Thus, the nodes are considered time synchronized. When the node receives beacons from all its neighbors, and the dT-vector is fully populated, the node is considered to be locally time synchronized. Protocols implementing the LS scheme can only achieve local time synchronization. To diffuse a common time between any two nodes in a MANET, it is necessary to know the MANET’s global topology. First, a route between two chosen nodes must be known. Then, the time transformation can be carried out along the route, hop by hop. This implies LS protocols must be aided by a routing protocol to synchronize time over the entire MANET. Moreover, each dT-vector corresponds to given topology – a spatial synchronized state. Whenever the MANET topology changes, the state of time synchronization is

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lost, and dT-vectors at some nodes requires an update. Thus, a dynamic MANET topology may decelerate time synchronization with the following LS scheme. This can be illustrated with the movement of a node in a set of k TBTT intervals. We can split the k TBTT intervals in two groups: T1 and T2 . In T1 , from 0 to k1 , consider that a node is in region C with n − 1 neighbors. In T2 , from k1 + 1 to k, the node moves to region D with another n − 1 neighbors. Regions C and D must be different so that the node can be considered to have moved in terms of topology. During T1 , the node receives beacons from m1 nodes in region C. When the node moves to region D, the node shall receive beacons from other m2 nodes. Given that n − 1 < m 1 + m 2 ≤ 2(n − 1),

(RLS6 )

the probability that the mobile node recovers its time-synchronized state at the end of T2 can be calculated as follows: • Event 1: During T1 , n − m2 − 1 nodes have beaconed, • Event 2: During T2 , m 2 + 1 nodes must beacon. Here, the additional term “1,” refers to the mobile node itself.

The probability of the mobile node recovering its time-synchronized state at the end of T2 is given by PT 2 = P(n − m 2 − 1, k1 ) · P[(n, k)|(n − m 2 − 1, k1 )] = P[(n, k), (n − m 2 − 1, k1 )].

(RLS7 )

As the event (n, k) and the event (n − m2 − 1, k1 ) are independent, PT 2 = P(n, k) · P(n − m 2 − 1, k1 ) < P(n, k)

(RLS8 )

because P(n − m2 − 1, k1 ) < 1. Thus, a node’s mobility will retard the MANET’s time synchronization . 11.3.3.2 Mobility and GS Scheme The GS scheme has advantage over LS scheme in terms of mobility in a MANET. Since only the standard time should be adopted within the MANET (here, the fastest time), and time synchronization would not be influenced by the movement of nodes. In fact, a node’s movement can accelerate the distribution of reference time during the synchronization phase of the GS scheme. Following the analysis in Section 11.3.2.2, in a ring MANET, the probability that the farthest node is

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synchronized, P(L, k), is only related to the distance and the elapsed time. Any movement would not affect the farthest distance L and the elapsed time k. Thus, GS is robust to mobility. Again, the ring topography is the worst case for GS to performance, comparing with any two-dimensional MANET topology. Thus, mobility of any node may form better MANET topology regarding GS scheme’s performance.

11.3.4 In Terms of Stochastic Time Delay In practice, GS schemes are not feasible without compensation for lack of precision. At each beacon, stochastic time delay may dirt time stamps. Precision errors will accumulate as the distance and time elapsed increase, resulting in widening distortion of reference time. In fact, a MANET’s reference time will never converge to the fastest time, but will drift along with accumulation of precision error. On the other hand, LS schemes are robust to precision errors. Even though every node still needs to beacon its time, every receiver would not update its own time, but only records the offset to update its dT-vector Precision errors may dirt the dT-vector, but they would not accumulate.

11.4 Theoretical Results In this section, LS and GS time-synchronization schemes were compared by obtaining the probabilities of converging time by varying parameters n – the number of neighbors in any broadcast area, and L – the maximum distance between a node possessing the fastest time and another node participating within the MANET (the farthest node). As node density is given, MANET topology would not affect the convergence time of LS. But for GS scheme, only the worst case–circle topology is considered.

Fig. 11.3 Convergence time vs. probabilities when n = 9

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Fig. 11.4 Convergence time vs. probabilities when n = 35

By analyzing Figs. 11.3, 11.4, and 11.5, it is observed that when n > 9 and h < 5, the performance of GS scheme is better than the LS scheme, with regard to convergence time. Figure 11.5 shows that GS is still better than LS, even if the MANET expands to seven hops, as long as the node density is high (n ≥ 55). GS time-synchronization scheme has advantage over LS time-synchronization scheme when nodes are mobile. If the participating nodes are synchronized to the fastest time, time synchronization will not be influenced by mobility. In fact, mobility will actually promote the distribution of fastest time. On the other hand, LS time-synchronization scheme will suffer due to mobility as a large overhead is involved when participating nodes have to adjust their dT-vectors to accommodate for new neighbors.

Fig. 11.5 Convergence time vs. probabilities when n = 55

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11.5 Conclusion and Future Work This research presents a theoretical basis for comparison between GS and LS timesynchronization schemes. It has been pointed out that GS schemes have guaranteed faster convergence probabilities than LS schemes whenever node density is greater than nine nodes/broadcast area, and maximum hop count of the MANET is less than five. Presently, laboratory verification is underway to corroborate theoretical results obtained herein. Further research will focus on relaxing parts of assumptions A2 , ALS1 , and AGS1 .

Appendix I Lemma 1 Inside an n-node IBSS, the probability that i nodes have beaconed after i TBTTs is given by: P(i, i) =

1 i! · (n − i)! n i

(RLS3 )

Proof. Omitting beacon collision, the event (1, 1), which a node beacons after a TBTT, will surely occur. Thus, P(1, 1) = 1. The event (2, 2), which two different nodes beacon after two TBTTs, can only be achieved via event (1, 1), because only one node is permitted to beacon at each TBTT. Additionally, the node that beacons at the second TBTT must be different from the node that has already beaconed at the first TBTT. Thus, P(2, 2) = P(1, 1) ·

n n−1 n! 1 n−1 = · = · 2. n n n (n − 2)! n

Similarly, event (3, 3) can only evolve from the event (2, 2). Additionally, the node that beacons at the third TBTT must be different from the nodes that beacon at the first two TBTTs. Thus, P(3, 3) = P(2, 2)

n! 1 n−2 n! 1 n−2 = = . n (n − 2)! n 2 n (n − 3)! n 3

By induction, the probability of the events of (4, 4), . . . , (i, i), . . . , (n, n) are obtained as n! 1 n−3 = · 4,... n (n − 4)! n i n! i! · i , . . . , P(n, n) = n P(i, i) = (n − 1)! n n P(4, 4) = P(3, 3) ·

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Appendix II P(L, k) can be further resolved to provide insight into time synchronization as the fastest time is diffused via intermediate nodes. For an intermediate node i lying between the source node and the farthest node, P(i·d, k) implies the probability that the fastest time has diffused a distance i·d in k TBTTs. This may not necessarily imply that fastest time has not diffused beyond node i toward (i + 1)th node or further. To determine the probability that the fastest time has actually diffused into ith node and no further than that, a correction probability factor needs to be applied to determine a more accurate snapshot regarding time synchronization of the ith node: Pcut (i · d, k) = P(i · d, k) − P((i + 1) · d, k).

(RGS7 )

Analogous to case I, we partition the nodes in two – those lying within the singlehop range h of the beacon node, and the outliers, so that, using (AGS1 ), the probability at which the node farthest from the fastest node is synchronized can be determined. When i ≤ 1/2(n − 1), the fastest time disperses within the radio range of a single hop: P(i · d, k) = 1 −

n−1 n

k

1 , i = 1, 2, . . . , (n − 1) 2

(RGS8 )

The argument behind (RGS8 ) is that after k TBTTs, the probability that the node with the fastest time has no chance to beacon is [(n − 1)/n]k , which also is equal to 1−P(i·d, k). For outlier nodes, the probability will be influenced by the correction provided by (RGS7 ). Lemma 2 All nodes of MANET are dispersed homogeneously along a line with internode distance d, and not all within a unit hop distance. Then, when i > 1/ (n − 1), the probability that the ith node is successfully time synchronized within k 2 TBTTs is given by: 1 n−1 · d, k − 1] − P(i, k − 1)} , P(i, k) = P(i, k − 1) + {P[ i − 2 n when i >

n−1 2

and k = 2, 3, . . . ,∞

(RGS5 )

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Proof. n−1 · d, k − 1 P(i · d, k) =P(i · d, k − 1) + P i− 2 % 1 n−1 + 1 · d, k − 1 · −P i− 2 n n−1 + P i− + 1 · d, k − 1 2 % 1 n−1 + 2 · d, k − 1 · −P i− 2 n n−1 + P i− + 2 · d, k − 1 2 % n−1 1 −P i− + 3 · d, k − 1 · 2 n ··· 1 + {P((i − 1) · d, k − 1) − P(i · d, k − 1)} · n n−1 · d, k − 1 =P(i · d, k − 1) + P i− 2 % 1 − P(i · d, k − 1) · , n the argument behind (RGS5 ) is that the ith node can be synchronized in k TBTTs in the following ways: when the ith nodes have been synchronized in k − 1 TBTTs, or, when the [i − (n − 1)/2]th node just synchronized its time with the fastest node in the k − 1 TBTT and shall beacon at the next TBTT, or, when the [i − (n − 1)/2 + 1]th node just synchronized its time with the fastest node in the k − 1 TBTT and shall beacon at the next TBTT, or, ... when the (i − 1)th node just synchronized its time with the fastest node in the k − 1 TBTT and shall beacon at the next TBTT.

References 1. Dai, H. and Han, R., “Tsync: A lightweight bidirectional time synchronization service for wireless sensor networks,” ACMSIGMOBILEMob. Comput. and Commun. Rev., vol. 8, no. 1, pp. 125–139, 1994. 2. Elson, J. and R¨omer, K., “Wireless sensor networks: a new regime for time synchronization,” in SIGCOMM Comput. Commun. Rev., vol. 33, no. 1, pp. 149–154, Jan. 2003.

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3. Elson, J., Girod, L. and Estrin, D., “Fine-grained Network Time Synchronization using Reference Broadcasts,” in SIGOPS Oper. Syst. Rev., vol. 36, pp. 147–163, Dec. 2002. 4. Ganeriwal, S., Kumar, R., Adlakha, S. and Srivastava, M. B., “Network-wide Time Synchronization in Sensor Networks,” NESL Technical Report, 2003. 5. Ghosh, T., Pissinou, N. and Makki, K., “Collaborative Trust-Based Secure Routing against Colluding Malicious Nodes in Multi-Hop Ad Hoc Networks,” Proceedings of 29th Annual IEEE Conf. Local Computer Networks (LCN), Tampa, Florida, USA, Nov. 2004 6. Graham, S., Kumar, P. R., “Time in general-purpose control systems: the Control Time Protocol and an experimental evaluation,” in Decision and Control, 2004, CDC. 43rd IEEE Conference on Decision and Control, vol. 4, pp. 4004– 4009, 14–17 Dec. 2004. 7. Hu, A. and Servetto, S. D., “Algorithmic Aspects of the Time synchronization Problem in Large-Scale Sensor Networks,” in proc. Mob. Netw. Appl., vol. 10, no. 4 pp. 491–503, Aug. 2005. 8. IEEE 802.11 (ISO/IEC 8802-11: 1999), “Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) specification,” 1999. 9. Intanagonwiwat, C., Govindan, R., Estrin, D., Heidemann, J., Silva F., “Directed Diffusion for Wireless Sensor Networking,” in Transactions on Networking, Feb. 2003. 10. Karp, R., Elson, J., Estrin, D. and Shenker, S., “Optimal and Global Time Synchronization in Sensornets,” CENS Technical Report 0012, Center for Embedded Networked Sensing, University of California, Los Angeles, Apr. 2003. 11. Kusy, B., Dutta, P., Lewis, P., Maroti, M., Edeczi, A., and Culler, D., “Elapsed time on arrival: A simple and versatile primitive for canonical time synchronization services,” Int. J. Ad Hoc Ubiq. Comput. Vol. 2, No. 1, 2005. 12. Lamport, L., “Time, clocks, and the ordering of events in a distributed system,” in Commun. ACM, vol. 21, no. 7, pp. 558–565, Jul. 1978. 13. Liao, C., Martonosi, M. and Clark, D. W., “Experience with an adaptive global-synchronizing clock algorithm,” Proceedings of 11th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA), pp. 106–114, New York, June 1999. 14. Mock, M., Frings, R., Nett, E. and Trikaliotis, S., “Continuous clock synchronization in wireless real-time applications,” in 19th IEEE Symposium on Reliable Distributed Systems (SRDS’00), pp. 125–133, Nurnburg, Germany, Oct. 2000. 15. Moon, S., Skelley, P. and Towsley, D., “Estimation and Removal of Clock Skew from Network Delay Measurements,” in proc. 19th IEEE INFOCOM 1999, New York, Mar, 1999. 16. R¨omer, K., “Time Synchronization in Ad Hoc Networks,” in proc. 2nd ACM International Symposium on Mobile Ad Hoc Networking & Computing (MobiHoc’01), Long Beach, Oct. 2001. 17. R¨omer, K. and Blum, L. M., “Time Synchronization and Calibration in Wireless Sensor Networks,” In I. Stojmenovic (Ed.), Wireless Sensor Networks, Wiley and Sons, 2005. 18. Sichitiu, M. L. and C. Veerarittiphan: “Simple, Accurate Time Synchronization for Wireless Sensor Networks,” In proc. IEEE Wireless Communications and Networking Conference (WCNC’03), IEEE, vol. 2, pp. 16–20, Mar. 2003. 19. Solis, R., Borkar, V. S. and Kumar, P. R., “A New Distributed Time Synchronization Protcol for Multihop Wireless Networks,” In proc. 45th IEEE Conf. Decision and Control (CDC ’06), San Diego, Dec. 2006. 20. Song, H., Zhu, S., Cao, G., “Attack-resilient time synchronization for wireless sensor networks,” in: IEEE MGSS, vol. 12, pp. 765–772, 2005. 21. Wang, H., Yip, L., Maniezzo, D., Chen, J. C., Hudson, R. E., Elson, J. and Yao, K., “A Wireless Time-Synchronized COTS Sensor Platform Part II – Applications to Beamforming,” Proceedings of IEEE CAS Workshop on Wireless Comm. And Networking, Pasadena, CA, Sept. 2002. 22. Zhang, L., Liu, Z. and Xia, C. H., “Clock Synchronization Algorithms for Network Measurements,” Proceedings of 21st IEEE INFOCOM 2002, New York, Jun. 2002.

Chapter 12

Universal Modular Framework for Sensor Networks Eli De Poorter, Benoˆıt Latr´e, Ingrid Moerman, and Piet Demeester

12.1 Introduction Research in wireless sensor networks has known a tremendous boost in the last few years [1]. Wireless sensor networks (WSNs) are becoming more and more widespread. Whereas sensor networks were originally used mainly for monitoring purposes, new applications such as process and asset monitoring, disaster intervention, and wireless building automation are rapidly emerging. These new and advanced applications impose new challenges and requirements on the design of WSNs. Special devices such as actors [2] are required, which can interact with the environment. Additionally, each application has its own set of specific QoS requirements, such as maximal delay, desired reliability, etc. Also, the sensors can become mobile, thus making communication more and more complex. Considering these facts, it is clear that future sensor networks will know a wider diversity regarding the capabilities of the sensor nodes. Whereas the first generation of sensor networks consisted of a large number of homogeneous nodes, additional computing power or functionality will be required in some. Sensor networks are thus evolving into heterogeneous networks. Even though new applications for sensor networks are being set up frequently, there is currently no protocol framework, which is widely applicable. For each layer, an application developer has to determine which protocols are most suited for the purposes of the intended application, and has to go through the complicated process of combining them into an optimized protocol stack. This comes at a great development cost, impeding the growth of sensor networks and hindering the cooperation between different sensor networks. Accordingly, there is currently a large need for a universally applicable framework for sensor networks in which existing protocols can easily be integrated. E. De Poorter Department of Information Technology (INTEC), Ghent University – IBBT – IMEC, Gaston Crommenlaan 8, bus 201, B-9050 Gent, Belgium e-mail: [email protected]

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In this chapter, we propose a new universal framework for wireless sensor networks. This framework is a generic one, which can be used by different types of applications. It is designed to allow for easy integration of current protocols and takes into account the heterogeneity of the sensor nodes. Furthermore, energyefficiency is optimally supported through cross-layer optimization. Finally, in order to support a wide range of applications, advanced functionality such as QoS and mobility can be supported. The remainder of this chapter is organized as follows. An overview of related work in the area of sensor network architectures and cross-layer communication in wireless networks is given in Section 12.2. Section 12.3 gives an insight of how we see WSNs evolving toward heterogeneous networks, and how we tend to cope with this evolution using node classifications. In Section 12.4 we discuss the advantages of a modular architecture. Some challenges when designing a modular architecture are given in Section 12.5. The universal modular framework itself is discussed in Section 12.6. In Section 12.7 we go into more detail on how to handle dependencies between modules. Finally, Section 12.8 gives some future directions and Section 12.9 concludes the chapter.

12.2 Related Work A myriad of protocols for sensor networks has been proposed in the last few years, taking on issues such as medium access, routing, and data manipulation. Most of the early developed protocols are based on a strict layered structure [1,3]. This way, a specific level needs no information about the inner workings of lower or higher levels. Functionalities at different layers can be altered without any impact on the other layers. This strict separation has proven to be a good solution for wired networks, allowing the protocol designers to focus only on a small subset of network functionality. However, it is not suitable for wireless networks [4,5,6]. On the other hand, the use of a cross-layer approach has several advantages: optimization is possible at several layers at once, a global optimization can be achieved and conflicts in optimizations at different layers can be avoided. Many cross-layer architectures have been proposed for ad hoc networks [4,7,8,9] and in lesser extent for sensor networks [11,12,13]. An overview is given in Fig. 12.1. Figure 12.1(a) shows the traditional layered structure. In the approach of Fig. 12.1(b), new interfaces between the existing layers are defined. An overview of protocols adopting this method can be found in [10]. A major drawback of this approach is the introduction of many dependencies between the different layers. A more holistic view is used in Fig. 12.1(c). A shared database is used, accessible by all the layers. Retrieval of parameters incurs additional overhead, but the resulting architecture is more clear. Another class of cross-layer design is the complete merge of two or more layers of the protocol stack, e.g. the MAC-layer and the routing layer as seen in Fig. 12.1(d). The last approach, shown in Fig. 12.1(e), completely discards the layered structure. The required functionalities are implemented in different modules or heaps [14], which interact and can be changed easily.

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Application Layer

Application Layer

Application Layer

Network Layer

Network Layer

Network Layer

MAC Layer

MAC Layer

MAC Layer

Physical Layer

Physical Layer

Physical Layer

Physical Layer

(a)

(b)

(c)

(d)

Cross-layer

Application Layer

Joint Network and MAC Layer Optimizations

Modular

(e)

Fig. 12.1 Overview of different cross-layer approaches. (a) Traditional layered structure (b) Passing of parameters across several layers (c) Holistic approach maintaining the different layers (d) Optimalizations spanning several layers (e) Modular approach

The cross-layer approach forms a first step toward a more uniform architecture for sensor networks. In order to boost the development of sensor networks, all the protocols defined for sensor networks need to be glued together. This vision is also stated in [15] where Culler et al. claim that “the primary factor currently limiting progress in sensornets is not any specific technical challenge but is instead the lack of an overall sensor network architecture.” Therefore, they propose an overall sensor network architecture (SNA) [15] based on the sensor protocol (SP) [16,17], which forms a narrow waist that sits between the network layer and link layer. SP is responsible for handling data transmission, data reception, and neighbor management. However, SNA does not take into account the heterogeneity of the sensor nodes and has limited support for advanced network functionalities. The framework we propose will handle these problems.

12.3 Future Sensor Networks 12.3.1 Vision of Future Networks As stated in Section 12.1, sensor networks are currently often considered as very large networks consisting of homogeneous nodes. In the future, these networks will evolve into heterogeneous networks where the nodes do not share the same properties. Generally speaking, we envisage two kinds of networks: custom-made and general purpose ones. The custom network is specifically designed to support one or more functions. Thus, custom networks can be highly optimized in terms of energy consumption or desired QoS. A drawback is that these networks will be expensive and only serve a single purpose. As such, little value will be given to compatibility with other protocols. This type of network will be used for applications with stringent requirements. General-purpose networks on the other hand, are more adaptable to changing network conditions and will support a wide range of applications that are unaware of underlying network conditions. These networks will have to support multiple tasks in one network. Through the use of both cheap sensor nodes and more

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expensive nodes, which can fulfill advanced functions, considerable cost reductions can be made when deploying a sensor network. Also, in a home environment, nodes with new functionalities can be added after deployment. Since these nodes may come from different manufacturers, the network will exist of nodes with diverging capabilities. As such, great care should be taken to allow interoperability with existing protocols. It is this class of networks that is targeted by our proposed framework.

12.3.2 Node Classification As said in the previous section, we envisage a network with diverse types of nodes. To prevent an unmanageable wild-growth of divergent nodes, we assume these different nodes can be categorized into several classes of nodes with similar characteristics. We assume that most sensor networks will not contain more than three classes of strongly differing nodes. However, if the need arises, the number of classes can be tailormade to the application needs following a similar logic as described in this chapter. Based on their capabilities, we define three types of nodes: lightweight, advanced and computing nodes. The lightweight nodes have very limited resources and only support basic functionalities, hence only the basic protocols are implemented. For example, the routing protocol can be as simple as forwarding sensed data to a more advanced node. The advanced nodes have more sophisticated functionalities. They implement the advanced functionality, which is needed for a scalable and energy-efficient WSN, such as advanced routing, clustering, and data-aggregation protocols. As such, advanced nodes typically fulfill the functions of relay nodes. The computing nodes are the most powerful nodes and have a much larger battery capacity (e.g., connected to the power grid) and computing power. They offer additional services, such as QoS, mobility support and network monitoring, which are not required for data gathering and relaying, but are necessary for more demanding applications. For example, a monitoring protocol can present valuable information for optimizing the routing protocol or for supporting mobility. Computing nodes thus fulfill regulating and supporting functions in addition to routing functions.

12.4 Modular Approach The evolution of sensor networks as described earlier clearly shows the need for an optimized, generic, application independent solution in which sensor protocols can be integrated. A long-term solution should be optimized to support heterogeneity and be adaptable to future advancements such as the creation of new physical carriers. Therefore, we have defined an architecture where functionality is divided in modules that interact with each other. This modular approach has several advantages.

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• Duplication of functionality can be avoided. Classic examples of duplicate functionalities are error correction and retransmission, which are currently implemented in several layers of the protocol stack. • Depending on the capabilities of the node, more modules (and thus network functionality) can be added. This way, heterogeneous networks can be supported. • By allowing intermodular parameter exchanges, cross-layer optimizations are possible. This results in much more energy-efficient protocols. Protocol information (such as neighbor tables) can be shared, resulting in better cooperation between protocols and less storage overhead. • Through the replacement of modules, it is easy to adapt to changing network conditions and future developments. The proposed modular framework is intended to be implemented on top of an existing operating system such as TinyOS [18] or SOS [19]. We envisage a compiler environment with several implementations of each module. When faced with an application scenario, application developers can choose which modules are required for a working solution (e.g., whether or not mobility or QoS support is needed). The framework should also benefit protocol developers: the interaction of the new protocol with existing network solutions can easily be investigated by choosing different implementations of the interacting modules. Thus, the freedom when choosing the appropriate modules allows for detailed fine-tuning of the framework for specific applications and allows for advanced testing of different networking aspects. Thus, various applications and networks with diverging requirements can be designed on the same foundations.

12.5 Challenges When Designing Modular Protocols Developing protocols in a modular way is a new paradigm and requires adjustments on the approach of designing network protocols. Some challenges when designing functional modules are the following: • The parameters to be exchanged by the different modules have to be determined. The exchanged parameters should have a substantial impact on the performance of the modules and the global system. The performance increase should at least compensate for the additional complexity introduced by the cross-modular interaction [20]. • There is a need to identify which parameters need to be optimized at design-time and which at runtime. When we are optimizing at design-time, optimal operation points are calculated offline for various predefined operational conditions. These operation points are then used at runtime. This means that a look-up table is used, which maps the optimal operational points for given operational settings. Generally, runtime solutions are more flexible and hence are better suited for dynamic networks, but these will require more complex nodes, leading to larger

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energy consumption. Depending on the complexity of the problem and the nature of the applied modules, real-time or offline solutions may be adopted. • The framework can be adaptive to changing network or application conditions. For example, it could be beneficial to have more than one routing module and to activate one of them depending on the network/application environment. • Due to the modular design, functional and regulating modules depend on the information of other modules. However, when replacing modules, it is possible that not all of the required information is available to the framework. When designing modules, one should keep in mind how the module will react when other modules do not supply some key parameters. Possible ways to define the available parameters are handled in Section 12.7. • When designing modules, careful consideration should be given to mutual dependencies. In particular, circular dependencies (where a steady-state cannot be obtained) should be avoided. For example, when choosing the next hop node, the decisions of the routing module (shortest path) may interfere with decisions of the QoS module (reliable link) or the energy management module (hop with most remaining battery power). To prevent unceasing competition, a priority system or arbiter (taking into account the different preferences) should be developed (see also Section 12.6.2). The interaction between different modules should thus be thoroughly examined.

12.6 Universal Modular Framework As an example of these principles, we have designed a universal modular framework (UMF) for sensor networks. A schematic overview of the universal modular framework is shown in Fig. 12.2. Generally speaking, UMF can be regarded as a hybrid combination of the architectural approaches shown in Fig. 12.1 (c) and (e). We distinguish four major parts in the UMF. The middle part is formed by the “Modular Heterogeneous Sensor network Architecture” or Mohesa. This part contains the modules which implement the needed protocols for the sensor network. A “Common Application Interface” between Mohesa and the applications is provided, which facilitates the deployment of different types of sensor networks. Further, a “Physical Interface” is provided, which can be adopted to interact with various types of physical layers. And finally, a common cross-layer database is used to form a generic interface for the exchange of cross-layer parameters. In the following sections, we give an example of a possible configuration of the sensor network, using the universal modular framework.

12.6.1 Cross-Layer Data Repository The main task of the cross-layer data repository is to provide a shared storage space for variables and to define a protocol that Mohesa’s modules can use to exchange parameters with other modules and layers.

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Load balancing

Multi-interest

Clustering

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Network Testing

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Basic modules

Optional Transmission control Congestion control

In order delivery

Physical Interface

PHY A PHY B

Fig. 12.2 Proposed universal modular framework for sensor networks

Even though it is possible for the modules to interact directly with each other, this does not promote reusability and interoperability. Therefore, we only allow interaction through a cross-layer database (see Fig. 12.3). The shared cross-layer database forms an independent data-repository (represented as a vertical layer in Fig. 12.2), which contains several data structures. Modules can register, request, or modify the needed parameters through well-defined interfaces. Thus, modules can interact with stored packets, can register to variables that are of interest to them and even create new variables or data structures to share [21] with other modules. Finally, the

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Fig. 12.3 In our modular approach, functionality is divided in modules, which interact with a central data-repository

cross-layer data-repository can have provisions for indicating which parameters are available. Using the cross-layer data-repository, modules can work together to fulfill advanced network functions. As an example, we give a possible interaction of the QoS module with some functional modules. • Several routing protocols exist, which can offer multiple next-hop candidates (e.g., Directed Diffusion [22]). The QoS module can request these from the database and can select the most energy-efficient, the fastest, or the most reliable one. • Once the optimal next hop has been determined, the QoS module can inform the transmission module of the required priority of the packet. Based on this priority, the transmission module knows the correct buffer for queuing the packet. • Finally, the QoS module can request the MAC module to reduce the transmission delay by selecting a lower back-off value for high-priority packets. Some examples of parameters which could (and probably should) be made available are the following: • For each neighboring node, the wake-up times, its position, its mobility information, the associated link quality, its remaining battery power, and its role (lightweight, advanced, or computing node) should be made available. • For each QoS class, the required reliability, the maximum delay, and the expected traffic load should be known. • For each current packet, its QoS class, the next-hop candidates, the number of hops it has traversed, and the time it has traveled.

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A more detailed study of cross-layer exchanges in sensor networks will follow in later work.

12.6.2 Modular Hetorogeneous Sensornetwork Architecture (Mohesa) Mohesa forms the core of the universal modular framework. It contains the modules which implement the network protocols. Application or protocol developers can select the needed protocols “a la carte”, depending on their needs. For the ease of application developers, in Fig. 12.2, the framework makes a visual separation into “basic modules” (which have to be supported in every wireless node), “advanced modules” (which should be supported by several nodes to obtain a scalable and energy-efficient network) and “optional modules”, which can be added according to the needs of the network. Internally, we discern two major types of modules: functional and regulating modules. Functional modules are modules, which are called when there are incoming or outgoing packets in the system. They are needed to either actively process the data flow (such as a MAC module, a data aggregation module, or an error check module) or to set up a correct processing state for the packets (such as setting the transmission power or checking QoS restraints). Thus, functional modules are called by a scheduler whenever a packet arrives at a node or whenever the node has packets to transmit. Regulating modules implement protocols, which do not actively process the data flow, but instead are needed for a correct internal state of the node. They are called regularly, independently of any actual packet processing. Typical examples are synchronization, position discovery, or energy management modules. The difference between both types of modules is schematically shown in Fig. 12.4.

Module X Regulating modules (periodic)

Timer Timer

Execution scheduler

Module Y

Timer

Module Z Packet arriving

Module A

Module B

Functional modules (processing)

Fig. 12.4 Functional modules are called upon receiving or sending a packet, regulating modules are called regularly

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12.6.2.1 Functional Modules We illustrate the principal elements with some example modules, starting with some functional ones. • The MAC module in lightweight nodes can be very simple: packets are sent using a simple CSMA/CA mechanism. The MAC module in advanced nodes is more advanced. For example, it can be responsible for generating time slots in which lightweight nodes can send their packets. Other possible features include giving priority to some packets, changing its wake-up scheme according to the traffic rate and required delay, or implementing some form of fairness. • Each node will have modules taking care of transmission control. The basic modules will handle segmentation and error correction. More advanced nodes can also be equipped with an advanced module, which can buffer packets for batch transmission. Finally, computing nodes can take care of complex transmission control functions, such as in-order delivery and congestion control. • The routing module in lightweight nodes can be very simple, e.g. just forwarding all generated data packets to a nearby advanced or computing node. Advanced nodes implement full-routing capabilities: they can create routes based on metrics such as hop distance or remaining battery power. Finally, computing nodes can have functionalities for translating and routing the sensor network packets to an IP-backbone. • Some modules are only implemented in sufficient capable nodes. For example, the computing nodes may provide QoS by examining incoming packets, adjusting their priority based on the time they are on their way and the distance they still have to travel. To fulfill reliability constraints, packets can be duplicated to a second route. Intermediate, noncomputing nodes only have to look at the packet priority, regardless of the required end-to-end QoS. Thus, services such as QoS can be offered to the application even if only a small subset of the nodes are computing nodes. • Several routing protocols exist where multiple next-hop candidates are stored in the routing table. After these candidates are selected by the routing module, a load balancing module can be used to select the optimal next-hop among these candidates. If the node is capable, the load balancing module can be replaced by a fully functional QoS module. The order in which modules are called is handled by an execution scheduler. The execution scheduler contains several call sequences. Depending on the situation, the appropriate call sequence is initiated. More advanced nodes will contain more advanced call sequences to handle more complex tasks. In Fig. 12.5 an example call sequence is given for handling locally generated packets in the different types of nodes. 12.6.2.2 Regulating Modules The second type of modules, which do not actually process packets, but instead influence the behavior of other modules, are called regulating modules.

12 Universal Modular Framework for Sensor Networks Execution scheduler

Execution scheduler

1. Application layer 2. Forwarding module 3. Segmentation module 4. Error correction module 5. Simplified MAC module 6. Retransmission module

1. Application layer 2. Clustering module 3. Data aggregation module 4. Routing module 5. Load balancing module 6. Batch transmission module 7. Segmentation module 8. Error correction module 9. Advanced MAC module 10. Retransmission module

Lightweight node

Advanced node

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Computing node

Fig. 12.5 Example call sequence when generating a packet in the different node types

The regulating functions implemented by the different types of nodes are shown in Table 12.1. Advanced regulating functions are typically found in computing nodes: since they are called often they limit the amount of time the node can spend in a sleeping state. There are many other possible regulating modules. For example, a topology control module could be developed. This module requests the discovered neighbors and, based on the estimated signal-to-noise ratio, selects a subset from those to which no connection may be made. The undesirable nodes can then be hidden by updating the cross-layer database with the new neighbor information. A last example of a regulating module is a role assignment module. The exact role of a node (lightweight, advanced, or computing node) can be determined at design time, but can also be determined based on the neighboring nodes. For example, when an overabundance of advanced nodes is detected, some advanced nodes can switch to a lightweight modus, provided that the necessary basic modules are available. Finally, note that some functionality can be implemented in both regulating modules and functional modules. For example: a node can contain a regulating

Table 12.1 Some regulating modules in the different types of nodes Type of node

Implemented functionality

Lightweight node

Neighbor Discovery Basic Power Management Basic Energy Management

Advanced node

Neighbor Discovery Synchronization Advanced Power Management Advanced Energy Management

Computing node

Neighbor Discovery Synchronization Advanced Power Management Advanced Energy Management Network Monitoring Position Discovery

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module for managing global QoS and a functional module where QoS can be monitored per packet.

12.6.3 Application Layer Mohesa provides a common application interface toward the application layer. This will ease application development as application designers do not need to know the specific characteristics of the underlying sensor network [23]. The uniform interface will guarantee a smooth interaction between applications and network modules. This interaction is necessary because some modules have a strong need for interacting both with other modules and with the application layer. Some examples of these interactions are given as follows: • In many scenarios, the method of data aggregation should be dictated by the application layer. Depending on the application, data aggregation can be as simple as calculating the average of several data sets or realize complex data processing. This requires a strong interaction of the data aggregation module with the application layer. On the other hand, also the QoS module should be informed by the data aggregation about the amount of introduced delay. • Localization is needed by many applications. It can be used for tracking purposes or decisions in the application layer, or for routing purposes. The position of the node may be calculated using GPS, controlled by the application, or based on radio information. As such, there is a strong need for interaction of the localization module with the application layer and the network modules.

12.6.4 Physical Layer The physical layer is a separate layer as its properties largely depend on the design of the hardware. In order to cope with different hardware nodes, the interface between the modular framework and the physical layer should be clearly defined. This is done at the “Physical Interface.” This Physical Interface can be extended to support various types of physical layers but still provides a common interface to Mohesa. The importance of interaction of other layers with the physical layer is profound as it results in strong optimizations of the protocols.

12.7 Coping with Interdependencies Between Modules In a truly universal framework, any kind of protocol can be integrated. However, this may lead to problems regarding interoperability. For example, a routing protocol may be developed, which assumes that all nodes are synchronized, or a QoS module may depend on the possibility of the MAC protocol to overhear packets for other destinations. Thus, there is clearly a need to verify and control dependencies between modules.

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We envisage two main approaches to ensure compatibility between modules. The first approach uses profiles consisting of compatible modules. The second approach is based on the characteristics of modules: one can either use a descriptive method where each of the individual characteristics are described, or one can classify protocols into groups with similar characteristics. The first method is through the use of standardized profiles. These contain sets of modules that are known to be compatible with each other and specify all known interdependencies. Profiles can either be created by enterprising individuals, or by an official standardization institute. By standardizing profiles for specific application domains, the development of sensor applications can be simplified. The second method for determining dependencies between modules is based on a descriptive approach. The first way to describe characteristics is by describing a number of possible implementation issues for each type of module. • Some characteristics of a MAC module are: whether it makes use of duty-cycling (uses sleeping periods), whether it uses contention or is contention-free, whether it is synchronous or asynchronous, whether it makes use of polling, whether it can overhear packets for other destinations, whether it has need of a second communication channel, whether it implements retransmissions, whether it supports broadcasts, etc. • Routing protocols characteristics can be based on the routing methods: datacentric, location based or hierarchical. Other characteristics can indicate whether the routing module supports mobility or path recovery, in which way QoS is supported, etc. When every module indicates the characteristics that are needed for their wellfunctioning, interdependencies between modules can be verified and controlled. The second way to use the descriptive approach is by using classification methods. Several efforts have been made to classify similar protocols into a hierarchical tree structure [24,25]. Similar protocols can be categorized in the same leaf of the tree, making it obvious which protocols have the same characteristics. A syntax can be developed whereby each module has a generic classification number indicating the function of the module, and more specific number indicating the characteristics of the protocol (see Fig. 12.6). For example: routing protocol B needs the presence of a synchronized MAC module (1.1.1.∗) or a MAC module designed to specifically work with this routing protocol (1.1.4.5). Furthermore, since this routing protocol already includes data-aggregation, no other data aggregation module (6.* ) may be implemented. The requirements for routing protocol B then become: (1.2.* OR 1.3.5.1) AND (NOT 6.* ). One disadvantage of the classification method using trees is that it is difficult to categorize new hybrid protocols that do not neatly fit into one of the developed classes. As such, the descriptive approach based on characteristics may be better suited for an innovative domain such as wireless sensor networks.

∗ corresponds

with the modules included in the subgraph that has vertex 1.1.1 as its root.

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1.2

Single channel

1.1.1

1.1.1.2 S-MAC

Multiple channel

1.1.3 Contention free

Asynchrone

1.1.1.1 T-MAC

Double channel

1.1.2

Synchronized

1.3

1.1.2.1 LPL

1.1.2.2 B-MAC

1.1.3.1 L-MAC

Fig. 12.6 An example classification of MAC modules with their corresponding classification number

12.8 Future Work We have explored several design issues and implementation possibilities for building a modular sensor network architecture. The framework presented here is only a preliminary proposal toward a universal sensor network architecture. Several challenges must still be overcome before we can truly speak of an overall sensor network architecture. In order to promote the development of new protocols, protocol designers need to analyze the other parts of the system at a fairly high level. Thus, the cross-layer framework should process several node, packet, and link statistics and present them at the right level of abstraction. Future work will focus on possible methods for this information exchange. The information needs of several network protocols will be thoroughly analyzed and based on this information, the cross-layer interface will be defined and finally put to test with several classes of protocols. We will further investigate whether there are any performance penalties in going with a universal framework rather than an implementation tailored to the application. We will also investigate the amount of overhead introduced by the use of the UMF. We presume that the additional overhead of the cross-layer interface will be compensated by the reduction of duplicate functionalities and storage of data structures. This would be in line with similar research, which concludes that the incurred overhead is minimal [16]. More research will be needed before any final conclusions can be made. Future research will also focus on designing modular network protocols, which are optimized for heterogeneous networks. In particular, we are interested in finding

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ways to exploit the additional capabilities of computing nodes in network consisting mainly of simple lightweight nodes. Our research will also comprise ways to autonomously assign nodes to classes of comparable capabilities and characteristics. Furthermore, the framework could be expanded with a role-assignment module, which decides at runtime which modules are activated, or which version of the module should be used. Lastly, the feasibility of the framework will be experimentally validated in a heterogeneous hardware testbed. Finally, our framework does not address any security related aspects. Security could be integrated using an independent method at MAC, routing and application level. However, we envisage the addition of a security module, which could use the cross-layer framework to provide a systemwide level of security.

12.9 Conclusion A lot of additional research is needed before sensor networks can be widely adopted. Current work mostly focuses on scalable and energy-efficient protocols. Although this research is very valuable for the development of sensor networks, there is at present no optimized architecture in which these solutions can be implemented. Support for energy-efficiency and heterogeneity has to be implemented at an architectural level, not only in isolated protocols that do not take the layer interaction into account. Furthermore, in order to promote interoperability of protocols and to reduce the cost of application development for sensor networks, there is a strong need for an application independent solution. Therefore, we propose a universal modular framework useful for a wide range of applications. The modular design has several key advantages: • Duplication of functionality is prevented; • Due to the possibility of cross-module information exchange more energyefficient protocols are supported; • Heterogeneity is promoted: modules can be added to a node according to its capabilities; • Through the replacement of modules, it is easy to adapt to changing network conditions and future developments. We have explored several ways for protocols to interact with each other. We are convinced that the use of a cross-layer interface can provide sufficient abstraction of the inner working of protocols to allow for effective cooperation between different modules. Also, we have shown that several requirements for future sensor networks, such as QoS, mobility and energy-efficiency, cannot be supported at a single protocol level. These functionalities should be implemented in dedicated protocols, which require a strong interaction with other protocols, such as routing and MAC protocols. These interactions are fully supported by the proposed modular framework.

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Finally, we are convinced that networks will become more and more heterogeneous, and that a universal sensor network architecture should support this evolution. The use of a modular framework is thus a very promising approach for sensor networks. Acknowledgments This research is partly funded by the Fund for Scientific Research – Flanders (F.W.O.-V., Belgium), by The Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen) through a Ph.D.grant for E. De Poorter and B. Latr´e and by the IBBT-WBA and IBBT-IM3 projects.

References 1. Akyildiz, I., Su, W., Sankarasubramaniam, Y., and Cayirci, S., “A survey on sensor networks”, IEEE Communications Magazine, Vol. 40, No. 8, August 2002, pp. 102–114 2. Akyildiz I., Kasimoglu, I.H., “Wireless sensor and actor networks: Research challenges”, Ad Hoc Network Journal (Elsevier), Vol. 2, No. 4, October 2004, pp. 351–367 3. Stojmenovic, I., “Handbook of sensor networks: Algorithms and architectures”, WileyInterscience, ISBN: 0471684724, December 2005 4. Srivastava, V., Motani, M., “Cross-layer design: A survey and the road ahead”, Communications Magazine, IEEE , Vol. 43, No. 12, December 2005, pp. 112–119 5. Chlamtac, I., Conti, M., and Liu, J., “Mobile ad hoc networks: Imperatives and challenges”, Elsevier Ad Hoc Networks, Vol. 1, No. 1, July 2003, pp. 13–64 6. Zhang, Y., Cheng, L., “Cross-layer Optimization for sensor networks.” New York Metro Arena Workshop 2003, New York, NY, September 2003 7. Toumpis, S., Goldsmith, A.J., “Performance, optimization, and cross-layer design of media access protocols for wireless ad hoc networks”, ICC 2003 – IEEE International Conference on Communications, May 2003 pp. 2234–2240 8. Conti, M., Maselli, G., and Turi, G., “Cross-layering in mobile ad hoc network design”, IEEE Computer, Vol. 37, No. 2, February 2004, pp. 48–51 9. Shakkottai, S., Rappaport, T.S., Karlsson, P.C., “Cross-layer design for wireless networks”, IEEE Communication Magazine, Vol. 41, No. 10, October 2003, pp. 74–80 10. Melodia, T., Vuran, M.C., Pompili, D., “The State of the art in cross-layer design for wireless sensor networks”, in Proceedings of EuroNGI Workshops on Wireless and Mobility, Springer Lecture Notes on Computer Science, LNCS 388, Como, Italy, July 2005 11. Marr´on, P.J., Lachenmann, A., Minder, D., Hahner, J., Rothermel, K., and Becker, C., “Adaptation and cross-layer issues in sensor networks”, in Proceedings of the First International Conference on Intelligent Sensors, Sensor Networks & Information Processing (ISSNIP 2004), pp. 623–628, December 2004 12. van Hoesel, L., Nieberg, T., Wu, J., and Havinga, P.J.M., “Prolonging the lifetime of wireless sensor networks by cross-layer interaction”, Wireless Communications, IEEE, Vol. 11, No. 6, December 2004, pp. 78–86 13. Kwon, H., Kim, T.H., Choi, S., and Lee, B.G., “A cross-layer strategy for energy-efficient reliable delivery in wireless sensor networks”, Wireless Communications, IEEE Transactions on, Vol. 5, No. 12, December 2006, pp. 3689–3699 14. Braden, R., Faber, T., and Handley, M., “From protocol stack to protocol heap: Role-based architecture”, SIGCOMM Computer Communication Review, Vol. 33, No. 1, January 2003, pp. 17–22 15. Culler, D., Dutta, P., Eee, C.T., Fonseca, R., Hui, J., Levis, P., Polastre, J., Shenker, S., Stoica, I., Tolle, G., and Zhao, J., “Towards a sensor network architecture: Lowering the

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waistline”, in Proceedings of the Tenth Workshop on Hot Topics in Operating Systems (HotOS X), 2005. Polastre, J., Hui, J., Levis, P., Zhao, J., Culler, D., Shenker, S., and Stoica, I., “A unifying link abstraction for wireless sensor networks”, SenSys ’05, San Diego, CA, USA, November 2005, pp. 76–89 Ee, C.E., Fonseca, R., Kim, S., Moon, D., Tavakoli, A., Culler, D., Shenker, S., and Stoica, I., “A modular network layer for sensornets”, in Proceedings of the 7th USENIX Symposium on Operating Systems Design and Implementation (OSDI 2006), Seattle, WA, November 2006 TinyOS operating system, http://www.tinyos.net/ SOS operating system, https://projects.nesl.ucla.edu/public/sos-2x/ Kawadia, V., Kumar, P.R., “A cautionary perspective on cross-layer design”, Wireless Communications, IEEE, Vol. 12, No. 1, February 2005, pp. 3–11 Lachenmann, A., Marr´on, P.J., Minder, D., Gauger, M., Saukh, O., and Rothermel, K., “TinyXXL: Language and Runtime Support for Cross-Layer Interactions”, in Proceedings of the Third Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks, Reston, VA, USA, pp. 178–187, September 2006 Intanagonwiwat, C., Govindan, R., and Estrin, D., “Directed diffusion: A scalable and robust communication paradigm for sensor networks”, Mobile Computing and Networking, 2000, pp. 56–67 Romer, K., Kasten, O., Mattern, F., “Middleware challenges for wireless sensor networks”, Mobile Computing and Communications Review, Vol. 6, No. 2, October 2002 The Mac Alphabet Soup: a MAC protocol taxonomy, https://apstwo.st.ewi.tudelft.nl/ koen/MACsoup/taxonomy.php Akkaya, K., Younis, M., “A survey of routing protocols in wireless sensor networks”, Elsevier Ad Hoc Network Journal, Vol. 3, No. 3, 2005, pp. 325–349

Chapter 13

Application and Evaluation of Hierarchical Agglomerative Clustering in Wireless Sensor Networks Chenjuan Zhou and Chung-Horng Lung

13.1 Introduction In wireless sensor networks (WSNs), a large number of sensor nodes could be deployed in various environments that cover large areas. These nodes sense environmental changes and collaborate to accomplish a common task such as environment monitoring or tracking. In many applications, sensor nodes must be self-organized because they usually are deployed in an infrastructureless network. Further, there are unique resource constraints and application requirements in WSNs, such as densely deployed nodes, extremely low power consumption, limited device capability, random topology, etc. [1]. Under various constraints, the hierarchical network architecture shows its advantages on sharing limited wireless channel bandwidth, balancing node energy consumption, reducing communication expense, enhancing management, and so on [2]. In a hierarchical network, similar nodes aggregate into clusters. In each cluster, one node acts as a cluster head (CH), which is in charge of coordinating among the nodes within its cluster as well as communicating with a base station (BS) or other CHs. The cluster members just need to transmit messages to their corresponding CH. An effective and efficient approach to grouping nodes into clusters and selecting appropriate nodes to be the CHs is critically needed. Many clustering approaches have been proposed for WSNs. The existing approaches typically first select a set of CHs among the nodes in the network by considering one or multiple factors, and then gather the rest of the nodes under the CHs. LEACH [7,8] is an important clustering protocol for WSNs as there are many approaches that are based on it. LEACH is fully distributed through randomly selecting CHs and rotating the CH task among nodes. Thus, the approach can uniformly distribute the energy consumption in the whole network. PEGASIS [9,10] C. Zhou Department of Systems and Computer Engineering Carleton University, Ottawa, Ontario, Canada K1S 5B6 e-mail: [email protected], [email protected]

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is based on LEACH and uses the greedy algorithm to organize all sensor nodes into a chain and then periodically promote the first node on the chain to be the CH. HEED [13] extends LEACH by initializing a probability for each node to be a tentative CH depending on its residual energy and making the decision according to the cost based on the connectivity degree of the node. These approaches have two main disadvantages. The first is the random selection of the CHs, which may cause higher communication overhead for (1) the ordinary member nodes in communicating with their corresponding CH, (2) CHs in establishing the communication among them, or (3) between a CH and a base station (BS) or other sinks. Another issue is the periodic CH rotation or election, which needs extra energy to rebuild clusters. To avoid the problem of random CH selection, there are many other approaches focusing on how to select appropriate CHs to achieve efficient communications. Stojmenovic et al. [11] proposed a dominating set algorithm, which focuses on the efficiency of broadcasting to all the nodes. The approach divides all the nodes into four types: gateway, intergateway, intermediate, and member. The selected gateway nodes, which form a dominating set, ensure high efficiency of information transmission. However, the dominating set is breakable because any change to the network may cause the entire network to update and recalculate the dominating set again. Yin et al. [12] proposed a novel cluster head selection algorithm using analytical hierarchy process (AHP). The approach considers three factors: energy, mobility, and the distance to the involved cluster centroid. However, the sinks performing the algorithm introduces another issue that increases the communication cost between CHs and the sinks with the administration information. Hierarchical agglomerative clustering (HAC) [3,6,14] is a conceptually and mathematically simple clustering approach. In this chapter, we advocate the HAC approach for WSNs. We will illustrate why and how to use the HAC approach to mitigate the problems encountered with current protocols. The following are the main advantages of the HAC approach: 1) Simple computation and easy implementation. Section 13.2 briefly illustrates this point. 2) Less restricted assumptions and more flexibility: HAC could use simple qualitative connectivity information of a network or quantitative data through received signal strength (RSS) or global positioning system (GPS). In addition, other factors could easily be incorporated into the algorithm. For instance, different weights could be assigned to different nodes or connections for specific scenarios. 3) Less resource for clusters establishment: Using the HAC approach, nodes can finish the CHs election and announcement, cluster establishment, and scheduling at the same time. It can greatly reduce resource dissipation. 4) Without the need of periodic reclustering or network updating: The HAC approach generates a logical CH backup chain during the cluster generation process. It makes clusters easily adaptive to network changes without extra information exchanges or the need of periodic announcement, such as CH. In the following, we will elaborate further on these previously listed advantages. In Section 13.2, we briefly introduce the concept of HAC algorithm. In Sections 13.3

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and 13.4, we discuss the HAC design in WSNs. The original idea of HAC requires the global knowledge. In Section 13.3, we will start our discussion with the assumption that each node has the global information of every other node for concept illustration. Then we will remove the assumption by introducing the distributed HAC algorithm (DHAC) in Section 13.4. We will compare the clustering results with different HAC algorithm methods in Section 13.5. Finally, this chapter is concluded in Section 13.6.

13.2 HAC Concept Introduction This section presents the basis of HAC (hierarchical agglomerative clustering). Many different numerical taxonomy or HAC clustering techniques have been researched and proposed [3,6,14]. All of these approaches comprise three common key steps: obtain the data set, compute the resemblance coefficients, and execute the clustering method. For each step there are various alternatives. For example, HAC has two important categories, divisive and agglomerative. Data types could be either quantitative or qualitative. Resemblance coefficient also has two types, dissimilarity coefficient and similarity coefficient. Our research does not focus on the clustering technique analysis and comparison. Instead, we will briefly describe the related concept of the HAC algorithm adopted in our research for WSNs and illustrate them with both quantitative and qualitative input data.

13.2.1 Input Data Set An input data set for HAC is a component–attribute data matrix. Components are the entities we want to group based on their similarities. Attributes are the properties of the components. For example, the attributes could be the location of mobile nodes, the nodes’ residual energy, or other features. Figure 13.1 shows a simple randomly generated network. The components are the nodes and the attributes are their locations as illustrated in Table 13.1. We can easily add or remove components, or modify attributes from the data set for different applications. Obviously, the more factors we consider, the more restricted assumptions and computations are needed.

13.2.2 Computation of Resemblance Coefficients A resemblance coefficient for a given pair of components indicates the degree of similarity or dissimilarity between these two components, depending on the way in which the data are represented. A resemblance coefficient could be quantitative or qualitative. Table 13.2 shows quantitative coefficients, which measure the literal distance between two components when they are viewed as points in a twodimensional array formed by the input attributes. The coefficients are calculated using the Euclidean distance based on the input data shown in Table 13.1.

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Fig. 13.1 A simple Eight-Node network

Table 13.1 Component–attribute data matrix for the Eight-Node network Component (Node)

Attribute x-axis

y-axis

1 2 3 4 5 6 7 8

3.78 3.56 6.06 7.71 0.63 7.23 8.52 4.43

2.9 4.83 7.34 8.46 0.01 5.78 3.46 0.48

Table 13.2 Resemblance matrix with quantitative data {1} {2} {3} {4} {5} {6} {7}

{2}

{3}

{4}

{5}

{6}

{7}

{8}

1.94 – – – – – –

4.99 3.54 – – – – –

6.81 5.51 1.99 – – – –

4.27 5.64 9.12 11 – – –

4.49 3.79 1.95 2.72 8.77 – –

4.77 5.15 4.59 5.07 8.61 2.65 –

2.51 4.44 7.05 8.63 3.83 5.99 5.06

The simplest form of qualitative coefficients is binary representation, for example, the value is either 0 or 1. To deal with the qualitative input data, there are various ways to calculate the resemblance coefficients. Three typical methods are [3,6,14]: 1) Jaccard Coefficient: cxy = a / (a + b + c), 2) Simple Matching Coefficient: cxy = (a + d) / (a + b + c + d), 3) Sorenson Coefficient: cxy = 2a / (2a + b + c),

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Where a, b, c, d are counts of 1–1, 1– 0, 0 –1, and 0 – 0 matches of attribute-pair between any two components x and y. An example is presented in Section 13.3.2.

13.2.3 Execution of the HAC Method Execution of HAC usually has six steps; each step merges two clusters together and updates the Resemblance Matrix. Updating the Resemblance Matrix is an important step and various methods could be adopted. There are four main types of HAC method [3]: 1) Single LINKage Method (SLINK). It is also called the nearest neighbor method. It defines the similarity measure between two clusters as the maximum resemblance coefficient among all pair entities in the two clusters. 2) Complete LINKage Method (CLINK). It is also called the furthest neighbor method. It defines the similarity measure between two clusters as the minimum resemblance coefficient among all pair entities in the two clusters. 3) Unweighted Pair–Group Method using Arithmetic Averages (UPGMA). It defines the similarity measure between two clusters as the arithmetic average of resemblance coefficients among all pair entities in the two clusters. UPGMA is the most commonly adopted clustering method in general. 4) Weighted Pair–Group Method using Arithmetic Averages (WPGMA). It is thesimple arithmetic average of resemblance coefficients between two clusters without considering the cluster size. In HAC, the clustering result is usually represented with a dendrogram. In Fig. 13.2, the height is the coefficient of two merged components/clusters. Using the UPGMA approach (c), for instance, we can get two clusters (3,6,4,7) and (1,2,8,5) if a cut is selected right above the merger of node 5 and cluster (1,2,8). See Section 13.3.1 for further explanation. We can also see that, with the same

Fig. 13.2 Dendrograms using different HAC methods

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data set, we may get different clustering results by using different HAC methods, for example, (a) and (b).

13.3 Cluster Generation for WSNs As stated earlier, HAC has been widely applied in many different areas [3,6,14]. Our research is to investigate the application of HAC in WSNs to set up clusters for communication efficiency. To illustrate the feasibility of HAC algorithms in WSNs, in this section, we start with the “best condition,” which encompasses the following assumptions about the network: 1) 2) 3) 4)

The nodes in the network are quasi-stationary. Propagation channel is symmetric. Nodes are left unattended after deployment. All nodes have similar capabilities, processing, communication, and initial energy. 5) Each node has the global information of every other node. (This assumption will be removed in Section 13.4.) In WSNs, HAC is carried out in the clustering process as follows: 1) Nodes exchange messages until they obtain all of other nodes’ location information. 2) Run the clustering method and generate a cluster tree. 3) Make a cut using a preconfigured threshold value (e.g., transmission radius, number of clusters, or cluster density) to determine clusters. 4) If the cluster size is less than a predefined threshold, Minimum Cluster Size, merge the cluster with its closest cluster. 5) Once we finish clustering, CHs can be initially determined by different strategies. Here, we simply use the nodes which satisfy two conditions: (1) the node is one of two nodes that are merged into the current cluster in the first step or at the lowest level, e.g., (3, 6) or (1, 2) in Fig. 13.2(b); (2) the node with the lower ID. The nodes that are merged at the lowest level have highest resemblance coefficient or are closest. Generally, they are also physically closer to the “middle” of a cluster.

13.3.1 Application of HAC with Quantitative Data To apply HAC with the quantitative data in WSNs, we have an assumption: nodes are location-aware. And hence, we use the location information to calculate the distance between any pair of nodes. We can use the nodes transmission radius as the threshold to cut the cluster tree or to determine clusters. The following steps and Fig. 13.3 demonstrate how to generate the clusters and determine the CHs.

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Fig. 13.3 Clustering steps and dendrogram using UPGAM method with quantitative data

Step 1: Execute HAC and get a cluster tree by using the UPGMA method. Step 2: Cut the cluster tree with the threshold of transmission radius. (The radius is 4.38 for this example based on a calculation using the total number of nodes and average node degree, but could also be based on actual transmission capacity or an application specific preconfigured value. For brevity, it is not shown here.) As a result, three clusters, {3, 6, 4, 7}, {5}, {1, 2, 8} are generated, as shown in Step 2. Step 3: The size of cluster {5} is smaller than the Minimum Cluster Size; it is then combined with its closest cluster {1, 2, 8}. Finally, we generate two clusters: {3, 6, 4, 7} and {1, 2, 8, 5} after Step 3. And at the same time, we can choose node 3 and node 1 as the CHs of these two clusters, since both are grouped with another node (nodes 6 and 2, respectively) in the first step and both have lower ID numbers. Those two clusters also correspond to the clustering sequence of the nodes in each cluster, which represents the cluster chain that can also be used for scheduling arrangement. For instance, cluster (3, 6, 4, 7) demonstrates that the sequence of serving as the CH in this cluster is 3, 6, 4, and 7. Without any extra scheduling process, the CHs election and announcement, cluster establishment, and scheduling can be completed at the same time. The clustering sequence of the nodes in each cluster can also be used to handle the dynamic network conditions. If a node, for example, node 3, cannot be a CH anymore, the next node in the cluster chain, for example, node 6, will be the new default CH without extra message exchanges due to the fact that each cluster member has the CH backup chain information. Similarly, if node 6 fails or becomes low in power, then the next node in the chain, node 4, will be the default CH. The decision of the scheduling policy can also be extended by considering the power level when an election of a CH is needed. In other words, node 4, for instance, may not have enough power. Node 4 in this case can simply elect the next node to be a CH even if it is the next node in the chain. With this mechanism, there is no need to re-execute clustering once we established clusters by using HAC.

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13.3.2 Application of HAC with Qualitative Data To apply HAC with less information of nodes in WSNs, for example, when location information of nodes is not available, qualitative data can be adopted. In the absence of location information, the connectivity information can be used as input. Each node merely knows its neighbors without distance or any other information. In other words, each connection can be represented with a binary value. In this chapter, we use a 1 value to represent one-hop connection and a 0 value to represent no direct connection. Hence, the input data for the eight-node network can be represented in Table 13.3. Table 13.3 lists all one-hop connections. Note that a 1 value is also used for a node to itself or the entries along the main diagonal to give more weight for the resemblance coefficient computation. Table 13.4 shows a resemblance matrix with the qualitative data by using the Sorenson method (see Section 13.2.2). Note that, to be consistent with the resemblance coefficient using quantitative input data, Table 13.4 demonstrates the dissimilarity coefficient instead of similarity coefficient to indicate the difference between any two clusters. In other words, the smaller the value of a dissimilarity coefficient, the more similar the two clusters are. For nodes 5 and 8, for instance, the parameters (see Section 13.2.2) and their values are a(1–1) = 3, b(1–0) = 0, c(0–1) = 0, d(0–0) = 5. Using the Sorenson method, we get the similarity coefficient between 5 and 8, which is 1, hence, their dissimilarity coefficient becomes 0 (1 – original Sorenson coefficient = 0). After establishing the resemblance matrix, we have experimented four different methods, SLINK, CLINK, UPGMA, and WPGMA, to update the resemblance coefficients and perform the clustering. Figure 13.4 shows the result of using the Sorenson method to calculate the resemblance coefficients and the UPGMA for clustering computation. The height value in Fig. 13.4 is the reversed Sorenson coefficient (1 – original Sorenson coefficient), which indicates the dissimilarity between two clusters. After using the threshold 0.5 to cut the cluster tree, the result shows that three clusters could be obtained. They are {3, 6, 4, 2}, {7}, and {5, 8, 1}. The size of cluster {7} is smaller than the Minimum Cluster Size. We then merge it with its closest cluster {3, 6, 4, 2}. Finally, we can get two clusters {3, 6, 4, 2, 7}, {5, 8, 1}, and

Table 13.3 One-hop network connectivity data ID

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8

1 1 0 0 1 0 0 1

1 1 1 0 0 1 0 0

0 1 1 1 0 1 0 0

0 0 1 1 0 1 0 0

1 0 0 0 1 0 0 1

0 1 1 1 0 1 1 0

0 0 0 0 0 1 1 0

1 0 0 0 1 0 0 1

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Table 13.4 Resemblance matrix with qualitative data using Sorenson dissimilarity coefficients {1} {2} {3} {4} {5} {6} {7}

{2}

{3}

{4}

{5}

{6}

{7}

{8}

0.5 – – – – – –

0.75 0.25 – – – – –

1 0.429 0.143 – – – –

0.143 0.714 1 1 – – –

0.778 0.333 0.111 0.25 1 – –

1 0.667 0.667 0.6 1 0.429 –

0.143 0.714 1 1 0 1 1

Fig. 13.4 Clustering steps and dendrogram for qualitative data using Sorenson and UPGMA methods

node 3 and node 5 are the CHs. The result is similar to that obtained from using the quantitative data as presented in the previous section, except that node 2 is now in the other cluster. Node 2 is sitting in between two groups. It could be clustered with either group. Discrepancies in clustering results are common when different input data or clustering methods are used, since there are generally various ways to group data. The more important point is to group nodes that share more commonalities or are physically closer. The main advantage of using the one-hop connectivity information is that it can be easily obtained through message exchanges with low or no extra communication overhead. Our initial experiment shows that HAC with qualitative data could achieve reasonably good result with less information. We have also conducted experiments using two-hop neighbor knowledge in the clustering process. In addition, one-hop neighbors and two-hop neighbors could have different weights. Several weight ratios between one-hop and two-hop connections have been evaluated, including 3:1, 2:1, and 8:3. The results, in general, were close. Our initial results also revealed that if we consider only the one-hop information, we could have smaller number of clusters with the same threshold value. However, further investigation is still needed and the remainder of this chapter focuses on one-hop information.

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13.3.3 Cluster Maintenance As presented in Section 13.3.2, using HAC, we can get cluster trees as shown in Figs. 13.3 and 13.4. We cut cluster tree with a threshold, then merge small cluster(s) into their closest cluster(s) based on the limitation of Minimum Cluster Size. After clustering, we need to perform the following tasks to maintain clusters. 1) Choosing an appropriate CH for each cluster. In previous examples, we simply used smaller node ID to choose CHs in each cluster step. In practical applications, we can use different CH selection method by using the information of distance to sink, node degree, or cluster size, etc. For example, in a network for habitat monitoring, a sink usually needs to communicate with several specific nodes, which requires many communications between a CH and the sink. In this case, choosing a CH which has shorter distance to the sink can reduce the total communication cost. If an application has more intercommunication, such as collecting data from sensor nodes periodically, choosing a CH which has higher node degree has higher efficiency. 2) Assigning the transmission schedule along the cluster chains. Once the clustering step is completed, a cluster chain is also generated, which can be used as the schedule for cluster members. Each cluster member follows the schedule to communicate with the CH only on its turn. A member node turns to the sleep mode when the time slots belong to other members for energy conservation. 3) Electing a new CH. In a hierarchical structure network, CHs spend much energy to maintain the cluster, aggregate data, transfer data to the sink, etc. To balance the energy consumption of nodes in the whole network and prolong the network life, we assign several CH candidates along the cluster chain. If the current CH serves as the CH for a fixed duration or its residue energy reaches a threshold, it promotes a CH candidate to be the CH and broadcasts the message to all cluster members. 4) Dealing node leave or join. When a node does not have enough energy to communicate with other nodes, we call this node as a dead node. In a cluster, a member node is dead if the CH has not received a message from the member for a certain amount of time. Once a member has been confirmed as dead member, the CH asks the following members to slide forward to fill the empty time slot. Conversely, if a node or a cluster requires to join a cluster by sending a request to the CH, the CH estimates the distance and residue energy of the applicant, then the CH assigns appropriate time slot(s) to the applicant.

13.4 Distributed HAC (DHAC) Algorithm The results obtained from the clustering methods depicted in Section 13.3 demonstrated the feasibility of the HAC approach. Some potential advantages include: (1) The CH election process is not periodic and the scheduling of CH within a cluster

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can generally follow the clustering chain. (2) Each CH can effectively communicate with its members within the cluster, since the battery power can be more efficiently used within a certain transmission range. However, the assumption that each node has the global knowledge of all the nodes is not realistic for WSNs. In this section, we briefly describe how the clustering algorithm can be modified for distributed environments. The idea is that for WSNs, we do not actually need the global knowledge. Specifically, a node can make use of only the one-hop neighboring knowledge for the computation. Nodes that are far apart will not be grouped into the same cluster anyway. Therefore, it is not necessary to include all the information for clustering. As a result, we can remove the assumption that each node has the global information of every other node. The rest of this section discusses the concept of distributed clustering for WSNs based on the quantitative location data and qualitative connectivity knowledge using the HAC approach.

13.4.1 DHAC Using Quantitative Data Without the global knowledge, we can make use of the neighboring information to determine if a node actually needs to perform the clustering task. The clustering could be conducted based on the location data or RSS. The rationale is that every node knows its one-hop or two-hop neighbors. Figure 13.5 illustrates the pseudocode of the DHAC implementation for WSNs. To set up the local resemblance matrix, in the beginning, each node elects itself as a cluster and exchanges the information via HELLO messages with its neighbors. In Fig. 13.5, lines 1–6 initialize the clustering process. Each cluster builds its own resemblance matrix with information from its neighbors. After establishing the local resemblance matrix, each cluster can easily find the minimum coefficient (MinV) in its matrix, and then it can find the corresponding cluster head (MinC) associated with MinV. If MinC satisfies the requirements, the cluster will send an INVITE message to the MinC. Lines 24–32 specify two requirements, the sender node must be the current cluster head and the sender NID must be smaller than MinC. Using a predefined threshold, the While loop in lines 7–23 control the size of clusters. During the clustering process, all clusters keep listening and waiting for messages. When a CH receives a message, it reacts based on the message type. In lines 10–17, when receiving an INVITE messages, the CH checks if the message is from its MinC. If yes, the CH sends a CONFIRM message back to the sender, elects the sender to be the new CH, then it turns to the sleep mode; if not, the CH sends back a REJECT message. After receiving a CONFIRM message, the cluster updates its neighboring list and resemblance matrix, the cluster merges with the cluster headed with MinC to form a new cluster (line 18–19, lines 33–38). Then, the new CH broadcasts an INFORM message to notify all the neighbors to update their resemblance matrices (lines 20–21, 37). The INFORM message includes the new cluster information and the combined neighbor list. When a cluster receives an

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C. Zhou, C.-H. Lung Definitions: NID: Node ID CID: Cluster head ID MinV: The minimum value in the Resemblance matrix; MinC: The CID of the cluster corresponds to the minimum value (MinV) in the Resemblance matrix. ResM: A node’s local Resemblance matrix. Setup phase: /*exchange information with neighbours*/ 1. CID NID; /*form a cluster by itself*/ 3. Send HELLO message to one–hop neighbours 4. Turn to listening mode; 5. Receive HELLO messages; 6. Establish ResM; DHAC execution phase: /* Clustering*/ 7. while (MinV<= threshold) 8. INITIALIZATION(); 9. Read message 10. if (Received message type == INVITE) 11. if (MinC == Sender CID) 12. send CONFIRM message; 13. CID sender NID; 14. Turn to sleep mode; 15. else 16. Send REJECT message back to Sender; 17. end if 18. else if (Received message type == CONFIRM) 19. MERGE (); 20. else if (Received message type == INFORM) 21. Update ResM; 22. end if 23. end while 24. proc INITIALIZATION () /* initialization procedure*/ 25. if (CID == NID) 26. MinV minimum value in ResM; 27. Find the MinC with MinV; 28. if (CID < MinC) 29. Send INVITE message to MinC; 30. end if 31. end if 32. end proc 33. proc MERGE() /* cluster merge procedure */ 34. Merge two clusters; 35. Combine neighbouring information of two clusters; 36. Update ResM; 37. Broadcast INFORM message to neighbours; 38. end proc

Fig. 13.5 Pseudocode of DHAC

INFORM message, it updates its resemblance matrix with the new cluster information. Without the global information, clusters can update their resemblance matrices by exchanging their neighbor information in each clustering step. To explain how the pseudocode works, we use the eight-node network shown in Fig. 13.1 as an example. In the beginning, each node forms one cluster and

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Cluster {1} {2} 1.94 {5} 4.27 {8} 2.51

Cluster {2} {1} 1.94 {3} 3.54 {6} 3.79

Cluster {3} {2} 3.54 {4} 1.99 {6} 1.95

Cluster {4} {3} 1.99 {6} 2.72

Cluster {5} {1} 4.27 {8} 3.83

Cluster {6} {2} 3.79 {3} 1.95 {4} 2.72 {7} 2.65

Cluster {7} {6} 2.65

Cluster {8} {1} 2.51 {5} 3.83

exchanges information with its neighbors. As shown in Fig. 13.1, cluster {4} exchanges information with only cluster {3} and cluster {6}. After collecting the neighboring information, every cluster can establish its own resemblance matrix. Figure 13.6 shows an example of the local resemblance matrices with the quantitative Euclidean distance using the location information from one-hop neighbors. With the resemblance matrices, each cluster can perform the DHAC algorithm to merge with other clusters. In our example, the matrix of cluster {1} has the smallest coefficient 1.94 with cluster {2}, so cluster {2} is its MinC, and vice versa. Based on the predefined protocol, the cluster with the smaller ID launches an INVITE message. So, cluster {1} sends an INVITE message to cluster {2}. Similarly, clusters {3} and {5} also find their corresponding MinCs, which have larger cluster IDs and they send an INVITE message to cluster {6} and cluster {8}, respectively. After receiving an INVITE message, clusters {2} and {6} send back a CONFIRM message, but cluster {8} sends back a REJECT message because cluster {8} finds that the distance between itself and cluster {5} is not the smallest. Figure 13.7 demonstrates that after receiving a CONFIRM message, cluster {1} merges with cluster {2} by updating its neighboring list and resemblance matrix. The new cluster {1, 2} broadcasts an INFORM message to its neighbors. The neighbor clusters then update their resemblance matrix based on the INFORM message. Cluster {3} also performs the same merge procedure with cluster {6}. At the end of the first step, we get two new clusters, cluster {1, 2} and {3, 6}. Figure 13.7 shows the updated resemblance matrices with the SLINK method. In the updated resemblance matrices, there are two new clusters, cluster {1, 2} and cluster {3, 6}.

268 Fig. 13.7 Updated resemblance matrices using SLINK after the first clustering step

C. Zhou, C.-H. Lung Cluster {1, 2} Member 2 1.94 {5} 4.27 {8} 2.51 {3, 6} 3.54

Cluster {3, 6} {1, 2} 3.54 {4} 1.99 Member 6 1.95

Cluster {4} {3, 6} 1.99

Cluster {5} {1, 2} 4.27 {8} 3.83

Cluster {7} {3, 6} 2.65

Cluster {8} {1, 2} 2.51 {5} 3.83

In the second step of the clustering, every cluster can easily find its MinV and MinC in its updated matrix. All clusters repeat lines 7–23 in the pseudocode until the MinV in matrices reaches the predefined threshold. Figure 13.8 shows the cluster trees of the centralized HAC and DHAC algorithm using UPGMA method with quantitative location data. The results are very similar. Note that the result obtained from the distributed algorithm may not be identical to that of the centralized clustering algorithm as depicted in Section 13.3.1. In practice, however, there are various ways to cluster the same input data. Moreover, realistically, it almost always involves tradeoffs in the design phase. In distributed clustering, where less information is available, estimation, for example, RSS of a two-hop neighbor could be used to achieve reasonably good results. Figure 13.9 shows a more complex example where the DHAC is applied to a 100-node network. The 100 nodes are uniformly distributed in a 100 × 100 field. The DHAC algorithm merges nodes to form five clusters by using the UPGMA method. The five clusters are represented by five separate chains with the CH (filled circle) leading the group, as illustrated in Fig. 13.7. The areas covered by all clusters are roughly in the same range.

Fig. 13.8 Comparison of centralized and distributed clustering using UPGMA with quantitative location data

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Fig. 13.9 Clustering using DHAC for 100-Node network with quantitative location data

13.4.2 DHAC Using Qualitative Connectivity Data Table 13.3 and 13.4 demonstrate the input data for general clustering methods with qualitative data. Entries with value “1” indicate that a connection exists between two corresponding nodes. In addition to the concept described in the previous section, in order to tailor it to the WSNs domain, the only other piece of information that is missing for qualitative data is the total number of nodes. In the clustering method, we need to know how many 0s to fill in the table for nodes that are not directly connected. This can be either estimated or preconfigured with a specific larger number depending on the total number of nodes. After establishing resemblance matrix, each CH performs DHAC as Fig. 13.5 illustrates. Figure 13.10 shows a comparison between the centralized clustering and

Fig. 13.10 Comparison of centralized and distributed clustering using UPGMA with qualitative connectivity data

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Fig. 13.11 Clustering using DHAC for 100-Node network with qualitative connectivity data

distributed clustering for the simple eight-node network shown in Fig. 13.1. The results are very similar. With the same network shown in Fig. 13.9, we apply DHAC using the UPGMA method with qualitative connectivity data. We also get five clusters, which are shown in Fig. 13.11 with CHs (filled circles), lead five separated cluster chains. Obviously, the result of qualitative data is quite different from the result of quantitative data. However, different results are not important. What matters is the efficiency of clustering on energy usage or other objectives. In Section 13.5, we will present the further discussion of DHAC with different methods.

13.5 Evaluation of DHAC In previous sections, we presented some options or variants at different parts, i.e., variation points, of the HAC algorithm. These options support more flexibility to accommodate different situations or technologies. Based on different environments, traffic patterns, and hardware, we can choose appropriate methods and adjust predefined parameters to apply HAC to WSNs. Figure 13.12 presents possible variants for different variation points (shown in the leftmost column) for the HAC approach. Section 13.4 presented a comparison between the centralized HAC and DHAC. However, the centralized HAC needs the global scope algorithm, which is unrealistic in WSNs. Therefore, this section demonstrates more detailed investigations of DHAC and evaluates the effect of several parameters and methods that are critical to DHAC. The effect investigated in this section includes cluster size and cluster range. The parameters considered in this section focus on the quantitative versus qualitative data, and clustering methods.

13 Application and Evaluation of HA Clustering in Sensor Networks Input data and resemblance coefficient calculation method Clustering method

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Fig. 13.12 Variation points and possible variants of applying HAC to WSNs

We applied DHAC to a network of 100 nodes. The 100 nodes are uniformly distributed in a 100 × 100 m2 field with different node degrees (different transmission radii). The topologies generated do not have isolated nodes. The average node degree is used for all scenarios and it will be referred to as node degree throughout this section. To ensure fair comparison and reduce the random effects caused by the simulation, we execute 30 simulation runs for each scenario and calculate the mean results.

13.5.1 Evaluation of Clustering Methods and Parameters There are many HAC algorithm methods. This section presents a comparison of four commonly used methods, SLINK, CLINK, WPGMA, and UPGMA. For each method, DHAC is carried out with node location information. The clustering tree is then divided into groups using a predefined threshold, C-HEIGHT, as depicted in Fig. 13.12. The number of clusters decreases when the node degree increases. The cluster size could affect the node and network life. The first evaluation then is to investigate the effect of various clustering methods on the number of clusters for each node degree. Figure 13.13 shows the number of clusters against the node degree. SLINK and CLINK results in two extreme cases, where SLINK tends to produce compact clusters. Figure 13.13 indicates that only one cluster is generated when the node degree reaches 5. The result also reveals that the size of the clusters generated by SLINK is widely spread, ranging from 2 to 98 when the node degree is below 5. Unbalanced cluster size could cause some nodes to die quickly while some nodes could not report data in time due to longer delay in scheduling. On the other hand,

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Fig. 13.13 Number of clusters versus node degree using different DHAC methods and quantitative location data

CLINK produces many clusters. More clusters provide shorter network reaction time at the expense of heavy intercluster communications. Compared to SLINK and CLINK, UPGMA and WPGMA generate similar and more balanced number of clusters. Cluster range is another important criterion to evaluate clustering methods. We define the cluster range as the maximum distance between any two cluster members. A cluster with a smaller range could consume less energy in intracluster communications. Similarly, large cluster ranges should be avoided in a network, because intracommunications cost could be high. Figure 13.14 shows the maximum cluster range (in meters) versus the node degree for different algorithm methods. To compare the cluster range, we form five clusters in each network. It can be observed that the cluster range generally decreases when the node degree increases. Based on the experimental results, SLINK generates the largest cluster range while UPGMA produces the smallest cluster range. With our proposed DHAC algorithm, different types of network information such as location, RSS, and connectivity can be used as input data. Using the node location information has two problems: higher device cost and more complicated localization protocols. RSS could replace the location information. RSS can be obtained from the antenna without any extra processing. However, it is sensitive to the environment. Qualitative connectivity data presents another simple alternative to obtain the relationship among nodes. Figure 13.15 compares DHAC with two different input

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Fig. 13.14 Maximum cluster range versus node degree using different DHAC methods and quantitative location data

Fig. 13.15 Maximum cluster range versus node degree using quantitative and qualitative data

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data types, quantitative location data and qualitative connectivity data, with a fixed number of clusters. For qualitative connectivity data, we used the Sorenson method. Based on the experiment, it is shown that the cluster ranges using two types of data are not significantly different. However, quantitative data tend to provide smaller cluster ranges than qualitative data. While using qualitative data, UPGMA does not remarkably outperform CLINK and WPGMA as it does when quantitative data are used. We further investigated the maximum cluster range using different resemblance calculation methods together with the qualitative connectivity data, as shown in Fig. 13.16. In addition, a comparison of those methods with the quantitative location data was conducted for evaluation. Many methods are available to calculate the resemblance coefficients. We chose three well-known methods, Jaccard, Sorenson, and simple matching. UPGMA method is used due to better results produced in pervious scenarios. The cluster tree is cut with the threshold of C-NUMBER. We observe that the cluster range drops with different rates when the node degree increases. All three methods using qualitative data generate larger maximum cluster range than that of quantitative location data. The simple matching method generates the largest cluster range. When the node degree increases, the cluster range of simple matching method remains almost unchanged while other methods decrease with different rates. The result obtained from the Sorenson calculation is closer to that of quantitative location data than other methods.

Fig. 13.16 Cluster range versus node degree with different resemblance calculation methods

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13.6 Conclusions and Future Work Clustering has generated a lot of discussion in WSNs and has also been a topic of interest in many different disciplines for a long time. Many clustering methods have been successfully used in other application areas. This chapter advocated the application of some well-understood HAC clustering methods to WSNs. Those methods are simple in concept and computation, and can be easily adapted to include other factors, such as battery power and different weights, into the clustering process. We have conducted a number of experiments using DHAC for different scenarios using various clustering methods including SLINK, CLINK, WPGMA, and UPGMA. Given networks with a fixed number of nodes that were uniformly distributed in a square field, we compared their performance against two criteria, number of clusters and cluster range. UPGMA and WPGMA had similar results, and both outperformed SLINK and CLINK in both criteria. We further compared DHAC using qualitative and quantitative data. The clustering results obtained from qualitative data were more fluctuant and more easily affected by the input data than those from quantitative data. However, the difference is not significant for UPGMA. Three resemblance calculation methods in qualitative data were then compared in terms of the cluster range. The result obtained from the Sorenson calculation was closer to that of the quantitative location data than Jaccard and simple matching. Our research results indicate that DHAC has the potential to provide a flexible way to manage clustering issues for WSNs, such as using either quantitative or qualitative input data, CH election, CH backup chain scheme, and scheduling. Using our proposed approach, nodes do not need to have the location information, which in general could reduce the cost. In addition, the CH election process is not periodic. If an ordinary member node drifts from one cluster to another or a node is newly added or removed (e.g., the battery is dead), clustering does not have to be triggered and the CH election is straightforward using the clustering chain. This chapter does not discuss the communications between CHs or intercluster communications. Several approaches have been proposed: (1) CHs are capable of operating in dual power modes [5]. A CH uses low power for intracluster communications and high power to communicate with the neighboring CHs. (2) CHs can communicate with a BS [8]. (3) Hierarchical clusters can be formed [4]. This is an area for future investigations. Currently, we are focusing on the following directions: 1) 2) 3) 4) 5)

Evaluate the performance of energy efficiency. Compare with other clustering-based protocols. Evaluate DHAC performance with different options. Incorporate different weights into the clustering process. Select a subset of member nodes for intercluster communications based on the resemblance information such that every CH can communicate with other CHs more efficiently. 6) Investigate mobility issues for more complicated scenarios.

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Acknowledgments This research was supported in part by Natural Sciences and Engineering Research Council (NSERC), Canada.

References 1. Akyildiz, I.F., Su, W., Sankarasubramaniam, Y., and Cayirci, E. (2002) A Survey on Sensor Networks, IEEE Communications Magazine, vol 40, no 8, pp. 102–116 2. Al-Karaki, J.N. and Kamal, A.E. (2004) Routing Techniques in Wireless Sensor Networks: a Survey, IEEE Wireless Communications, vol 11, no 6, pp. 6–28 3. Anderberg, M.R. (1973) Cluster Analysis for Applications, Academic Press, New York 4. Banerjee, B. and Khuller, S. (2001) A Clustering Scheme for Hierarchical Control in Multihop Wireless Networks, IEEE INFOCOM, pp. 1028–1037 5. Chatterjee, M., Das, S.K., and Turgut, D. (2002) WCA: A Weighted Clustering Algorithm for Mobile Ad Hoc Networks, Cluster Computing, Kluwer Academic Publishers, pp. 193–204 6. Everitt, B. (1980) Cluster Analysis, Heinermann Educational Books Ltd, London 7. Heinzelman, W.R., Chandrakasan, A., and Balakrishnan, H. (2000) Energy-Efiicient Communication Protocol for Wireless Micro sensor Network, Proc of the 33rd Hawaii International Conference on System Sciences, pp. 1–10 8. Heinzelman, W.R., Chandrakasan, A., and Balakrishnan, H. (2002) An Application-Specific Protocol Architecture for Wireless Microsensor Networks, IEEE Transactions on Wireless Communications, vol 1, no 4, pp. 660–670 9. Lindsey, S. and Raghavendra, C. (2002) PEGASIS: Power-Efficient GAthering in Sensor Information Systems, Proc of the IEEE Aerospace Conference, vol 3, 9–16, pp. 1125–1130 10. Lindsey, S., Raghavendra, C., and Sivalingam, K. (2002) Data Gathering Algorithms in Sensor Networks Using Energy Metrics, IEEE Transactions on Parallel and Distributed Systems, vol 13, no 9, pp. 924–935 11. Stojmenovic, I., Seddigh, M., and Zunic, J. (2002) Dominating Sets and Neighbor Elimination-Based Broadcasting Algorithms in Wireless Networks, IEEE Transactions on Parallel and Distributed Systems, vol 13, no 1, pp. 14–25 12. Yin, Y., Shi, J., Yinong Li, and Zhang, P. (2006) Cluster Head Selection Using Analytical Hierarchy Process for Wireless Sensor Networks, Proc of the 17th IEEE International Symposium on Personal, Indoor, and Mobile Radio Communications, pp. 1–5 13. Younis, O. and Fahmy, S. (2004) Distributed Clustering in Ad hoc Sensor Networks: A Hybrid, Energy-Efficient Approach, Proc of the IEEE INFOCOM, pp. 629–640 14. Romesburg, H.C. (1990) Cluster Analysis for Researchers. Krieger Publishing Company, Malabar Florida

Chapter 14

A Fault-Tolerant Scheme for Detection of DDoS Attack Patterns in Cluster-Based Wireless Sensor Networks Zubair A. Baig and Asad I. Khan

14.1 Introduction Last few years have witnessed a significant increase in the deployment of wireless sensor networks (WSNs) for various critical applications. Such applications include bush fire monitoring, structural health monitoring, battlefield monitoring, and surveillance. Wireless sensor networks consist of hundreds to thousands of resource-constrained and inexpensive devices called sensors or sensor nodes [20]. These sensors observe their environments for phenomena such as temperature changes, humidity fluctuations, and object movement. Information is also processed and communicated by these devices to a more powerful central entity called the base station. The mission-critical nature of applications of such networks demands the need for protection of sensory resources from malicious attacks. A Distributed Denial of Service (DDoS) attack is one such form of an attack, which is launched by a cooperative set of malicious entities toward a victim. In this attack, the attackers send a large number of hoax packets toward a victim, with the intent of incapacitating it from further participation in network operations [3,5,9]. The victim thus cannot process any further requests that may be crucial for correct operations of the network. In a wireless sensor network, such an attack is launched by a set of malicious nodes with the intent of exhausting the limited energy resources of target sensors [1]. As a result, the targets are overwhelmed with higher-than-normal intensities of traffic inflow, thus leading to the rapid exhaustion of their limited energy resources; incapacitating them from further participation in crucial network operations [2,22]. The primary resource of a sensor node is its energy content, which needs to be used efficiently to maximize the sensor’s lifetime. The goal of our scheme is to maximize the lifetimes of individual sensor nodes by means of timely detection of DDoS attacks. As a result, the overall network lifetime will be increased, and frequent Z.A. Baig Monash University, Melbourne, Australia e-mail: [email protected]

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replacement of dysfunctional sensor nodes deployed in inaccessible environments can be avoided. We model a typical DDoS attack as a distributed pattern recognition problem, and postulate that timely detection of such attacks can be achieved by facilitating distributed detection of patterns of traffic flow in the network toward a set of potential target nodes, by a set of collaborating attack-detector nodes. We extend a decentralized pattern recognition algorithm called the Graph Neuron [14] for detection of distributed attack patterns in the network. Distinct patterns of network traffic flow for routine sensory operations are defined and preconfigured into an array of nodes called the Graph Neuron (GN) nodes. An attack is defined as an observed deviation in the pattern of traffic flow through the nodes of the network. In our model, we assume that the adversary class consists of both the nodes injected in the network with the intent of generating large traffic, as well as laptop-class adversaries with much higher magnitudes of computational power than normal sensor nodes. Our scheme is intended for cluster-based networks, and is tolerant to failures owing to node loss due to compromise or failure. Clusters of GN nodes are formed at network initialization time to operate independently without the need to collaborate with GN nodes belonging to other clusters (Fig. 14.1). The scheme tolerates failures of GN nodes due to energy loss or compromise, by confining the extent of damage to the cluster of operation of the lost GN node(s). Nodes belonging to other clusters continue uninterrupted with their task of detecting DDoS attack patterns. The scheme is defined for a cluster-head network topology, wherein the cluster head (CH) is responsible for aggregation and forwarding of sensory readings to the base

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station through a well-defined multihop path of intermediary nodes called the data aggregation (DA) nodes. Considering the significance of extending the lifetimes of the CH and the DA nodes, for smooth and accurate network operations, we define them as target nodes for our scheme. We also derive a tradeoff equation to compute the optimal cluster sizes based on the node deployment density, node compromise ratio, network dimensions, and the internode distances. The contributions of this chapter are as follows: • A fault-tolerant, distributed, pattern recognition scheme for DDoS attacks in cluster-based wireless sensor networks is proposed. • A tradeoff equation is defined for computing the optimal cluster sizes based on several network parameters and node loss ratio. • A detailed simulation analysis has been done to test the effectiveness and performance of our scheme. This chapter is organized as follows: The related work is given in the next section. Following which, the Graph Neuron pattern recognition algorithm is discussed. We present the DDoS attack detection scheme in the subsequent section, and evaluate the scheme. Finally, we enlist the concluding remarks.

14.2 Background 14.2.1 Related Work Although several pattern recognition schemes for network intrusion detection have been proposed in the literature, their centralized nature, with intensive resource demands make them infeasible for deployment on sensor networks. In [11], the authors propose a centralized neural network–based technique to detect DDoS patterns by means of processing of extracted traffic flow features on a centralized pattern recognition engine. In [16,18,24], Self-Organizing Maps (SOMs) have been used for anomaly intrusion detection in high-performance networks. SOM-based approaches impose a high demand on processing and memory resources, and are not inherently distributed in nature. A cooperative, distributed DDoS attack mitigation approach for high-performance networks has been proposed by [23]. In their scheme, individual nodes perform local detection of anomalous traffic, and subsequently rely on gossip information to share their observations, so as to achieve accuracy in packet dropping process. In [15], the authors have derived solutions for the optimal numbers of cluster heads to reduce the overall energy consumption of the network. All cluster heads communicate with the base station using a single-hop mechanism, and thus consume more energy than the other nodes in the cluster. In their scheme, it is assumed that all nodes operate in a trusted environment without the threat of an attack that may lead to compromise and/or energy depletion of the sensor nodes.

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We consider the issue of DDoS attack detection in this chapter. The lack of a single entry point to the network implies that such attacks need to be detected by a set of cooperating nodes operating in a distributed manner in the network. The observation and comparison of network traffic with known patterns of normal network behavior is an effective approach for detecting such attacks. We therefore postulate that if patterns of known traffic flow in the network are preconfigured and constantly updated in attack detector nodes, observations and comparisons can be made to detect anomalies in the traffic flow. The Graph Neuron is an ideal algorithm for detecting such attacks as it is inherently distributed and imposes minimal computation and communication overheads on the sensor nodes. Our proposed algorithm relies on the cooperative intelligence of the set of detector nodes, namely GN nodes, for attack detection purposes.

14.2.2 The Graph Neuron Traditionally, graphs have been used for universal representation of information in various scientific fields of study. The Graph Neuron (GN) is a finely distributed parallel pattern recognition algorithm for lightweight devices, which preserves the data relationships in a graph-like memory structure [12,13,14]. The GN structure and its data representations are analogous to a directed graph, the processing nodes of the GN application constituting the GN array are mapped as the vertex set V of the graph and the internode connections (i.e., the communication channels) belong to the set of edges, E. The inter-GN node communications are restricted to the adjacent nodes of the GN array; hence, there is no increase in the communication overheads with corresponding increases in the number of nodes in the network [12]. The information presented to each of the nodes is in the form of a (value, position) pair. Each of these pairs represents a data point in a two-dimensional reference pattern space. Hence, the GN array converts spatial/temporal patterns into a graph-like structural representation, and then compares the edges of the graph with subsequent inputs for either memorizing the new pattern or recalling a previously seen pattern. For our scheme, in addition to their routine sensing operations, the GN nodes promiscuously monitor traffic in their local neighborhoods and subsequently collaborate with peer GN nodes at designated intervals of time to reconstruct patterns of network traffic flow. The observed patterns are compared with stored patterns depicting bounds on the tolerable traffic flow toward the target nodes. These patterns are calculated based on three factors: the topology of the underlying network, the network data delivery model (taxonomy), and the approximate rate of decline of energy contents of the target nodes. The patterns are stored in the GN nodes of the GN array and are constantly updated based on an energy content approximation model. The GN nodes detect pattern and have a nominated mGN node within each of the clusters responsible for the decision making. It may be noted that the mGN node may or may not be the CH and is selected randomly at network initialization time.

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Table 14.1 Scheme notations N C copt N Q MAC Ki j th1 r th2 r ,. . ., thn r sigr n (⌬i) Pl pnsucc(n) r pnpred(n) r nsucc(n) Npred(n) M

Number of GN nodes in the network Number of clusters in the network Optimal number of clusters Total Number of Nodes Compromised Node Ratio Message Authentication Code Pairwise shared key between GN/mGN nodes ε n Threshold values for a target node r Attack detection signal for a target node r generated by GN node n at the end of time epoch ⌬i Length of a complete pattern Subpattern (threshold) for target r stored in GN node n’s successor Subpattern for target r stored in GN node n’s predecessor Successor node of GN node n Predecessor node of GN node n Set of mGN nodes = {mGN1 , mGN2 , . . . mGNc }

14.2.3 Notations Following are the notations to be used throughout the chapter (Table 14.1):

14.3 Attack Model The analytical model of a sensor network undergoing a DDoS attack consists of two types of network traffic: normal and attack. The flow of traffic in a typical sensor network is directed from the sensors to the base station. Nodes follow a predefined set of paths for forwarding their sensory readings to the base station. In this chapter we consider a cluster head (CH)–based network topology, wherein each CH is responsible for the cluster administration, data gathering, and data forwarding operations within its cluster of operation. The CHs aggregate and forward the sensory data to the base station in a multihop fashion. The data, whilst progressing through the network from a source node toward the base station, is aggregated on its way at aggregation points to minimize the overall traffic in the network. The traffic flow from the sensor nodes of a cluster through the CH and the aggregation nodes can be expressed as f = { f1 , f2 ,. . ., fL(f) }, where L( f ) is the length of path from node f to the base station. For our network model, we consider the taxonomy of the network to be continuous [21] wherein the sensory data are delivered by the CHs to the base station constantly every t intervals of time. Target nodes are defined as nodes located at critical points in the network. For instance, aggregation nodes closer to the base station as well as the CHs can be tagged as potential targets. The total traffic received by a target node r in a given time epoch (⌬i ), and that needs to be monitored by our scheme, is given by: λr =

f

λr, f f +

l

a

λr,a,l a,l ,

(14.1)

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where λr,f f is the normal traffic rate belonging to flow f, and λr,a,l a,l is the attack traffic rate from flow a originating from an attacker belonging to the attacker set l. Each node in the network is considered to bear a single queue, with average time for packet processing and transmission being si . The intensity of the arriving traffic at node r is thus given by: ρr = si · (

f

Ir, f f +

l

Ir,a,l a,l )

(14.2)

a

Ir,f f is defined as normal traffic intensity, whereas Ir,a,l a,l is defined as the attack traffic intensity. We consider the case of attack detection by means of studying the overall traffic intensity intended toward a set of target nodes in the network. The traffic arrival intensity at node r thus is a function of the individual arrival intensities of both the normal sensory traffic as well as the attack traffic. The attack patterns are a set of threshold values depicting the maximum number of packets that may be receivable by a target node during a given frame of time. These packets may arrive at the target node from different regions of the network, and therefore, a collaborative effort is needed to detect anomalous traffic flow rates toward the victim nodes. Sensor nodes participating in the GN array are trained at network initialization time to store subpattern values pertaining to each of the r target nodes in the network. These subpatterns are composed of a (value, position) pair in the GN array, where the value field of a GN node i for a target node r is an integer defining the threshold thr i of the maximum number of requests that may be accepted by node r within a given time period from the region of operation of node i. The threshold values are computed by the pattern generation algorithm, as given in Algorithm 1. The position fields of the GN pairs (subpatterns) identify the location of the GN node in the GN array. This field is necessary for defining the structure of the GN array, that is, successor and predecessor nodes at network initialization time. As can be seen from Algorithm 1, the proximity of a detector node to the base station defines the value of the threshold generated. The values of thr n stored in the GN nodes thus facilitate the classification of the observed traffic flow into attack or normal traffic. For a continuous data delivery model, the value of α, defining the rate of delivery of sensory data to the cluster head, will be known beforehand. The data aggregation (DA) nodes in the network are responsible for accumulating the messages received from cluster heads lower in the hierarchy. Therefore, total number of messages, that is, packets that need to be transmitted by a DA-node are much lesser than the number of packets needed to be transmitted by a CH. In addition, the Euclidean distance of each of the n GN nodes from the victim nodes

Algorithm 1 Attack pattern generation for i = 1 to n do for j = 1 to r do thj i = α . (dBS j + dGN(j) (i)) end end

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Table 14.2 Threshold (subpattern) values for target nodes R1 and R2 Node ID

(0,0)

(0,1)

(0,2)

(0,3)

(1,0)

(1,1)

(1,2)

(1,3)

thR1 thR2

94 35

96 41

92 46

90 47

44 88

41 85

49 87

54 89

signify the need for a GN node to detect traffic flow toward a particular victim. Therefore, note that higher values of dGNj (i) make the observed values of traffic flow toward node j from GN node i less significant to the detection process. Figure 14.1 depicts a scenario wherein the network is operating with two clusters. Traffic flow toward two example target nodes, R1 and R2, needs to be monitored by the GN nodes. Table 14.2 gives the threshold values stored by the GN nodes. The GN node ID is a two-tuple, given by . As can be seen from Table 14.2, for target R1, GN nodes (0, x) stores relatively high subpattern values. In other words, nullifies the effect of their observation to the attack detection process. However, nodes belonging to the cluster 1 have lower threshold values for the same target indicating the significance of their observations for traffic flow toward R1. Similarly, GN nodes (1, x) depict high threshold values for distant target node R2, whereas GN nodes (0, x) being in the vicinity of the target node, have smaller threshold values.

14.4 The Detection Scheme The attack detection scheme proposed in this chapter generates and maintains clusters of GN nodes in the network. Each cluster is autonomous in nature and performs its attack detection process without the need to collaborate with GN nodes belonging to the other clusters. The purpose of having clusters for pattern recognition is to facilitate tolerance to failure of GN nodes due to compromise or energy loss. The cluster-based GN algorithm requires bifurcations in the complete pattern depicting an attack based on the cluster ID. The GN nodes in a cluster are thus responsible for collaborating with peer GN nodes within their clusters alone for pattern reconstruction purposes. In the event of node compromise or failure, the extent of damage is concerned only to the particular cluster in question, with the remaining clusters operating unfazed.

14.4.1 Assumptions Sensor node locations are assumed to be static after initial deployment. All communication packets have a node ID tag appended to them for identifying both the source as well as the intended destination. Node IDs can be generated from unique knowledge possessed by a given sensor node [17]. For instance, the relative location of the sensor node may also serve as the node’s unique knowledge, which can be preset into the sensor memory at initialization time. In this case, the ID for node n

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at location lxy is given by: IDn = f(lxy ). The GN detector nodes of each of the c clusters are preconfigured with the knowledge of neighboring sensor nodes to facilitate construction of patterns constituting a GN array depicting normal traffic behavior in the network. For this purpose, the GN nodes are preset with location details of their neighbor nodes within the network. In [8], the authors propose the use of beaconless approach toward storing location details in sensor nodes. Similarly, in [19], a location discovery scheme wherein node locations are derived as relative coordinates with respect to a given reference point in the network. Any of the aforementioned schemes will suffice for purposes of our proposed scheme. The GN nodes are assumed to be loosely time synchronized to ensure timely and accurate completion of the communication phase of the GN application. One of several schemes for time synchronization proposed in the literature, such as [6,10], will suffice for our scheme. Each GN node shares a pairwise distributed key with three other nodes, namely successor, predecessor, and the masterGN (mGN) node, and therefore, will store three pairwise keys in its memory. The mGN nodes store all keys, which they share with the GN nodes in their cluster, as well as a key that they share with the base station. The keys are scalar quantities with no direction information, therefore, KB A = KA B . All GN and mGN nodes are preconfigured with these keys at network initialization time using one of several key predistribution schemes such as [2,4,7] proposed in the literature. The intent of having a shared key is to ensure the message origin authentication and message integrity check of all inter-GN node communication using a Message Authentication Code (MAC). A counter value (ctr), as a function of the current time epoch (Δi ) value, is appended to the message to ensure protection against message replay attacks. All messages exchanged between GN/mGN nodes/base station will have the following format: A → B m, M AC(K A B , m, ctr (Δi )

(14.3)

where, A = GN/mGN source node B = <nsucc(A) v npred(A) v qA v base station> ctr(Δi ) = counter value as a function of the current time epoch Δi .

14.4.2 Optimal Cluster Size Large numbers of clusters in the network will tolerate node compromise to a larger extent. Similarly, smaller numbers of clusters will lead to improved resource usage at the cost of reduced tolerance to node compromise. For a network of size N with c clusters, the total number of nodes excluding the CH in a cluster are: n = Nc − 1, which also defines the number of GN nodes operational in the network. If the value of c is large, the overall energy consumption rate of the scheme will be very high

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due to the added cost of CH operations. Similarly, having a small number of clusters will reduce the success rate of the detection scheme. Therefore, an optimal value of c must be found to achieve the goal of reducing the energy consumption of the network for a reasonable degree of accuracy in attack detection. We define an analytical model to determine the optimal number of clusters, copt , for a given network with given dimensions and node deployment densities. The network area is assumed to be a square grid with side a. The total number of grids in the network is equal to the number of clusters c. For a network with N nodes, the average number of nodes per cluster is n = Nc − 1, and the total number of cluster heads is c. It is also assumed that each cluster head is located approximately in the center of its grid. For a network with N nodes and side of grid = a, the expected distance from the CH to individual nodes in the cluster is given by: E[d C H ] =

0.707a √ c

(14.4)

In a scenario without node loss due to compromise and/or failure, the total energy consumed by the network is given by: E total = c.[E C H + (

N − 1).E nodes ], c

(14.5)

where ECH is the energy consumed by the cluster heads and Enodes is the energy consumed by the non-CH nodes in a cluster. The cluster heads aggregate data and follow a multihop route for data delivery to the base station. For shorter communication distances, the free-space model is used to model the power loss (power loss is the square of the internode distance d2 ), whereas for longer distances (between the CH and the base station), the multipath fading model is used, where the power loss is the fourth power of the distance (d4 ). The value of ECH is a function of energies utilized for the following processes: receiving data from the n nodes, aggregation of data from n nodes (EDA ), and data transmission to base station (EBS = Eelec + εmp (d4 BS )). εmp is the energy utilized for transmission of a bit of message over a given distance (multipath fading model). Eelec is the electronics energy, which depends on operations such as digital coding, modulation, filtering, and spreading of the signal [15]. The energy consumed by a CH for an l-bit message is given by: E C H = l.[n.E elec + n.E D A + E elec + εmp d B S 4 ].

(14.6)

Since the non-CH nodes are in vicinity of the CH, we consider the energy consumption to follow the Friss free-space model, where the power loss is a square of the distance between the nodes and the CH, (d2 CH ). The non-CH nodes only transmit data to the CH, and therefore the energy consumption of these nodes is given by: E nodes = l.[E elec + ε f s .(dC H 2 )],

(14.7)

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where εfs is defined as the energy utilized per bit of message transfer using the free-space model. We define q as the ratio of nodes lost due to compromise by an adversary. We also define γ = 1 – q. In untrusted environments of operation with non-zero likelihood of node compromise, Equation 14.5 is modified as follows: E total = c.[E C H + γ .n.E nodes ] = l.[(N − c).E elec + N .E D A + cE elec + cεmp d B S 4 γ N ε f s (0.707a)2 − γ cE elec − γ ε f s (0.707a)2 ] + γ N E elec + c

(14.8)

¯ derivative The optimal number of clusters, copt , is therefore a solution of the rst of (14.8), given by: copt =

γ N ε f s 0.499a 2 εmp(d B S 4 ) − γ E elec

(14.9)

In Fig. 14.2, we have plotted the values of copt for varying numbers of nodes in the network, and varying node compromise ratios, q. The values of the constants were taken as: l = 10 bytes, εfs = 10 pJ/bit/m2, εmp = 0.0013 pJ/bit/m2, Eelec = 50 nJ/bit, EDA = 5 nJ/bit/signal, a = 100, and dBS = 56 m [from simulations]. It can be seen that the value of copt does not double with proportional increases in the value of N. For instance, with q = 10%, the optimal number of clusters is 21 for N = 512, and is nearly 28 for N = 1024.

14.4.3 The Scheme The attack detection scheme, as illustrated in Algorithm 2, consists of the following five phases of operation: copt vs N

106 91

copt

76 61

q = 1% q = 10% q = 15%

46 31 16 1

128

256 512 1024 Number of Nodes (N)

Fig. 14.2 Optimal cluster number vs. Number of nodes

2048

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287

Algorithm 2 The DDoS attack detection scheme 1. Initialization for i = 1 to c do pick random decision-making GN node (mGNc ) end Pattern Generation & Learning for i = 1 to n do Generate pattern: pn = {pn 1 , pn 2 ,. . ., pn r } end 2. Observation for i = 1 to n do for j = 1 to r do Monitor traffic flow toward r targets and Update traffic flow table locally end end 3. Communication for i = 1 to n do for j = 1 to r do if traffic flow table entry for r > thr n then Communicate with neighboring nodes nsucc ˆ npred to reconstruct subpattern {pn r , pnsucc ,r pnpred r } end end for i = 1 to c do mGNi receives r observations from n = Nc − 1 nodes for i = 1 to r do Generate decision signal: attackc r or normalcyc r end end end 4. Verdict for i = 1 to c do for all r, if attackc r = 1, Transmit attackc r to base station end 5. Pattern Update for i = 1 to n do Update thr n End

Initialization: At network initialization time, the base station randomly selects one of the GN nodes in each cluster to operate as a master GN (mGN) node. Step 2 of this phase involves the selection of GN nodes in each of the c clusters by the base station. In our scheme, we assume that all cluster nodes participate in the GN array, and therefore this step of the algorithm is redundant. Each GN node is initialized with two tables in its local memory, namely, traffic flow table and pattern table. The GN nodes store the maximum threshold value, thr n , associated with each of the r targets within their respective pattern tables. Once initialized, these threshold

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values are updated only during Phase 5 of the detection algorithm. The traffic flow table has constantly changing values based on the observation of the neighborhood traffic flow toward the r targets. A comparison between corresponding values for a given target r in these two tables at the end of a given time epoch Δi decides the output signal sign r (Δi ) to be generated by the GN node n for transmission to its designated mGN node. Observation: In this phase, each GN node promiscuously monitors packets initiating or transiting through its neighborhood toward one of the r critical target nodes. The GN node updates its traffic flow table with the incoming request counter for the target node and the source address of the traffic. At the end of the current time epoch Δi , the traffic flow table values are compared with corresponding values stored in the pattern table. It may be noted that addition of new targets and deletion of existing ones is done by the base station at network initialization time. Communication: The completion of the observation phase is marked with the onset of the communication phase when each GN node GNn communicates with exactly two other adjacent nodes, namely, the successor (nsuccn ) and the predecessor (npredn ), to form a dual-point linked chain of GN nodes. The purpose of having a dual-point linked chain is to facilitate reconstruction of complete traffic patterns from individually observed subpatterns of traffic flow. Consequently, a complete traffic flow pattern for each of the given target nodes r for a given time frame is generated. At each GN node, if the number of incoming requests for a particular target r during the current time epoch exceeds the stored threshold thr n value in the pattern table and its successor and predecessor nodes have also detected similar anomalies given by their respective subpatterns, pr nsucc and pr npred , the GN node n will generate an attack signal for the current time epoch. On the contrary, a normalcyr signal generated by the GN nodes implies incomplete or no-match between the observed traffic pattern and the stored pattern of anomalous behavior for traffic destined for node r. All GN node communication takes place in parallel, and therefore, the overall communication delay incurred is minimal. After comparison with the adjacent GN nodes, the outcome of a pattern recognition process from each individual GN node is communicated to its designated mGN node. Verdict: Ideally, if half of the operating GN nodes communicate with their respective mGN nodes at the end of a given time epoch, a complete traffic pattern can be reconstructed since the complete pattern reconstruction from individual subpatterns had been accomplished during the previous phase. However, for purposes of ascertaining peer readings, we expect all GN nodes to convey their findings to their designated mGN nodes at the end of each time epoch. At the end of the current time epoch Δi , if the number of GN attack signals = n = Nc − 1, for any or all of the specified targets arriving at the mGNc for cluster c, the traffic flow is classified as an N −1 c. attack, that is, for all r, attack cr (i) = 1, then an attack against r is confirmed as i=1

being in progress.

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Pattern Update: The decaying energy contents of individual sensor nodes in the network demand the need for constant update of pattern values stored in the Pattern Tables of the GN nodes. The accuracy of the pattern recognition scheme depends on the frequency of update of the thr n values. If the update rate is not at pace with the rate of declining energy resources of the target nodes (energy consumption rates), incoming attack traffic may lead to exhaustion of energy of the target nodes and remain unnoticed by the observing GN nodes. We modeled the energy resource drop rate for the target nodes as follows: α.[E trans + Er ecv ] t α.l.E elec + α.[l E elec + lε f s d 2 ] , = t α.l.[2.E elec + ε f s d 2 ] = t

μr =

(14.10)

where Erecv = Energy required to receive l bits, Etrans = Energy required to transmit l bits over a distance of d meters, t = Time interval = 1 msec, μr = Energy consumption rate of node r, α = 3 packets/msec Upon successful confirmation of an attackr signal, the base station sends a signal to induce node r into sleep mode for a finite period of time. Subsequently, the base station ensures that if alternative resources are available, a signal is sent to designate them the task of continuing with the sensing operations from the region of operation of node r. For instance, if node r belonged to a DA-based topology responsible for aggregation of received data, the base station sends a request to another active node available within the vicinity of node r instructing it to take over the data aggregation responsibilities of r.

14.5 Evaluation In this section, we provide a detailed analysis of the simulations performed for varying simulator parameter values. The purpose of our experiments was to test the following hypothesis: • Compromise of detector nodes will have a receding impact with decreasing cluster sizes. • Fewer detector nodes need to operate for networks with lower deployment densities.

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14.5.1 Experimental Setup Simulations were performed for a network of size 100 × 100 m with varying node deployment densities. The deployment of sensor nodes follows a uniform distribution throughout the network. The deployment region is a square grid with side a = 100. We assume that all nodes are equally likely candidates for loss owing to failures, battery exhaustion, or compromise. In addition to their routine sensing operations, the attack detector GN nodes also participate in the attack detection process. It may therefore be safely presumed that the task of selectively identifying and launching attacks against the detector nodes by an adversary is nontrivial. Sensor nodes are assumed to have a single interface for both transmit and receive operations. We considered a standard sensor node with average energy consumptions for transmission Etrans = 100 nJ/bit and Erecv = 50 nJ/bit, with the maximum radio range of each sensor node being 10 m. The following hypotheses were tested through the simulations: • Increasing node densities will lead to improved detection rates • Detection rate will be the highest for c = copt .

14.5.2 Simulation Parameters The following parameters were used in the simulation setup: • SR: The transmission range of a sensor node = 50 m. • Δ: Time epoch length for detection scheme convergence. • TI (Traffic Intensity): Packets generated toward the r target nodes during a given time epoch (Δ). • copt : Optimal cluster size for a network with given dimensions. • q: Percentage of compromised nodes.

14.5.3 Analysis Simulations were carried out for varying values of the input parameters to study: the attack detection rates and the energy decay value as well as the convergence delays of the detection scheme. In order to set the thresholds in the attack patterns, the network was trained by testing it with varying values of traffic intensities (both attack and normal). In addition, the time epoch length, Δ, was taken as 30 ms, and the corresponding traffic intensity, TI , was taken as 500 packets/Δ, implying that the expected numbers of packets by each of the r target sensor nodes during Δ is 500. It may be noted here that in a real-world scenario, to increase the longevity of the sensor nodes the value of TI must be lowered. We also assumed that all cluster nodes, n = Nc − 1, participate in the attack detection process.

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14.5.3.1 Detection Rate vs. Node Loss Ratio We study the attack detection rates for variations in the value of q. As mentioned earlier, the DDoS attack detection scheme proposed in [1] does not tolerate node losses caused by energy exhaustion and/or compromise. In our proposed scheme, the use of multiple clusters operating in parallel, to detect DDoS attack patterns, ensures that node losses up to a certain extent do not significantly affect the detection success rate. In Fig. 14.3, the detection rate reaches nearly 34% for q = 1% and c = copt . For the same value of c, about 27% of the attacks are detected even when node loss ratio q reaches 15%. For smaller values of c (0.2copt , 0.5copt ), the detection rate varies from 28% for q = 1%, to 24% for q = 15%. Fewer numbers of clusters (small c) lead to reduced tolerance to node loss, and therefore lower the overall detection rate. The detection rate reaches 0% for nearly 30% node loss for smaller values of c. However, for larger values of c, the network, being more tolerant to node failure, demands 50% node loss before reaching the zero success rate point. In Figure 14.4, the detection rate shows a significant improvement as compared to the 128 node case. With c = copt and q = 1%, the detection rate is nearly 80%, and reduces to 61% for q = 15%. The improved success rate here is due to the higher densities of node deployment, which ensures that the overall delay associated with the convergence of the detection scheme is reduced due to the smaller communication distances between the GN nodes. Similarly, Fig. 14.5 shows further improvements in the detection rates for increasing numbers of clusters. For c = copt and q = 1%, the detection rate is nearly 85%, and for q = 15%, the detection ratio is around 68%. The attack detection process is thus reasonably accurate even when 15% of the nodes in the network are lost. For networks with higher node deployment densities (Figs. 14.6 and 14.7), the detection rate is nearly 94% when all N nodes are operational, and c = copt , and is nearly 72% when q is 15%. It may be noted here that even when c = 0.5copt , the detection rate is very high. This implies that for larger N, after a certain number of clusters are operational in the network, the role of increasing values of c in improving the attack detection rate is diminished. In such scenarios, lower c values can achieve

Detection Rate

0.4

c = 0.05 c = 0.1 c = 0.2 c = 0.5 c = copt

N = 128

0.3

0.2

0.1 0.01 0.03

0.05

0.09 0.13

0.15

0.30 0.50

Compromise Ratio (q)

Fig. 14.3 Detection rate vs. q (128 node network)

0.70

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Z.A. Baig, A.I. Khan N = 256

c = 0.05 c = 0.1 c = 0.2 c = 0.5 c = copt

0.9 0.8 Detection Rate

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.01

0.03

0.05 0.09 0.13 0.15 Compromise Ratio (q)

0.30

0.50

Fig. 14.4 Detection rate vs. q (256 node network) 1

N = 512

Detection Rate

0.9 0.8 0.7

c = 0.05 c = 0.1 c = 0.2 c = 0.5 c = copt

0.6 0.5 0.4 0.3 0.2 0.1 0.01 0.03 0.05 0.09 0.13 0.15 0.30 0.50 0.70 Compromise Ratio (q)

Fig. 14.5 Detection rate vs. q (512 node network)

1

N = 1024

Detection Rate

0.9 0.8

c = 0.05 c = 0.1 c = 0.2 c = 0.5 c = copt

0.7 0.6 0.5 0.4 0.3 0.2 0.1

0.01 0.03 0.05 0.09 0.13 0.15 0.30 0.50 0.70 Compromise Ratio (q)

Fig. 14.6 Detection rate vs. q (1024 node network)

14 A Fault-Tolerant Scheme for Detection of DDoS Attack Patterns in WSNs

Detection Rate

N = 2048

c = 0.05 c = 0.1 c = 0.2 c = 0.5 c = copt

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

293

0.01 0.03 0.05 0.09 0.13 0.15 0.30 0.50 0.70 Compromise Ratio (q)

Fig. 14.7 Detection rate vs. q (2048 node network)

high detection rates with the advantage of lower scheme convergence delays and at the cost of slightly higher energy decay rates. From the analysis of the experiments, it can be concluded that the optimal value of c given by copt gives an upper-bound on the success in attack detection for smaller N. However, for larger values of N, suboptimal c values are sufficient for achieving reasonably high detection success rates. The attack detection process relies on parallel internode communication for collaboration and pattern reconstruction purposes (see Algorithm 1). The increasing densities of node deployment in the network will reduce the overall distances between the attack detector nodes, and thus will significantly reduce the overall convergence delay of the scheme. As a result, the success in the attack detection process improves significantly. However, this improved success rate is subdued by the increasing value of q. As can be seen from Fig. 14.8, increasing values of N lead to improved success rates in attack detection. For c = copt and q = 10%, the detection rate is nearly 81% when the Detection Rate vs N (q = 10%) 0.9

Detection Rate

0.8

c = 0.05 c = 0.1 c = 0.2 c = 0.5 c = copt

0.7 0.6 0.5 0.4 0.3 0.2 0.1 128

256 512 1024 Network Size (N)

Fig. 14.8 Detection rate vs. Network size

2048

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network has 2048 nodes, and is nearly 31% when the network has 128 nodes. For c = 0.1copt , the detection rate increases from nearly 12% for N = 128, to 60% for N = 2048. Thus, the attack detection rate shows a steady improvement for increases in the total numbers of clusters in the network. Corollary 1 Larger N will increase tolerance to node loss more than smaller N, and therefore, higher node deployment densities improve the overall effectiveness of the attack detection scheme. 14.5.3.2 Scheme Convergence Delay The communication phase of the attack detection algorithm converges at the end of each time epoch, Δ. As can be seen from Table 14.3, the scheme has a significantly less delay associated with convergence for larger values of c as compared to smaller c values. For the 128 node scenario, there is a 20% increase in the delay associated with convergence for higher values of c, that is, more number of clusters. This is because the cost of convergence relies on the maximum number of parallel communications that can be achieved within each cluster of operation. Smaller values of c imply larger sized clusters, thus more parallelism, and lower delays. With increasing values of N, the convergence delay improvements for increasing c are negligible. For instance, in the N = 2048 scenario, a 2% increase in the delay is observed between c = 0.5copt and c = copt . This is because even with fewer operating clusters (large c) the total number of nodes within each of the clusters is still very high. In such a scenario, the lower delays due to parallelism are fully exploited, and therefore increases in delay are negligible. 14.5.3.3 Energy Decay Rate Table 14.4 illustrates the overall energy consumption rate of the network per unit of time. As expected, the optimal cluster number c shows the lowest energy consumption rates for all values of N. Increasing node deployment densities lead to increase in the total energy consumption rates. However, it may be observed from the table that for N = 2048 and c = copt , the energy consumption rate is not a 10 × multiple of the N = 256 case. This is because for smaller N, larger distances need to be traversed by the messages exchanged between the nodes, and therefore longer delays. In addition, the total number of messages exchanged in the N = 256 scenario will be much less than when N = 2048. Therefore, the energy loss associated with increasing

Table 14.3 Scheme convergence delay (msecs) N=

128

256

512

1024

2048

0.05 copt 0.1 copt 0.2 copt 0.5 copt copt

6.29 6.36 6.56 7.01 7.85

12.04 12.1 12.4 13.1 14.2

23.4 23.6 23.9 24.8 26.5

46.17 46.4 46.8 48.12 50.3

91.7 92.0 92.7 94.6 97.9

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Table 14.4 Energy decay rates (␮Joules/sec) N=

128

256

512

1024

2048

0.05 copt 0.1 copt 0.2 copt 0.5 copt copt

509 255 104 52 43

511 342 151 76 63

1025 415 215 110 92

1370 692 332 165 134

1653 841 463 230 196

values of N is compensated with corresponding reductions in the internode distances for increasing N. From the simulation results it may be deduced that optimal values of c may not be the most appropriate setting in certain network conditions. Scenarios where longer delays are not tolerable, the value of c can be taken as 0.5copt at the cost of slightly degraded attack detection rates. Similarly, in mission-critical environments, wherein the accuracy in attack detection is more important, the c = copt setting is more appropriate.

14.6 Conclusions A fault-tolerant, cluster-oriented mechanism is proposed to detect DDoS attack patterns in Wireless Sensor Networks. The Graph Neuron algorithm is extended to facilitate timely and accurate detection of attacks. A tradeoff equation is formulated to compute the optimal number of clusters based on several parameters including the expected number of nodes lost due to failure and compromise. The scheme compares traffic flow with predefined knowledge of known patterns of normal network traffic behavior. Simulations were performed to test the impact of the variation of the number of clusters on the performance of the scheme in terms of the energy consumption rates, scheme convergence delays, and the accuracies in the detection process. We showed that our scheme performs well even with suboptimal numbers of clusters for certain network scenarios. Acknowledgments We would like to thank Professor Bala Srinivasan, Faculty of Information Technology, Monash University, for his invaluable comments and suggestions on our research. This research was partially funded by the Australian federal government’s Data Acquisition, Accessibility, Annotation e-Research Technologies (DART) project.

References 1. Baig, Z., Baqer, M., and Khan, A. (2006) A Pattern Recognition Scheme for Distributed Denial of Service (DDoS) Attacks in Wireless Sensor Networks. In Proceedings of the 18th International Conference on Pattern Recognition 2. Chan, H., Perrig, A., and Song, D. (2003) Random Key Predistribution Schemes for Sensor Networks. In Proceedings of the IEEE Symposium on Security and Privacy 3. Chang, R. (2004) Defending Against Flooding-based Distributed Denial of Service Attacks: A Tutorial. IEEE Communications Magazine: 42–51

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4. Du, W., Deng, J., Han, Y., Chen, S., and Varshney, P. (2004) A Key Management Scheme for Wireless Sensor Networks Using Deployment Knowledge. In Proceedings of IEEE INFOCOM 5. Elliot, J. (2000) Distributed Denial of Service Attacks and the Zombie Ant Effect. IT Pro: 55–57 6. Elson, J., Girod, L., and Estrin, D. (2002) Fine-grained Network Time Synchronization using Reference Broadcasts. ACM SIGOPS Operating Systems Review 36: 147–163 7. Eschenauer, L., and Gligor, V. (2002) A Key-Management Scheme for Distributed Sensor Networks. In Proceedings of the 9th ACM Conference on Computer and Communications Security 8. Fang, L., Du, W., and Ning, P. (2005) A Beacon-less Location Discovery Scheme for Wireless Sensor Networks. In Proceedings of IEEE INFOCOM 9. Gligor, V. D. (2003) Guaranteeing Access in Spite of Service-Flooding Attacks. In Proceedings of Int’l Workshop on Security Protocols 10. Hu, A., and Servetto, S. (2003) Asymptotically optimal time synchronization in dense sensor networks. In Proceedings of ACM International Conference on Wireless Sensor Networks and Applications 11. Jalili, R., Imani-Mehr, F., Amini, M., and Shahriari, H. (2005) Detection of distributed denial of service attacks using statistical pre-processor and unsupervised neural networks. In Proceedings of First Information Security Practice and Experience Conference 12. Khan, A. (2002) A Peer-to-Peer Associative Memory Network for Intelligent Information Systems. In Proceedings of the Thirteenth Australasian Conference on Information Systems 13. Khan, A., Isreb, M., and Spindler, R. (2004) A parallel distributed application of the wireless sensor network. In Proceedings of the 7th Int’l Conference on High Performance Computing and Grid in Asia Pacific Region 14. Khan, A., and Mihailescu, P. (2002) Parallel Pattern Recognition Computations within a Wireless Sensor Network. In Proceedings of the Int’l Conference on Pattern Recognition: 777–780 15. Kim, H., Kim, S., Lee, S., and Son, B. (2005) Estimation of the Optimal Number of Cluster-Heads in Sensor Network. Knowledge-Based Intelligent Information and Engineering Systems: 87–94 16. Lei, J., and Ghorbani, A. (2004) Network intrusion detection using an improved competitive learning neural network. In Proceedings of the Second Annual Conference on Communication Networks and Services Research 17. Newsome, J., Shi, E., Song, D., and Perrig, A. (2004) The Sybil Attack in Sensor Networks: Analysis and defenses. In Proceedings of IEEE Conference on Informantion Processing in Sensor Networks (IPSN’04) 18. Ramadas, M., Ostermann, S., and Tjaden, B. (2003) Detecting anomalous network Traffic with self-organising maps. In Proceedings of the Sixth Intl. Symp. on Recent Advances in Intrusion Detection 19. Shih, K., and Wang, S. (2005) Distributed Direction-Based Localization in Wireless Sensor Networks. In Proceedings of the 10th IEEE Symposium on Computers and Communications (ISCC’05) 20. 20. Sinha, A., and Chandrakasan, A. (2001) Dynamic Power Management in Wireless Sensor Networks. IEEE Design and Test of Computers 5: 62–74 21. Tilak, S., Abu-Ghazaleh, N., and Heinzelman, W. (2002) A Taxonomy of Wireless Microsensor Network Models. ACM Mobile Computing and Communications Review (MC2R) 22. Wood, A., and Stankovic, J. (2002) Denial of Service in Sensor Networks. IEEE Computer Magazine: 54–62 23. Zhang, G., and Parashar, M. (2006) Cooperative Defense against DDoS Attacks. Journal of Research & Practice in Information Technology: 69–84 24. Zheng, J., and Hu, M. (2006) An Anomaly Intrusion Detection System Based On Vector Quantization. IEICE Transactions on Information and Systems (2006): 201–210

Chapter 15

Forming Energy-Efficient Bluetooth Scatternets for Sensor Networks Sain Saginbekov

15.1 Introduction Energy is a very important resource in wireless sensor networks. The choice of wireless communication technology for a sensor network has an effect on the lifetime of the network since different wireless technologies have different power parameters. Another factor that greatly impacts the energy spent in a sensor network is the routing scheme used in the sensor network, because the routing scheme affects how many times and over what distances packets have to be transmitted. Bluetooth is one of the wireless technologies available today and that can be a candidate for being the wireless communication technology for some type of sensor networks. Its low-cost, low-power, and small size are the main features that make it a good candidate technology. A Bluetooth scatternet spanning all the sensor nodes, however, has to be formed first before transmitting data in the sensor network, and scatternet formation policies and algorithms are not well specified in Bluetooth standards. Since the topology of a scatternet affects the routing scheme, it also affects the energy consumption in the sensor network. Therefore, it is important to form scatternets that are energy efficient. In this chapter, we propose an energy-efficient scatternet formation algorithm for Bluetooth-based sensor networks. The main objective of the algorithm is to prolong the lifetime of a sensor network by reducing the total energy consumed during data transfer from all sensor nodes to the base station. The proposed algorithm is a centralized algorithm that is executed at the base station. Therefore, it requires the base station to know the exact locations of sensor nodes so that the base station can compute the connectivity information among the nodes. The chapter also gives simulation results to evaluate the proposed algorithm. The simulation results show that the proposed algorithm causes a sensor network to spent total energy not significantly more than the lower bound. S. Saginbekov Computer Engineering Department, Suleyman Demirel University, Almaty, 050043, Kazakhstan e-mail: sain [email protected]

S.K. Makki et al. (eds.), Sensor and Ad Hoc Networks, C Springer Science+Business Media, LLC 2008 DOI: 10.1007/978-0-387-77320-9 15,

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The rest of the chapter is organized as follows. In Section 15.2, we give some background information and describe some of the related work. In Section 15.3, we give our model of a sensor network for which the algorithm is developed. In Section 15.4, we describe the proposed algorithm in detail. Section 15.5 describes how the data is routed to the base station. In section 15.6, we provide and discuss some results to evaluate the algorithm. Finally, in Section 15.7, we give our conclusions.

15.2 Background and Related Work Various wireless communication technologies can be considered as the underlying communication technology for a sensor network. However, not all of these candidate technologies satisfy the requirements and constraints of sensor networks and sensor nodes. A sensor node should be low-cost, consume low-power, and should be of small size. Bluetooth [8] can be a good candidate technology since it is low-power, low-cost, and has small form factor. As stated in [2], today’s available hardware platforms for sensor networks can be divided into four classes: special purpose sensor nodes, generic sensor nodes, high-bandwidth sensor nodes, and gateway nodes. The power requirements of those nodes increase respectively. Bluetooth technology can be used as part of sensor nodes that fall into the third class. Current sensor nodes that use Bluetooth as an underlying communication technology are BT node (developed in 2001) and Imote 1.0 (developed by Intel Research in 2003). The less energy consuming 802.15.4 and Zigbee can be used in sensor nodes that are included in the second class. 802.15.4 provides a data rate in the order of 250 Kbps, whereas Bluetooth provides a raw data rate of 1 Mbps. Therefore, Bluetooth is better for sensor networks applications that are bandwidth demanding. Bluetooth technology supports nodes to form ad hoc networks that are selfconfiguring. This property of Bluetooth is also important for sensor networks, which are also required to be usually self-configuring and dynamic. Bluetooth devices can be categorized into three classes with respect to the energy consumption during transmission: 1. A class 1 Bluetooth device has a communication range of 100 m and a transmit power of 100 mW (20 dBm). 2. A class 2 device has a communication range of 50 m and a transmit power of 2.5 mW (4 dBm). 3. A class 3 device has a communication range of 10 m and a transmit power of 1 mW (0 dBm). Bluetooth supports different power modes. This is another feature of Bluetooth that can be utilized by sensor network applications. The available power modes are: active mode, sniff mode, hold mode, and park mode. In sniff mode, master and slaves agree on certain time intervals to communicate. The master then sends packets to a slave only on the agreed periods. In this way, a slave can go into

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sniff mode and sleep. This enables a slave to spend less energy. Hold mode is used by slaves to switch to other piconets. For that a slave goes into hold mode in the current piconet, and then switches to another piconet and becomes active in that piconet. When a slave is in hold mode in one piconet, it does not consume any energy, since it is not involved in any communication activity in that piconet. Park mode is a mode where the device is not active. In this mode, a device also does not retain its temporary Media Access Control (MAC) address. In this way, more than seven slaves can be connected to a single master. Some of these slaves will be in active mode (at most seven of them) and the others will be in park mode. In a sensor network, nodes usually do not transmit and receive data continuously, but at regular times or when an event occurs. Therefore, supporting sniff and hold modes makes Bluetooth a good technology that can utilize the characteristics of sensor networks for energy conservation. There are two ways to form a Bluetooth network. The first way is forming a piconet. However, a piconet may have at most eight devices in it, and therefore, most sensor networks cannot be established as a single piconet. The second way to form a Bluetooth network is forming a Bluetooth scatternet. A Bluetooth scatternet consists of overlapping Bluetooth piconets. These overlapping piconets are interconnected with some special Bluetooth nodes called bridges. A bridge node takes part in two or more piconets in a time-shared manner. Each piconet has a different frequency hopping sequence. Therefore, taking part in a piconet requires switching to the hopping sequence of that piconet. Constructing a scatternet is not a well-defined process in Bluetooth standards. There are several studies in the literature [3,4,9,10,11] that propose algorithms to form scatternets. Whatever the algorithms is, the final scatternet topology must satisfy the Bluetooth constraints such as each node having at most a degree of seven. The construction of scatternet can also consider the requirements of applications that will be run over the constructed scatternet. For example, a sensor network application usually requires the data to flow from sensor nodes to a single base station. Hence, a scatternet can be constructed with this property in mind so that some metrics can be optimized or improved. One such metric is energy efficiency. Once a Bluetooth scatternet is formed, how to route the traffic over the scatternet is another issue that has to be addressed. Depending on the topology characteristics of the scatternets, the topology may also determine the routing policy. For example, if the topology is tree-shaped, then the routing scheme to be used is trivial: a node should send packets to its parent or vice versa. Hence, the scatternet topology affects the routing scheme that is used. Depending on the sensor network applications, the routing scheme may be optimized in various ways for energy efficiency. There are routing schemes proposed for sensor networks that are based on various metrics. A routing scheme, for example, can try to reduce the total energy consumed in the network per unit time; another routing scheme may try to distribute the load on sensor nodes evenly so that all nodes die nearly at the same time.

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There are many studies on Bluetooth scatternet formation problem and many studies on routing problem in sensor networks. Those studies are separate from each other. There are very few studies, however, that are investigating both of the problems. One [6] of these few studies that consider both of the problems mentioned earlier, forms a scatternet for a sensor network application using a clustering approach. The protocol, abbreviated as DCP, is divided in two phases: a setup phase and a steady-state phase. In setup phase, each node learns its neighbors and at least one packet forward address (PFA). A node in a network can take one of the two roles: cluster member or cluster head. Cluster heads are selected randomly with a given probability. In steady-state phase, PFA is used to forward the data to the base station. Cluster members in a cluster periodically forward sensed data to their cluster head, and the cluster head, after fusing or compressing data, forward the data to the base station. If the cluster head is not in the communication range of the base station, it forwards the data through another cluster head. In DCP, a node in the formed network is not necessarily a master or a slave. They allow more than seven nodes to connect to a single node. However, the authors do not describe how a node can get associated with more than seven nodes. Moreover, simulation results show that for a given probability, the number of unconnected nodes is high for a communication range of 10 m. In [5], a Bluetooth-based sensor network is formed using the Bluetree protocol mentioned in [12]. This scatternet can be used in sensor networks. However, since the main consideration in Bluetree algorithm is not energy consumption, it is not a very good choice for sensor networks. The scatternet formation algorithm proposed in [4] is divided again into two phases: knowledge discovery phase and connection setup phase. In knowledge discovery phase, some characteristics about the sensor nodes are gathered by the base station. In the connection setup phase, base station starts selecting one-hop apart nodes as slaves, those slaves select their neighbors as slaves, and this process is repeated until the leaves are reached. Since there can be only up to seven slaves in a piconet, they propose a new technique to select nodes as slaves according to some criteria. They have used simulated annealing [3] for this purpose.

15.3 Model and Problem Statement A model for a sensor network depends on various factors: the type of sensor network application, the characteristics of the information collected, the capabilities of sensor nodes, the properties of the communication technology, and so forth. Hence, a model requires some reasonable assumptions to be made. We make the following assumptions in establishing our model for which we provide a solution. • Nodes are using class 3 Bluetooth radio chips to communicate with each other and with base station. This implies that the range of transmission is 10 m and the transmit power is 1 mW (0 dBm).

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• Each node is in the radio coverage of at least one another node. • The devices are capable of power control. Hence, the energy required to transmit a fixed size packet over a single hop is different and is dependent to the distance. • Sensor nodes and the base station are stationary. • Data aggregation is not used. This implies that if a node receives several packets, it does not combine them into a single packet to transmit them to the next node. It sends them separately to the next node. This is because, for some applications, data aggregation may not be allowed due to application semantics. • The base station has complete knowledge about the location of sensor nodes. Therefore, the base station knows which nodes are directly reachable from a given node. • All nodes do not have to be in the communication range of each other. • All nodes are homogeneous and using Bluetooth technology to talk with each other and to the base station. Now the problem is to construct a Bluetooth scatternet spanning a set of given sensor nodes with the properties listed earlier so that the total energy spent during a single round of data transfer from all sensor nodes to the base station is kept as low as possible by making the total distance of a scatternet as small as possible. Since not all nodes are in the range of base station and since the degree of a Bluetooth node can be at most seven, we need multihop communication for carrying data from sensor nodes to the base station. The solution for this problem will be explained in next section. Also, in the next section, solution for a case where data aggregation is used will be explained.

15.4 Algorithm In this section, we explain our proposed algorithm for forming energy-efficient scatternet. Before explaining our algorithms, we define some terminology that will be used in our proposed algorithm. Distance between two nodes N and M is the length of a path between nodes N and M. Label of a node N is the distance between the root to node N. Level of a node is the number of hops between that node and a root. Descendants of a node N are the nodes which are connected to a root through N. NumOfDescendant of a node N is the number of descendants of node N. SumOfLabelsOfDescendant of a node N is the sum of labels of descendants of node N. Degree of a node N is the number of nodes that are connected to node N. maxDeg is the maximum degree that a node can have in a tree. In our case maxDeg is 7. Round of communication is the activity in which each node senses the environment (hence obtains data) and sends the data to the base station using multihop communication. In our algorithm, where no data aggregation is assumed, first we form shortest path tree rooted at base station using Dijkstra’s Single Source All Shortest Path Tree [1] algorithm. After forming a shortest path tree, the labels of the nodes must

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be the smallest. Therefore, this tree consumes minimal energy per round of communication according to our third assumption (see Section 15.3). However, we cannot directly use Dijkstra’s algorithm because it does not consider the degree constraint when forming a tree. So we have to solve the degree constraint problem when forming a Bluetooth scatternet. Since our aim is to make the total distance between the root and all other nodes as small as possible, while reducing the degree of a node to 7, we should make the changes on the shortest path tree such that the total change in distance is the smallest; in other words, the change in labels should be minimal. Having formed the shortest path tree by Dijkstra’s algorithm, we start from the topmost level searching for a node with degree greater than maxDeg. Assume that degree(k) > maxDeg for some node k. It means that this node violates the degree constraint of a tree. So, we have to reduce the degree of this node. To do so, we choose a node s among the children of k and node m such that if we disconnect s from k and connect it to m, the total change in labels of descendants of node s will be minimal (see Algorithm 1). Change in labels of descendants of node s is determined by the change in label of node s. This difference is added to all descendants of node s. It means, S1 = sumOfLabelOfDescendant(s) will be S2 = [label(m)+distance(m,s)–label(s)] × numOfDescendant(s)+S1 . So, we choose the nodes m and s such that is minimal. This way we can reduce the degree to maxDeg. However, after changing the parent of node s, distances of some descendants from the root may not be the shortest. To make it shortest, for each descendant r of node s, we choose node f such that if we disconnect r from its parent and connect it to f, the label of r decreases (see Algorithm 2). We do all these steps until the degree of node k is no more than maxDeg. Figure 15.1a shows aforementioned situation. Assume that degree(k) > maxDeg. Further assume that label(k) = 10, distance(k,s) = 5, distance(s,r) = 3, label(m) = 11, distance(m,s) = 6, distance(m,f) = 4, and distance(r,f) = 4. After applying our algorithm on shortest path tree, node s is connected to m making the new label(s) = 17 and label(r) = 20. From here, we can see that label(r) = 20 is not the shortest because if we connect node r to node f, the new label(r) will be 11 + 4 + 4 = 19. Figure 15.1b shows the final obtained tree.

(b)

(a) k

k m

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Fig. 15.1 Scatternet formed (a) before and (b) after Algorithm

s

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Algorithm 1 DCBT (Degree Constrained BlueTree) Input: Coordinates of each node Output: Degree Constrained BlueTree Form Shortest Path Tree using Dijkstra’s Single Source All Shortest Paths Algorithm for each level p = 0 to heightOfTree do for each node k of level p if degree(k) > maxDeg then while numberOfChildren(k) ≤ maxDeg do choose node m from rest of the nodes and s among children such that [label(m)]+distance(m,s)–label(s)]*numOfDescendants(s) + +sumOfLabelsOfDescendants(s) is minimal and degree(m)<7 disconnect s from k connect s to m Reconnect(s) end while end if end for end for

Another algorithm that solves the degree-constrained shortest path tree problem is d-Dijkstra’s algorithm. We call this d-Dijkstra’s because it works like a traditional Dijkstra’s algorithm. There is only one change. In this algorithm, when selecting the next node, algorithm checks whether a degree of node to be connected is no more than a specified value. If the degree is smaller, then it connects new node to a tree, if not, it tries to connect another node to a tree. As we will see in simulation results, the scatternet obtained by our algorithm lives longer than the scatternet formed by d-Dijktra’s algorithm and it is near to lower bound. Algorithm 2 solves the problem that considers the case when there is no data aggregation (see Section 15.3, fifth assumption). When we have data aggregation, we can solve this problem by any Minimum Spanning Tree (MST) algorithm like Prim’s and Kruskal’s without any modification to these algorithms. In other words, we do not need to solve degree problem after forming MST. It is because after

Algorithm 2 Reconnect(s) for each descendant r of node s do choose node f such that label(f) + distance(f,r) is minimal and degree(f)<maxDeg if label(f) + distance(f,r) < label(r) then disconnect r from its parent connect r to f end if end for

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forming MST, no node will have a degree more than 6. By geometrical observation, if a node has degree more than 6, it is not MST.

15.5 Routing The routing in our scatternet is simple. As we mentioned earlier, in piconet each node can communicate with other nodes only through a master node. After forming a scatternet (see Fig. 15.2), each parent node will take a function of a master and its children take a function of slaves. Each node sends its data to its master. And the master node sends the collected data to its master and so on, till reaching the base station.

15.6 Simulation Results To check the efficiency of our algorithm, we did simulation experiments. We have implemented our simulation using C++ programming language. The nodes are randomly deployed in an area of 50 m × 50 m. We took maxDeg = 7, and the maximum distance = 10 m, that means only the nodes that are at most 10 m apart to each other can be connected. In our simulation, we compare the total distance obtained from a tree formed by our algorithm with Dijkstra’s algorithm and d-Dijkstra’s algorithm. Dijkstra’s algorithm gives us the lower bound on the distance, telling us that the total distance obtained from a tree formed by this algorithm is the smallest. Figure 15.3 shows the comparison of total distance between the root and all other nodes of a tree formed by Dijkstra’s algorithm, d-Dijsktra’s algorithm, and our algorithm. We call our algorithm Degree Constrained BlueTree (DCBT). We use the total distance of shortest path tree formed by Dijkstra’s algorithm just to compare results obtained from our algorithm, to find how good our algorithm is. d-Dijktrsa’s algorithm considers the degree constraint of a node, but as we can see in Fig. 15.3, it is not very efficient. In the tree formed by d-Dijktsra’s algorithm, as the number of nodes increases the total distance increases sharply. The total distance of a tree formed by our algorithm is much better than the total distance formed by d-Dijkstra’s algorithm, and a little larger than the total distance

Fig. 15.2 Routing in scatternet formed by second algorithm Master (Base station) Master/Slave • Slave

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12000 10000 8000 6000 4000 2000 0

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Fig. 15.3 Comparison of total distance between root and all other nodes in a tree formed by three different algorithms

of a shortest path tree formed by a Dijkstra’s algorithm. This implies that in DCBT the energy is less consumed.

15.7 Conclusion Bluetooth’s short-range, low-cost, low-power features allows this technology to be used in sensor networks. In this work, we proposed a new algorithm that forms an energy-efficient Bluetooth scatternet for sensor network applications. In our algorithm, we used Dijkstra’s Single Source All Shortest Path Tree algorithm and reduced the degree of each node to a miximum of seven while keeping the overall distance as small as possible. We compared our result with the lower bound. The future work can focus on solving the stated problem not in a centralized way but in a distributed way. In other words, the scatternet formation will not be done by a base station.

References 1. Cormen, T.H., Leisorson, C.E., Rivest, R.L., and Stein, C. (2001) Introduction to Algorithms, second edition, MIT Press, 2001 2. Hill, J., Horton, M., Kling, R., and Krishnamurthy, L. (2004) The Platforms Enabling Wireless Sensor Networks. Communications of the ACM, 47:41–46

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3. Kirkpatrick, S., Gelatt, C.D., and Vecci, M.P. (1983) Optimization by Simulated Annealing. Science, 220:671–680 4. Law, C., Mehta, A.K., and Siu, K.Y. (2001) A Bluetooth Scatternet Formation Algorithm. In Proceedings of 2001 ACM International Symposium on Mobile Ad hoc Networking and Computing: 183–192 5. Leopold, M., Dydensborg, M., and Bonnet, P. (2003) Bluetooth and Sensor Networks: A Realty Check. In Proceedings of SenSys 2003 6. Mathias, H., Jan, D., and Dirk, T. (2004) Energy-efficient Data Collection for Bluetooth-based Sensor Networks. IEEE Instrumentation and Measurement Technology Conference 7. Mehta, V., and El Zarki, M. (2002) Fixed Sensor Networks from Civil Infrastructure Monitoring – An Initial Study. In First Annual Mediterranean Ad Hoc Networking Workshop (Med-hoc-Net 2002) 8. Miller, B.A., and Bisdikian, C. (2001) Bluetooth Revealed: The Insider’s Guide to an Open Specification for Global Wireless Communications. Prentice Hall 9. Petroli, C., Basagni, S., and Chlamtac, I. (2003) Configuring Bluestars: Multihop Scatternet Formation for Bluetooth Networks. IEEE Transactions on Computers, 52:779–790 10. Prabhu, B.J., and Chockalingam, A. (2002) A Routing Protocol and Energy Efficiency Techniques in Bluetooth Scatternets. Design and Test of Computers 11. Salonidis, T., Bhagwat, P., Tassiulas, L., and LaMaire, R. (2001) Distributed Topology Construction of Bluetooth Personal Area Networks. In Proceedings of 28th Annual Joint Conference of the IEEE Computer and Communication Societies IEEE INFOCOM 2001, 3:1577–1586 12. Zaruba, G.V., Basagni, S., and Chlamtac, I. (2001) Bluetrees-scatternet Formation to Enable Bluetooth-based Ad hoc Networks. In Proceedings of IEEE International Conference on Communications, 1:273–277

Index

3-SAT, 206 A Access point, 101, 124, 161 Actuator-aware routing, 185–186 Ad hoc, 1–15, 19–24, 26, 27, 28, 30, 31, 38, 43, 44, 76, 108, 124, 125, 126, 127, 136, 144, 145, 161–163, 165, 221–222, 224, 238, 298 Ad hoc network, 1–13, 19–22, 24, 26, 27, 28, 30, 31, 38, 44, 76, 127, 144, 161–163, 221–222, 238, 298 Adjustment, 130–133, 135, 137, 138, 141, 142, 143–144, 241 Analytical model, 45, 53–66, 68, 69, 281–283, 285 Anchor-node, 203 Asymptotical optimality, 178 Asymptotic behavior, 19, 27, 75 Asymptotic connectivity, 23, 30, 31, 37–38 Attempted, 139 B Backbone, 3, 9, 102, 103, 112–115, 116, 117, 119, 147, 148, 161–163, 165, 167, 168, 169, 170–172, 173, 174, 175, 177, 178, 246 Backbone based approach, 112–115, 116, 117, 118 Beacon mechanism, 223 Best angle heuristic, 168, 169 Bidirectional, 108 Blind flooding, 161 Blocked, 137, 139, 140 Bluetooth, 2, 297–298, 299, 300, 301, 302 Borel–Cantelli lemma, 35 Boundary, 44, 45, 46, 47, 48, 50, 51, 53, 85, 86, 88, 89, 90, 91, 92, 95, 97, 166, 167, 170, 172, 173, 174

Boundary effect, 44, 45, 46, 47, 48, 50, 51, 52, 53 C Capacity, 2, 9, 19, 20, 21, 23, 29, 74, 85, 101, 102, 108, 124, 125, 130, 131, 132, 134, 144, 145, 240, 261 Cellular, 20–21, 123, 124, 125, 126, 127, 130, 133–135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145 Centralized algorithm, 211, 212, 218, 297 Channel assignment, 101–103, 105, 106, 107, 108, 111, 112, 114, 115, 116, 117, 118, 119 Channels, 20, 95, 101–103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 123, 144, 145, 149, 203, 249, 255, 260, 280 CLDP, 178 Cluster-based networks, 278 Clustering, 6, 7, 8, 102, 148, 184, 197, 240, 255–257, 259, 260, 261, 262, 263, 264, 265, 266, 268, 269, 270, 271–274, 275, 300 Communicate, 7, 20, 29, 44, 85, 101, 104, 107, 109, 112, 113, 125, 136, 181, 195, 213, 264, 265, 275, 277, 279, 288, 298, 300, 304 Communication, 2, 4, 7, 9, 10, 11, 12, 23, 43–44, 74, 76, 85, 90, 92, 102, 104, 105, 106, 112, 123, 124, 125, 127, 144, 147, 148, 150, 161, 162, 163, 165–168, 175, 176, 178, 182, 184, 185, 186, 188, 194, 196, 197, 204, 209, 210, 212, 213, 215, 237, 238, 249, 255, 256, 260, 263, 264, 272, 275, 280, 283, 284, 285, 287, 288, 291, 293, 294, 297, 298, 299, 300, 301, 302

307

308 Concurrent, 124, 137, 139–140, 142, 153, 186, 209 Confidence level, 68, 70 Connected dominating set, 119, 147, 159 Connection, 114–115, 124, 125, 127, 128, 129, 130, 131, 132, 133–134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 195, 206, 209, 213, 247, 256, 262, 263, 269, 280, 300 Connectivity, 1, 19, 21, 23, 24–26, 27, 30, 31, 32, 37–38, 43–44, 45–53, 63, 70, 76, 101, 104–105, 108, 109, 110, 111, 119, 123, 124, 125, 148, 212, 256, 262, 263, 265, 269–270, 272, 274, 297 Connectors, 112, 113–114, 147, 206, 207 Convergence time, 223, 230, 231 Coverage, 1, 9, 10, 14, 44–45, 46, 47, 48, 49, 51, 52, 54, 59, 66, 68, 70, 74, 75, 76, 89, 97, 124, 125, 127, 131, 133, 136, 137, 140, 141, 144, 146, 161, 301 Coverage area, 44, 45, 46, 47, 48, 49, 51, 52, 54, 68, 144 Critical transmission power, 109 Cross-layer, 194, 197–198, 238, 239, 241, 242–245, 247, 250, 251 Cross-layer services, 197–198 D Data aggregation, 184, 240, 245, 248, 249, 279, 282–283, 289, 301, 303 Data centric routing, 184 Deployed area, 43, 63 Deployment area, 44, 45, 46, 47, 51, 63, 64, 209, 215, 216, 218 Deployment region, 44, 48, 49, 51, 52, 68, 103, 204, 215, 216, 219, 290 region types, 215 Depth first search traversal, 179 Dijkstra’s algorithm, 302, 303, 304, 305 Distributed computation, 204 Distributed Denial of Service, 277, 278, 279, 280, 281, 287, 291, 295 Distributed pattern recognition, 278, 279 Dominatees, 112–113, 114–115 Dominating set, 75–76, 112–113, 119, 147, 151–152, 205, 210, 211, 213, 214, 222, 256 Dominators, 112, 113, 114, 147, 148, 150, 151, 153, 155, 156, 157, 158, 159, 212 Downlink, 123–124, 125, 129, 130–133, 137, 138–139, 140, 141, 143, 144, 145

Index Dropped, 124, 137, 138, 140, 142, 143, 162, 167, 174 dT-vector, 224, 228–229, 230, 231 E EAMCDS, 148, 150–153, 158, 159 Effective area, 46, 55, 56 Effective connectivity, 43–44, 45–53, 54, 55, 56, 57, 62, 63, 64 Effective coverage, 44–45, 46, 59, 66, 70 Election factor, 149, 151, 153 Energy, 3, 7, 8, 9, 10–11, 29, 30, 74, 75, 76, 85, 87, 90, 94, 95, 98, 147–148, 149–153, 155, 156, 157, 158–159, 161, 162, 165, 166, 175, 176–177, 178, 183, 184–185, 188–190, 191–193, 196, 204, 209, 215, 224, 238, 239, 240, 241, 242, 244, 245, 255–256, 257, 260, 264, 270, 272, 275, 277–278, 279, 280, 283, 284, 285, 286, 289, 290, 291, 293, 294–295, 297–298, 299, 300, 301, 302, 305 Energy life, 148, 149–150, 151, 153, 157, 158–159 Error-realization, 206 NP-hardness, 205–208 F Factor, 6, 57, 76, 84–91, 98, 104, 114, 130, 131, 137, 149, 151, 153, 177, 183, 204, 206, 212, 223, 233, 239, 255, 256, 257, 275, 280, 297, 298, 300 Frequency, 12, 20, 86–87, 102, 108, 125, 144, 289, 299 Fundamental performance limits, 19, 22 G Gabriel graph, 148, 164, 167, 175, 177 Geographic routing, 148, 162, 164, 203 Geometric random graph, 24, 25, 28, 38 Global time synchronization (GS), 221, 223, 224, 226–228, 229–230, 231 GMR, 166, 168 GMREE, 166, 168 Graph, 19–40 drawing, 27, 31, 209 filtration, 209 force-directed, 214, 219 undirected, 27, 205 Graph Neuron, 278, 279, 280–281 Greedy, 134, 140, 162, 166, 167, 175, 176, 177, 178, 256

Index H Heterogeneity, 3, 14, 123, 238, 239, 240, 251 Heterogeneous, 3, 4, 5, 85, 123–124, 144, 196, 237, 238, 239, 241, 250–251, 252 Hierarchical agglomerative clustering (HAC), 255–276 CLINK, 259, 262, 271, 272, 274 Distributed HAC algorithm (DHAC), 257, 264–274 SLINK, 259, 262, 267, 271, 272 UPGMA, 259, 261, 262, 263, 268, 269, 270, 271, 272, 274, 275 WPGMA, 259, 262, 271, 272, 274 Hierarchical routing, 184 I IEEE, 802.11, 106, 108, 125, 144, 145, 175, 221, 223, 224 Independent basic service set (IBSS), 221, 224, 225, 226 In-network services, 194, 197, 198 Integrated, 55, 59, 60, 61, 64, 65, 74, 123, 124, 125, 126, 127, 128, 130, 135, 137, 138–139, 140, 145–146, 188, 237, 240, 248, 251 Interference models, 102, 103, 106, 107, 117 range, 104, 106, 107, 112, 117 temperature, 102 Intrusion detection, 92, 279 J Jaccard, 258, 274 K Knapsack, 131–132, 133, 134, 135 L Lamport clock, 221 Localization anchor-free, 203–204, 208–209 centralized, 205 hardness results, 205–208 hierarchical, 208–214 Localized algorithm, 76, 162, 178 Localized delaunay triangulation, 153, 158, 159, 164 Local measurements, 205 absolute, 205–206 directions, 205, 210, 212–213 distances, 205, 206, 209, 210, 211, 212, 218 erroneous, 210 relative, 205, 210, 214, 218

309 Local time synchronization (LS), 221–222, 223, 225–226, 228 Location-based routing, 185 Location database, 164 M MCDS, 147–148, 157 MFACE, 161–179 delivery guarantees, 162, 166, 167, 172 face intersection property, 168–172 face switch, 165, 170 loop free operation, 162, 166, 167, 173 multicast split property, 162, 168, 170–172 traversal start, 168, 170, 171, 174 Middleware services, 194–197 MKAR, 131, 137, 143 Mobile node, 43–44, 53, 101, 125, 128, 136, 229, 257 Mobility model, 14, 43–44, 53, 54, 59, 62, 63, 64, 66–67, 85, 86, 95–96, 136 Model, 2, 6, 7, 8, 13–14, 19, 20, 21, 22, 23, 24, 25, 26–30, 32, 33, 37, 38, 39, 43–44, 45–66, 67–68, 69–70, 74, 76, 85, 86, 92, 95–96, 97, 101, 102, 103–104, 106, 107, 108, 110, 114, 117, 124, 127–129, 135–136, 144, 148, 149–150, 166, 175, 176, 178, 188–189, 195, 205, 215, 278, 280, 281–283, 285, 286, 298, 300–301 Modular architecture, 238 MSTEAM, 165, 167, 168, 177 Multicast routing, 161, 162–163, 178 Multivariate, 101–120 N Neighborhood, 21, 23, 112, 115, 148, 151, 161, 162, 163, 164, 167, 177, 187, 205, 209, 210, 212, 213, 221, 280, 288 k-hop, 113, 133, 205 nesC, 188, 191 Network capacity, 19, 20 Network density, 175, 176, 177 Network embedding, 4, 73, 204, 205, 206, 207, 208, 209 folding free, 209 Network topology, 9, 20, 23, 26, 28, 29, 108, 147, 162, 178, 189, 278–279, 281 NodeB, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 139, 140, 141, 142, 144 Node connectivity, 44, 45–53, 63 Node coverage, 44–45, 68

310 Node degree, 6, 21, 22, 23, 24, 25, 30, 31, 37–38, 39, 113, 212, 215, 217, 219, 264, 271, 272, 274 Node density, 63, 90, 189, 230, 231, 232 Node orientation, 218 NP-complete, 111 NP-hard, 111, 118, 147, 204, 205–208 O On-demand service, 224 Overlay network, 144–145, 205, 209, 210, 212, 213 P PBM, 166, 167, 168 Piconet, 299, 300, 304 Planar graph, 148, 153, 162, 164, 165, 167, 175, 177, 178 Positioning, see Localization Profile, 3, 136, 249 Propagation, 25, 26–27, 28–29, 85, 135, 150, 260 Protocol integration, 240, 248 Proxy AP, 126, 130, 133, 138 Proxyed-connection, 138, 139, 140 Proxyed user, 131, 134, 140–141, 143 Q QoS, 123–124, 125, 126, 130, 131, 138, 140, 145, 237, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 251 Qualitative coefficients, 258 Quantitative coefficients, 257 Quasi unit disk graph, 163, 164, 178 R Radio range, 215, 223, 224, 233, 290 Random graph, 19–20, 24, 25, 26, 27, 28, 31, 37, 38 Random network model, 24, 27 Random vertex model, 27, 31, 38 Random walk, 43, 53, 54, 56, 59, 62, 63, 64, 65, 66–68, 69, 75, 80 Random waypoint, 43–44, 62, 63, 64, 68–70, 136 Rate, 8, 20, 21, 68, 74, 85, 87, 88, 89, 90, 91, 93–94, 95, 98, 123–124, 125, 126, 130–134, 135, 137, 138–139, 140, 143–144, 280, 282, 284–285, 289, 290, 291–295, 298 Region, 44, 45, 46, 47, 48–49, 50–51, 53, 54, 55, 56, 57, 60, 61, 63, 64–66, 68, 70, 74, 76, 78, 80, 81, 82, 84, 86,

Index 87, 103, 106, 109, 112, 115, 184, 185, 204, 215, 216, 219, 229, 282, 289, 290 Regional divisions, 45, 46 Relative neighborhood graph, 148, 164, 177 Robustness, 203, 215, 219, 223 Routing, 1, 4, 8, 9–10, 11, 12, 14, 20, 76, 102, 105–106, 118–119, 125, 136, 144, 145, 147, 148, 153, 157, 161, 162–163, 164, 165, 166, 167, 168, 170, 173, 175, 176, 177, 178, 181–187, 188, 190, 192, 193, 198, 203, 213, 214, 238, 240, 242, 244, 246, 248, 249, 251, 297, 299, 300, 304 S Scalability, 1, 3, 8–9, 19–20, 23, 37, 38–39, 188–190, 191, 203, 204, 219 Scatternet, 297–298, 299, 300, 301, 302, 303, 304 formation, 297, 300 SDRP, 182, 183, 186–187, 188, 189, 190, 193, 194, 198 Sensor networks, 2, 3–13, 14, 15, 19–20, 22, 24, 28, 38, 73–74, 75, 76, 84, 92, 147, 149, 161–163, 165, 177, 181–183, 184, 194, 196, 197, 199, 203–205, 209, 222, 237–238, 239–240, 242, 248, 250, 255–257, 277–279, 281, 297–298, 299, 300 architecture, 238, 239, 250 Service-driven query routing, 181–200 Shuffling, 131, 133, 134, 135, 138, 140–142, 143, 145 Simple matching, 258, 274, 275 Simplification, 77, 131, 137, 143, 227 Simulation, 9, 11, 13, 14, 44, 45, 63, 67, 68–70, 79, 80, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 103, 110, 116, 117, 119, 124, 133, 135–137, 141, 143, 153–159, 175, 188, 205, 214–218, 271, 279, 290–295, 304–305 SOAP, 7 Sorenson, 258, 262, 263, 274, 275 SOSANETs, 194 Spatial density, 63, 69 Spectrum scarcity problem, 102 Stochastic time delay, 221–222, 223, 230 Subnetwork, 103, 147, 185 T Target beacon transmission time (TBTT), 223, 225, 226, 227, 228, 229, 234

Index Threshold, 6, 44, 84, 85, 95, 103, 106, 109, 126, 131, 132, 148, 150, 151, 153, 157, 158, 159, 187, 188, 260, 261, 262, 263, 264, 265, 268, 271, 274, 282, 283, 287–288, 290 Throughput, 13, 19, 20, 21–24, 101, 102, 103, 105–107, 108, 112, 117, 123–124, 125, 137, 138–139, 144 Time synchronization, 221–234 Time synchronization function (TSF), 221, 223 TinyDB, 188, 191, 192, 193–194 TinyOS, 5, 187–188, 192, 241 TinySOA, 5, 183, 187–188, 190, 191–192, 193, 198–199 Topology control, 1, 19, 39, 75, 147–149, 150–153, 178, 203, 247 Transition phenomena, 103, 104–105, 109–111 Transmission area, 44, 53 power, 37, 39, 44, 106, 109, 153, 158, 245 radius, 20, 22, 23, 24, 25, 26, 38, 41, 103, 260, 261 range, 25, 28, 31, 44, 45, 48, 53, 63, 64, 68, 69, 104, 108, 109, 110, 112, 115, 117, 119, 149, 154, 156, 158, 265, 290

311 U UMTS, 124–125, 136, 144 Unicast face routing, 165–166 Uniform coverage, 44, 68 Uniform density, 54 Uniform model, 68, 70 Unit disk graph, 109, 114, 163, 164, 175, 178, 204 UTRAN, 124, 125, 126, 127 V Vanishing throughput effect, 20, 21–22, 23 W WiFi, 123, 124 Wireless, 1–2, 3, 5, 7, 12, 14, 19, 43–44, 76, 85, 101–103, 104, 105, 106–107, 108–109, 110–111, 113, 114, 115, 116–117, 123–124, 125, 127, 144, 147, 148, 153–154, 161, 163, 197, 203, 204, 222, 237–238, 245, 249, 255–257, 277–279, 297, 298 Wireless interference, 102, 103, 106–107, 108 Wireless network graph, 163 Wireless sensor networks, see Sensor networks WLAN, 4, 123, 124, 125, 126, 127, 136, 144, 145 WWAN, 4, 123, 124, 125, 126

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