NODE ACTIVATION POLICIES FOR ENERGY-EFFICIENT COVERAGE IN RECHARGEABLE SENSOR SYSTEMS

Transcription

1 NODE ACTIVATION POLICIES FOR ENERGY-EFFICIENT COVERAGE IN RECHARGEABLE SENSOR SYSTEMS By Neeraj Jaggi A Thesis Submitted to the Graduate Faculty of Rensselaer Polytechnic Institute in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Major Subject: Computer and Systems Engineering Approved by the Examining Committee: Koushik Kar, Thesis Adviser Ananth Krishnamurthy, Member Alhussein A. Abouzeid, Member Shivkumar Kalyanaraman, Member Rensselaer Polytechnic Institute Troy, New York May 2007

2 NODE ACTIVATION POLICIES FOR ENERGY-EFFICIENT COVERAGE IN RECHARGEABLE SENSOR SYSTEMS By Neeraj Jaggi An Abstract of a Thesis Submitted to the Graduate Faculty of Rensselaer Polytechnic Institute in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Major Subject: Computer and Systems Engineering The original of the complete thesis is on file in the Rensselaer Polytechnic Institute Library Examining Committee: Koushik Kar, Thesis Adviser Ananth Krishnamurthy, Member Alhussein A. Abouzeid, Member Shivkumar Kalyanaraman, Member Rensselaer Polytechnic Institute Troy, New York May 2007

3 c Copyright 2007 by Neeraj Jaggi All Rights Reserved ii

4 CONTENTS LIST OF TABLES vii LIST OF FIGURES viii ACKNOWLEDGMENT ABSTRACT x xi 1. Introduction Rechargeable Sensor Systems Effect of Spatial Correlation Effect of Temporal Correlation Node Activation Question Need for Localized Algorithms Contributions of this Thesis Background and Related Work Energy Management in Ad-hoc and Sensor Networks Coverage and Connectivity Issues Correlation Modeling in Sensor Networks Node Activation in Rechargeable Sensor Systems Introduction Problem Formulation Performance Metric Challenges and Basic Approach System Model and Assumptions Sensor Lifetime Models Threshold Activation Policies Analysis Upper Bound on Ū I and Ū C Threshold Activation Policies for the IL Model Threshold Activation Policies for the CL Model Comparison of IL and CL Models iii

5 3.5 Numerical Results Performance under IL and CL models Distribution Independence Summary Distributed Activation Policies under Random Sensor Deployment Distributed Node Activation Algorithm Upper Bound on Optimal Time-average Utility Sensor Lifetime Models Simulation Results and Discussion Node Activation in Partially Rechargeable Sensor Systems Introduction Model, Formulation and Contribution System Model and Formulation Methodology and Contribution Preliminaries Recharge and Discharge Process Models Identical Sensor Coverage Spatial Correlation Models Upper Bound on the Optimal Time-average Utility Aggressive Activation Policy Analysis Simulation Results Threshold Activation Policies Analysis of Threshold Policies Simulation Results Activation Policies in a General Network Scenario Distributed Threshold Activation Algorithm Choice of Threshold Discharge and Recharge Event Models Simulation Results Summary iv

6 6. Rechargeable Sensor Activation under Temporally Correlated Events Problem Formulation On-Off Periods System Observability Activation Policies Aggressive Wakeup (AW policy Correlation-dependent Wakeup (CW policy Activation under Perfect State Information Upper Bound on Achievable Performance Optimal Policy Optimal Policy evaluation using Value Iteration Activation Algorithm Activation under Imperfect State Information Structure of Optimal Policy MDP Formulation Properties of ǫ-optimal policies Optimal Policy evaluation using Value Iteration Energy Balancing Correlation-dependent Wakeup Policies Upper Bound on CWP Performance Performance of EB-CW policy Performance Effects of Boundary Conditions Performance of AW Policy Simulation Results Temporally Uncorrelated Event Occurrence Summary and Conclusions Effect of Temporal Correlations in multiple-sensor systems Problem Formulation Performance Metric Threshold based Activation Policies Time-invariant Threshold Policy (TTP Correlation-dependent Threshold Policy (CTP Performance Evaluation Upper Bound on Achievable Performance Performance of Threshold Policies v

7 7.2.3 Simulation Results Summary Concluding Remarks and Future Work Future Directions LITERATURE CITED vi

8 LIST OF TABLES 3.1 Performance ratio of threshold policies for low detection probability Performance ratio of threshold policies for high detection probability ǫ-optimal actions for perfect state information Optimal actions for sample cases Performance for various threshold pairs vii

9 LIST OF FIGURES 1.1 Wireless Sensor Networks: Applications Rechargeable Sensor: States and Transitions Utility Function based Performance Metric Queuing network representation for the IL model Queuing network representation for the CL model Queuing network model of intermediate system Performance of threshold policies for low detection probability Performance of threshold policies for high detection probability Transient sensor system behavior Threshold policy performance under various distributions of recharge and discharge intervals Performance with global thresholds Performance with local thresholds Performance with global thresholds and event correlation Performance with local thresholds and event correlation Quantum-queue model of a sensor Performance of Aggressive Activation Policy Queuing System representation of sensor system IDR Modification Models CDR Modification Models Performance of Threshold Policies Network Performance with local thresholds Energy discharge-recharge model of the sensor Temporally correlated event occurrence viii

10 6.3 Threshold energy wakeup functions Threshold energy wakeup functions for symmetric case Sensor activation under CW policy Event occurrence upon activation for AW policy Performance of CW Policies Performance of Threshold Policies ix

11 ACKNOWLEDGMENT I am grateful to my research advisor Prof. Koushik Kar for his guidance and support throughout the course of my PhD. His enthralling ideas and witty comments provided me with the needed encouragement and paved the way towards a successful thesis. I am indebted to Prof. Ananth Krishnamurthy for his kind and gentle attitude, and for the fruitful discussions we had during the process of this research. I am thankful to Prof. Alhussein A. Abouzeid and to Prof. Shivkumar Kalyanaraman for providing their consents to be a part of my doctoral committee. My friends Nabhendra Bisnik, Vicky Sharma and Vijay Subramanian need special mention here, as they have been a substantial part of my life at RPI. Sharing their experiences and discussing my own experiences with them, helped me grow personally as well as professionally. I am grateful to Shu Han, who provided supportive companionship throughout the course of my stay at RPI. I am grateful to my brother Pankaj for providing me with the initial motivation to pursue a PhD, and to his friend Prof. Biplab Sikdar for encouraging me to join RPI. Last but not the least, I acknowledge the sincere efforts and affection of my family and friends, who stood by me throughout, and without whose support my PhD would not have materialized. x

12 ABSTRACT Advances in sensor network technology enable sensor nodes with renewable energy sources, e.g. rechargeable batteries, to be deployed in the region of interest. The random nature of discharge and recharge, along with spatio-temporal correlations in event occurrences pose significant challenges in developing energy-efficient algorithms for sensor operations. An important issue in a system of rechargeable sensors is the node activation question How, when and for how long should a sensor node be activated so as to optimize the quality of coverage in the system? We consider two different energy consumption models for a sensor, namely (i Full Activation model, where a sensor could only be activated when fully recharged, and (ii Partial Activation model, where the sensor can be activated even when it is partially recharged. In the presence of spatial correlations in the discharge and/or recharge processes, with identical sensor coverages, we show analytically that there exists a simple threshold activation policy that achieves a performance of at least 3 of 4 the optimum over all policies under Full Activation, and is asymptotically optimal with respect to sensor energy bucket size under Partial Activation. We extend threshold policies to a general sensor network where each sensor partially covers the region of interest, and demonstrate through simulations that a local information based threshold policy achieves near-optimal performance. We then consider the scenario where the events of interest show significant degree of temporal correlations across their occurrences, and pose the rechargeable sensor activation question in a stochastic decision framework. Under complete state observability, we outline the structure of a class of deterministic, memoryless policies that approach optimality as the sensor energy bucket size becomes large. Under partial observability, we outline the structure of the history-dependent optimal policy, and develop a simple, deterministic, memoryless activation policy based upon energy balance which achieves near-optimal performance under certain realistic assumptions. With multiple sensors having identical coverages, threshold based activation policies achieve near-optimal performance. The energy-balancing threshxi

13 old policies are thus robust to spatio-temporal correlations in the discharge and recharge phenomena. xii

14 CHAPTER 1 Introduction Major innovations in hardware technologies in recent years have led to the development of small, low-cost sensor devices. It is envisioned that in the next few decades, these devices will be deployed in large numbers over vast areas, with the purpose of gathering data from the deployment region. Applications of such large-scale data gathering systems are numerous, and include military surveillance, environmental and health monitoring, and disaster recovery [3]. The data gathered could be used for various purposes, like constructing a temperature or pollution map of the region, determining the location of a herd of wild animals or a shoal of fish, or detecting unusual movements in the area under surveillance. Figure depicts some of the envisaged applications of a large-scale Wireless Sensor Network. In many of these applications, however, sensors are heavily constrained in terms of energy. Sensors are often powered by battery, and limitations on the size of the sensor puts constraints in terms of the battery energy. In applications that involve long-term monitoring such as those depicted in figure 1.1, typical battery lifetimes may be significantly smaller than the time over which the region of interest needs to be monitored. Therefore, effective management of energy is crucial to the performance of these large-scale sensing systems. For energy-efficiency reasons, we would like to activate (or switch on a sensor only when it is expected to improve the system performance significantly; the rest of the time, the sensor can remain in an inactive state (or switched off so as to conserve energy. 1.1 Rechargeable Sensor Systems A large number of sensor network applications involve monitoring of a geographically vast area over an extended period of time. Since the deployment region is vast, and often inaccessible, periodic replacement of sensor batteries may not be a viable solution. For long term monitoring of such environments, sensors can be 1 courtesy http : // content.php?idcat = 76 1

15 2 Figure 1.1: A variety of envisioned applications of Wireless Sensor Networks. deployed with rechargeable batteries which are capable of harnessing the energy from renewable sources in the environment such as solar power [40, 60]. Note that recharging can be a very slow process, possibly influenced by random environmental factors like the intensity of sunlight, speed of wind etc. Typically, the average rate of recharging would be significantly less than the average energy discharge rate during the sensing period. As a result, a sensor could need to spend most of its lifetime in the off state, when it is not sensing, but only recharging. In addition, these sensor devices, although cheap, are typically unreliable. Therefore, to improve sensing reliability, we want multiple sensors to cover the area of interest simultaneously. These factors motivate redundant deployment of sensors to cover the area of interest, so that the sensor system remains operational with high probability at any given time. If larger number of sensors are deployed, it is likely that more number of these sensors would remain charged (and hence can be used for sensing at any given time.

16 Effect of Spatial Correlation In general, the random process that governs the sensing environment will show a significant degree of spatial correlation. As an example, pollution level at any point is expected to have high correlation with respect to both space and time. In other words, if the pollution level at a point is currently above a certain threshold, it is likely to exceed this threshold at neighboring points in the near future. Since the energy discharge rates at sensors often depend on the detection and reporting of such interesting events, the energy discharge process at sensors, which are active at any particular time, could show some degree of spatial correlation. Moreover, in certain cases, the recharging process could also exhibit spatial correlations to a significant extent. This is true, for instance, in sensors that are recharged by solar power, since intensity of sunlight exhibits correlation in space and time. The dynamic nature of the sensing environment dictates that an efficient data gathering strategy must be adaptive in nature. The presence of spatial correlations in the discharge and/or recharge processes complicate the design of the optimal data gathering strategy. In some cases, prior knowledge of the degree of correlation could be used to activate or deactivate the sensors appropriately so as to optimize system performance. Spatial correlation of energy discharge and recharge processes could significantly affect the system performance. Thus, there is a need to develop data gathering strategies which would be robust even in the presence of spatial correlations Effect of Temporal Correlation In addition, the event occurrence process might exhibit significant correlation in time. For instance, if the temperature at any location in a forest rises above 100 F (representing a possibility of forest fire, then with high probability it will remain above the given threshold in the near future as well. Similarly, if the temperature is much below a critical threshold, it is expected to remain so for a while. Smart sensor node activation decision policies should take into account the degree of temporal correlation in (and the current status of the event occurrence process, while deciding to activate or deactivate (put to sleep a sensor node dynamically.

17 4 1.2 Node Activation Question The data gathering objective in a sensor network is to reliably sense and communicate the events observed by the sensor system. Loosely speaking, an event is an interesting occurrence at any point in the monitored region that we would like to know about. For instance, in pollution monitoring applications, an event can correspond to the level of pollution exceeding a predetermined level at any point in the region. Since detecting and reporting of events requires energy and sensors are energy constrained, developing efficient data gathering strategies is closely related to efficient use of sensor energy. In addition, the low-cost and failure-prone nature of sensor nodes, together with infeasibility of accurate sensor placement under dire circumstances, leads to a random and redundant deployment of such nodes. We pose the data gathering problem for rechargeable sensor systems as a dynamic sensor node activation question. The dynamic node activation question involves determining when each sensor should be involved in data gathering (activation and when they should be put in the sleep mode (deactivation, so as to maximize the long-term reliability index of the system. The measure of system reliability can be formulated in terms of the quality of coverage provided or by the event detection probability in the system. Note that since the sensors are heavily energy-constrained, activating a sensor whenever possible may not be a good node activation strategy. The key to obtaining efficient node activation policies is to activate some sensors currently, while keeping a sufficient number of sensors in store for future use. For a system with a single sensor node, efficient activation decisions would lead to a larger fraction of events being detected in the long run Need for Localized Algorithms Since events and sensor discharge and/or recharge constitute random processes, obtaining optimal solutions to the dynamic node activation questions we consider, require solving complex stochastic decision problems. However, these problems are computationally very difficult to solve optimally even in simple special cases, particularly when the region of interest is covered by all the sensor nodes in the system. Moreover, exact solutions to these stochastic decision questions require

18 5 global knowledge and coordination, and can only be useful as a static or off-line approach. Whereas, in practical scenarios, a sensor node would typically have access to only local topology and state information, and would be required to take an activation decision based only upon this local information. Hence, there is a need to develop distributed, low-overhead and local information based algorithms towards addressing the node activation questions in a rechargeable sensor system. 1.3 Contributions of this Thesis We start by answering the node activation question for a system of rechargeable sensors, wherein the sensor nodes could only be activated when fully charged. To find the optimal sensor node activation policy in such a case is a very difficult decision question, and under Markovian assumptions on the sensor discharge/recharge periods, it represents a complex semi-markov decision problem. With the goal of developing a practical, distributed but efficient solution to this complex, global optimization problem, we first consider the activation question for a set of sensor nodes, where all the sensors are able to cover the region of interest (identical coverage. For this scenario, we show analytically that there exists a simple threshold activation policy that achieves a performance of at least 3 4 of the optimum over all policies. We extend this threshold policy to a general network setting where each sensor partially covers the region of interest, and the coverage areas of different sensors could have partial or no overlap with each other, and show using simulations that the performance of our policy is very close to that of the globally optimal policy. Our policy is fully distributed, and requires a sensor to only keep track of the node activation states in its immediate neighborhood. We also consider the effects of spatial correlation on the performance of threshold policies, and the choice of the optimal threshold. We then consider the case where the recharge process at a sensor node is a continuous process, regardless of the current state (active or inactive of the sensor node. This scenario is motivated by the fact that renewable energy sources, such as sunlight, could drive the rechargeable batteries at the sensor nodes. In this system model, a sensor node can hold upto K quanta of energy, and can be activated even

19 6 when it is partially recharged. For the case of identical sensor coverages, we show that the class of threshold policies is asymptotically optimal with respect to K i.e. the performance of such a policy for a chosen threshold parameter approaches the optimal performance as K becomes large. We also show that the performance of the optimal threshold policy is robust to the degree of spatial correlation in the discharge and/or recharge processes. We then extend this approach to a general sensor network, and demonstrate through simulations that a local information based threshold policy, with an appropriately chosen threshold, achieves a performance which is very close to the global optimum. Finally, we consider the node activation question where the events of interest show significant degree of temporal correlations across their occurrences. The optimization question in such systems is how should the rechargeable sensor be activated in time so that the number of interesting events detected is maximized under the typical slow rate of recharge of the sensor. We first consider the activation question for a single sensor, and pose it in a stochastic decision framework. The recharge-discharge dynamics of a rechargeable sensor node, along with temporal correlations in the event occurrences makes the optimal sensor activation question very challenging. Under complete state observability, we outline the structure of a class of deterministic, memoryless policies that approach optimality as the energy bucket size at the sensor becomes large; in addition, we provide an activation policy which achieves the same asymptotic performance but does not require the sensor to keep track of its current energy level. For the more practical scenario, where the inactive sensor may not have complete information about the state of event occurrences in the system, we outline the structure of the deterministic, history-dependent optimal policy. We then develop a simple, deterministic, memoryless activation policy based upon energy balance and show that this policy achieves near optimal performance under certain realistic assumptions. For the case with multiple sensors having identical coverage, we show that threshold based activation policies are, in general, robust to temporal correlations and achieve near optimal performance. This thesis is organized as follows. We review the background literature on energy efficiency in wireless ad-hoc and sensor networks in Chapter 2. We also discuss

20 7 related work in energy management and correlation modeling in sensor networks and outline the approaches and techniques proposed in the past. We present the dynamic sensor node activation question in the rechargeable sensor systems in Chapter 3. We start with modeling the sensor states and transitions with respect to their energy levels. We then formulate a utility based global perfomance criteria which serves as a measure of performance for the node activation policies we develop and analyze. We study the performance characteristics of a certain class of activation policies, namely threshold activation policies and derive analytical bounds on the performance of such policies for a chosen threshold parameter, for the case where all the sensor nodes can completely cover the region of interest. Threshold activation policies are particularly of interest, due to their simplicity and the ease of distributed implementation based only upon local information. We also study the effects of spatial correlation on the performance of threshold activation policies and show that these effects are dependent upon the threshold parameter chosen. We then extend these threshold based policies to a distributed network setting in Chapter 4, wherein a sensor node covers the region of interest only partially, and the coverage areas of any two sensor nodes may overlap partially, completely or none at all, depending upon the random placement of the sensor nodes in the network. We develop distributed implementations of threshold policies, evaluate their performance through extensive simulations and show that these policies perform very close to the optimal performance for an appropriate choice of threshold. Particularly, we show that a local information based policy achieves near-optimal performance in a randomly deployed network of rechargeable sensors. The sensor model considered in Chapters 3 and 4 is restrictive since it does not allow a sensor node to be activated while it is being recharged. In practice, the recharge process may be a continuous process occuring at all the sensor nodes simulatenously and at all times. This motivates the need to be able to activate the sensor even when it is partially recharged i.e. as long as it has a non-zero energy level. In Chapter 5, we model the partially rechargeable sensor nodes such that they can hold upto K quanta of energy and can be activated at any time if they have

21 8 the sufficient energy level to be able to sense. We model the recharge and discharge processes at the sensor nodes as poisson processes and study the performance of the class of threshold activation policies in such partially rechargeable sensor systems. Particularly, we show that the class of threshold policies is asymptotically optimal with respect to the energy buffer size K for the special case where all the sensors are able to cover the region of interest i.e. for an appropriately chosen threshold, the performance of the threshold activation policy approaches the optimal performance as K. We also model spatial correlation in the discharge and recharge processes at the sensor nodes and show the robustness of the chosen threshold policy in the presence of such correlations. Similar to the technique we followed for rechargeable sensor systems, we extend our threshold policies to a distributed network of partially rechargeable sensors in Chapter 5. We develop distributed threshold based activation policies, evaluate their performance through extensive simulations and show that these policies perform very close to the optimal performance for an appropriate choice of threshold. Next, we consider the node activation question in rechargeable sensor systems where the occurrence of interesting events is correlated in time. We first consider the effect of such temporal correlations on the performance of systems with a single sensor node in Chapter 6. We model the sensor system evolution under complete observability as a Markov decision process, and under partial observability as a Partially Observable Markov decision process. Under complete state observability, we show that a simple, correlation-dependent activation policy achieves optimal performance for large energy bucket size K. Under partial observability, where the inactive sensor may not have complete information about the state of event occurrences in the system, we outline the structure of the deterministic, history-dependent optimal policy. We observe that the optimal policy is heavily dependent on system parameters, and is not easily implementable in practice. Therefore, we develop a simple, deterministic, memoryless activation policy which is based upon energy balance and achieves near optimal performance under certain realistic assumptions. We consider the node activation question for a recharegable sensor system with multiple sensors in Chapter 7, and show that threshold policies are, in general, robust

22 9 to the presence of temporal correlations across events. We develop threshold based activation policies which achieve near optimal performance under these scenarios. Chapter 8 summarize our results and conclusions. We also provide further directions to future research work in this newly formulated and promising area of research.

23 CHAPTER 2 Background and Related Work There has been tremendous research interest in ad-hoc and sensor networks in recent years. An excellent survey of different sensor networks applications, as well as a discussion on some major issues in sensor networks, is provided in [3]. Some of the important issues considered in wireless sensor networks include coverage, connectivity, energy efficiency, data aggregation, and network lifetime. A survey of various algorithms employed to address the above issues in sensor networks is provided in [63]. In recent years, there has been a considerable degree of interest in energy management issues in individual sensors, sensor systems, and wireless adhoc networks. We outline some of these contributions in Section 2.1. A measure of energy-efficiency in non-rechargeable sensor networks is the network lifetime. There have been approaches suggested to extend the network lifetime in the presence of coverage and/or connectivity constraints, and energy-constrained sensor nodes. We discuss issues related to energy-efficient coverage and connectivity in Section 2.2. Section 2.3 disusses approaches used to model spatio-temporal correlations in sensor networks. Note that, there does not exist sufficient literature on the management of energy-constrained rechargeable sensor systems, and on the effect of spatio-temporal correlations while managing such sensor systems. Therefore, many of these perspectives listed below are not directly related to the node activation questions we consider in rechargeable sensor systems. 2.1 Energy Management in Ad-hoc and Sensor Networks There has been considerable amount of work on energy-efficient medium access control and adaptive wakeup of sensors, although all these perspectives consider energy-constrained, but non-rechargeable sensors. Energy-efficient medium access control protocols have been studied in [21, 22, 61, 80, 81]. The problem of minimizing power consumption during idle times is addressed in [19, 46]. In [10], the authors 10

24 11 use occupancy theory to analyze the effect of switching off idle nodes on the network lifetime. A discussion on the importance of energy management in ad-hoc and sensor networks, along with a description of various performance objectives, is outlined in [69]. Energy-efficient battery management strategies have been studied in [1, 2]. [20] proposes a framework that allows each battery-powered terminal to autonomously derive its optimal power management policy. Through the derived policy, an optimal trade-off between packet loss probability and mean packet delay on one hand, and energy consumption on the other hand is obtained. Energy-conscious medium access control and scheduling has been considered in [5, 59, 62]. [39] proposes adaptively choosing the ATIM (Adhoc traffic indication message window according to the network load in order to save energy without degrading throughput. [58] considers transmitting a packet over a longer time period to reduce power consumption, and involves a trade-off between delay incurred and energy consumption. In [54], the effects of power conservation, coverage and cooperation on data dissemination is investigated for a particular data sharing architecture. Optimization based energy-efficient routing strategies have been studied in [17, 18, 42, 49]. [17] uses an exponential cost function defined in terms of residual energy at the nodes and the link costs in order to select routes and power levels such that the network lifetime is maximized. In the process, the energy consumption rates at the nodes turn out to be proportional to their residual energies. Various other energy-efficient routing protocols have been proposed in [25, 67]. [30] proposes LEACH (Low energy adaptive clustering heirarchy, which is a self-organizing, localized coordination routing protocol, and results in even distribution of energy dissipation, thus enhancing the network lifetime. Tradeoffs between energy and robustness in ad-hoc network routing is studied in [47], where the authors argue that single path routing with high power can also be energy efficient, compared to the conventional approach of multipath routing to provide robustness. In [82], the authors study the trade-offs between routing latency and energy usage, and provide methods of computing efficient data gathering trees. Other interesting work related to energy-minimization include [31, 72, 77, 84]. Some of the node activation

25 12 problems discussed in this thesis are related to the energy management questions outlined above and in [68, 78, 79]. However, most of these works do not consider the node activation question in the context of data gathering applications. Moreover, they do not consider rechargeable sensor systems, or spatio-temporally correlated event phenomena. Lin et. al [50] consider sensors with renewable energy sources and focus on the development of an efficient routing strategy in a network with rechargeable sensors. It uses a worst-case competitive analysis approach in comparison to the stochastic decision framework, as in our case. Machine learning approaches towards adaptive power management have been considered in [73], where the authors also discuss the advantages of using a model (POMDP based approach to model unobservable user behavior during the process of optimal decision making. Borkar et al. [11] consider efficient scheduling of transmissions for an energyconstrained wireless device. The possible decisions for the device include transmission, remaining idle or reordering battery. Here the goal is to minimize the overall cost of transmission decision policy, and the authors show that the optimal decision policy to reorder battery is threshold based, where the threshold represents the relative difference between the current charge level of the battery and the current buffer length. Recently, the problem of controlling the activity of a rechargeable sensor node has been studied in [6], where the Norton s equivalent of a closed three-queue system is obtained to show optimal rate control policies for various combinations of rate structures and utility functions. 2.2 Coverage and Connectivity Issues The issue of coverage has been studied extensively in the literature. Area coverage, where the goal is to monitor a specified region, has been considered in [70, 83, 75]. Target (or point coverage has been studied in [13, 15, 14, 41, 24]. Coverage has also been studied from the perspective of maximal support (or breach path in [53, 65]. In [24], deterministic sensor placement allows for topology-aware placement

26 13 and role assignment, where nodes can either sense or serve as relay nodes. Zhang and Hou [83] show that if the communication range of sensors is at least twice as large as their sensing range, then coverage implies connectivity. They also develop some optimality conditions for sensor placement and develop a distributed algorithm to approximate those conditions, given a random placement of sensors. An important method for extending the network lifetime for the area coverage problem is to design a distributed and localized protocol that organizes the sensor nodes in sets. The network activity is organized in rounds, with sensors in the active set performing the area coverage, while all other sensors are in the sleep mode. Set formation is done based on the problem requirements, such as energy-efficiency, area monitoring, connectivity, etc. Different techniques have been proposed in literature [75, 83] for determining the eligibility rule, that is, to select which sensors will be active in the next round. This notion of classifying the sensor nodes into disjoint sets, such that each set can independently ensure coverage and thus could be activated in succession, has been considered in [13, 70]. Cardei and Du [13] show that the disjoint set cover problem is NP-complete and propose an efficient heuristic for set cover computations using a mixed integer programming formulation. A similar centralized heuristic for area coverage has been proposed in [70], where the region is divided into multiple fields such that all points in one field are covered by the same set of sensors. Then, a most-constrained least-constraining coverage heuristic is developed which is empirically shown to perform well. In [15] the constraints for the set of sensors to be disjoint and for these sets to operate for equal time intervals, are relaxed and two heuristics, one using linear programming and the other using a greedy approach are proposed and verified using simulation results. [29, 85] consider connected coverage and provide approximation algorithms to find one minimal subset of sensor nodes to guarantee (k-coverage and connectivity. An intergrated coverage and connectivity framework [75] has also been proposed where the goal is to allow configuring varying degrees of coverage and to maximize the number of sensor nodes scheduled to sleep at each stage. The coverage configuration protocol [75] is integrated with SPAN [19] to ensure connectivity in the network. However, the authors note that the network lifetime in such a framework

27 14 does not scale linearly with the number of sensing nodes due to periodic beacon exchanges. In [33], a greedy iterative disjoint set computation algorithm is developed to ensure coverage and connectivity in the network, and it is shown through extensive simulations that the network lifetime scales linearly with the number of sensor nodes in the network. 2.3 Correlation Modeling in Sensor Networks [4, 74] consider exploiting spatial and temporal correlations in the sensed data to develop efficient MAC and transport layer communication protocols. The issues faced include controlling the representative sensors (which are allowed to transmit and their transmitting frequencies, in order to comply with the desired maximum distrotion level and minimizing energy consumption in the process. Information theoretic aspects of correlation in sensor networks have been studied in [26]. Data aggregation schemes to perform routing with compression in the presence of spatial correlations have been studied in [56].

28 CHAPTER 3 Node Activation in Rechargeable Sensor Systems 3.1 Introduction In this chapter, we consider a system of rechargeable sensor nodes deployed redundantly in the region of interest for monitoring and data gathering purposes. As discussed in Chapter 1, if large number of sensors are deployed, it is likely that more number of these sensors would remain charged (and hence can be used for sensing at any given time. Thus, the overall system performance would typically improve (possibly with diminishing returns with a more redundant deployment of sensors. We assume that sensor nodes involved in sensing get discharged after a certain duration of time, and need to be recharged till they can start sensing again (Full Activation model. We consider the decision problem of when the recharged sensors should be activated (i.e. switched on, so as to maximize the long-term utility of the system. In Section 3.2, we formalize the node activation problem, describe the performance metric considered and discuss the challenges involved. We elaborate on the system model and the underlying assumptions in Section 3.3. We describe a particular class of node activation policies, namely threshold activation policies in Section Section 3.4 discusses performance bounds for node activation policies and performance evaluation of specific threshold activation policies. We present numerical results depicting performance of threshold activation policies in comparison to the derived bounds in Section 3.5 and summarize our analytical and numerical results in Section Problem Formulation states: At any instant of time, a rechargeable sensor node could be in one of the three 15

29 16 Figure 3.1: Rechargeable Sensor: States and Transitions under Full Activation model Active: The sensor is sensing or is activated. A sensor in the active state suffers a gradual depletion of its battery energy, and enters the passive state when its battery gets completely discharged. Passive: The sensor is switched off or deactivated, due to complete discharge of its battery energy. It is simply recharging its battery and is not sensing. Ready: The sensor has completely recharged its batteries and can be activated or put to sensing. The sensor does not participate in sensing, and waits to get activated. Figure 3.1 explains the three sensor states, and the transitions between them. Let discharge time denote the time a sensor spends in the active state, and recharge time denote the time a sensor spends in the passive state. In a realistic sensing environment, the discharge and recharge times will depend on various random factors. Sensors can transmit information (resulting in energy usage on the occurrence of interesting events, which may be generated according to a random process. Therefore in our system model, we assume that the discharge and recharge times are random, although we study the special case of deterministic discharge and recharge times as well. Although a sensor can power itself off during the ready state, it has to wake up periodically and exchange messages with its neighboring sensors, to keep track

30 17 of the system state in its neighborhood. Therefore, in reality, we would expect that energy will be drained even in the ready state, but probably at a fairly steady rate (possibly due to polling its neighbors to check out the system activation state. However, the energy discharge rate in the ready state can be expected to be much slower than the discharge rate in the active state Performance Metric The ability to equip the sensor node with rechargeable batteries adds a new dimension to the energy management issues in sensor networks. As outlined in Chapter 1, the network lifetime is an appropriate metric to measure the energy efficiency of a proposed routing or node activation policy in networks of non-rechargeable sensors. However, the ability to recharge allows a completely discharged sensor node to regenerate itself after some time. This allows the sensor network to continuously sustain itself, provided there is sufficient redundancy in the number of sensor nodes deployed in the network. In this case, network lifetime no longer remains to be the desired metric. Therefore, an appropriate performance metric needs to be formulated in order to evaluate the performance of node activation policies in such scenarios. We characterize the performance of the rechargeable sensor system by a continuous, non-decreasing, strictly concave function U satisfying U(0 = 0. More specifically, U(n represents the utility derived per unit area, per unit time, from n active sensors covering an area. Note that different sensors can be located at different points in the overall physical space of interest, and the coverage patterns of different nodes can be different. Therefore, the coverage areas of different sensors will typically be different. This implies that at any time, utilities in different parts of the area of interest can differ significantly from one another. Note that the strict concavity assumption merely states the fact that the system has diminishing returns with respect to the number of active sensors. As an example of a practical utility function, consider the scenario where each sensor can detect an event with probability p d. If the utility is defined as the probability that the sensing system is able to detect an event, then U(n = 1 (1 p d n, where n

31 18 Utility Function: U(n p d = 0.1 p d = 0.5 p d = Number of active sensors (n Figure 3.2: Utility function characteristics for a range of values of detection probability p d. is the number of sensors that are active. Note that this utility function is strictly concave, and satisfies U(0 = 0. Figure 3.2 depicts the shape of this utility function for various values of detection probability p d. The long-term performance is represented by the time-average utility of the system. Let A denote the physical space of interest, and A denote a generic area element in A. Let n P (A, t denote the number of active sensors that cover area element A at time t, when activation policy P is used. The time-average utility under policy P, is given by 1 lim t t t 0 A U(n P (A, t da dt. (3.1 In Euclidean coordinates system, da = dx dy, and n P (A, t = n P (x, y, t, in the above expression. The decision problem is that of finding the activation policy P such that the objective function in (3.1 is maximized. As mentioned before, our decision problem is that of determining how many sensors to activate at any time, from the set of ready sensors. Note that if we activate more sensors, we gain utility in the short time-scale. However, if the number of active sensors is already large, since the utility function exhibits diminishing returns, we

32 19 may want to keep some of the ready sensors in store for future use Challenges and Basic Approach The stochastic nature of the discharge and recharge times of sensors makes the determination of optimal activation policies very hard in a general setting. Further, spatio-temporal correlations imply that at any point in time, the optimal activation policy for a sensor might depend on the history of the states of all the sensors in the network. Although under specific cases the optimal policies may be formulated as semi-markov decision problem, determining optimal policies can be computationally prohibitive. Since sensors are energy constrained, we seek policies that can be implemented in a distributed manner with minimal information and computational overhead. Therefore, we focus on simple threshold policies (defined precisely in Section and examine their performance. To simplify the analysis and obtain fundamental performance insights, we examine the performance of threshold policies for a system of sensors, such that all the sensors are able to cover the region of interest i.e. the region lies inside the sensing (or coverage radius of all the sensors in the system. In this case, the objective function in (3.1 reduces to a single integral over the time domain. We consider two extreme correlation models of the discharge and recharge times of the different sensors: one in which these times are highly correlated, and the other in which these times are independent of one another. Assuming that the discharge/recharge times are exponential, we formulate the problem as a continuoustime Markov decision problem and provide a procedure for determining the optimal policy. Since the associated computation complexity is significant, we focus on the class of threshold decision policies. Threshold policies yield closed-form expressions, and the optimal threshold policy can be computed efficiently. Under Markovian assumptions we derive tight bounds on the performance of threshold policies for two different lifetime correlation models of the sensor nodes. Particularly, we show that the time-average utility of the appropriately chosen threshold policy is at least 3 4 of the best possible performance, for both correlation models. Moreover, we show that correlation in the discharge and recharge times of the sensors degrades