The Pennsylvania State University The Graduate School DISTRIBUTED ENERGY-BALANCED ROUTING IN WIRELESS SENSOR NETWORKS

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1 The Pennsylvania State University The Graduate School DISTRIBUTED ENERGY-BALANCED ROUTING IN WIRELESS SENSOR NETWORKS A Dissertation in Industrial Engineering by Chang-Soo Ok c 2008 Chang-Soo Ok Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2008

2 The dissertation of Chang-Soo Ok was reviewed and approved by the following: Soundar R.T. Kumara Allen E. Pearce and Allen M. Pearce Chaired Professor of Industrial Engineering Dissertation Advisor, Chair of Committee A. Ravi Ravindran Professor of Industrial Engineering Tao Yao Assistant Professor of Industrial Engineering Prasenjit Mitra Assistant Professor of School of Information Science and Technology Richard J. Koubek Professor of Industrial Engineering Head of the Harold and Inge Marcus Department of Industrial and Manufacturing Engineering Signatures are on file in the Graduate School.

3 Abstract Wireless Sensor Networks (WSNs) are large-scale, dynamic, and limited in power. These WSNs can be used for various application areas such as military, environmental, health, home, and other commercial applications. A fundamental objective of WSNs is to report events of predetermined nature or transmit sensed data to sink nodes or the base station for further analysis. To achieve this objective, a routing algorithm for WSNs should consider the following requirements. First, it should pursue energy-efficiency in order to prolong the lifetime of sensor networks. Second, the algorithm should have a distributed decision-making scheme which is applicable for large-scale networks. Third, it needs to be robust for dynamics in network topology and event generation patterns. To satisfy the requirements, the research conducted observes that energy balance induces maximum lifetime and robustness of WSNs. This thesis investigates decentralized routing algorithms to attain energy balance of sensor networks and, consequently, realize sensor networks with maximum lifetime and robustness to network dynamics. This thesis introduces a new network topology, which applies a decentralized decision-making scheme, to design such a routing algorithm. In the topology, each sensor can communicate with its neighboring nodes and the base station. Each sensor has its neighboring nodes within a fixed distance and the fixed distance is called as the neighbor distance. We will show that, in the proposed network topology, the neighbor distance determines the tradeoff between computational effort and solution quality. This tradeoff is investigated by an Integer Programming (IP) problem whose objective is to maximize the lifetime of the WSN subject to the network topology. With different neighboring distances, the best tradeoff between computational effort and solution quality is examined. The optimal solution of this problem can be ideally used as routing policies for sensors with a high computational capability iii

4 and global information. Since a high computational capability and availability of global information is not possible for routing in WSNs, we proposed three heuristic routing algorithms which require only local information. We compare the performance of these proposed routing algorithms with the optimal solution from the IP problem and highlight their significance. The three decentralized energy-balanced routing algorithms are: 1) Distributed Energy Adaptive Routing (DEAR): DEAR is a decentralized routing algorithm that use a new metric, Energy Cost, to prolong the lifetime of sensor networks. The proposed metric, Energy Cost, considers a sensor s remaining energy and its energy-efficiency simultaneously. We will show that DEAR, by using this metric as its guide, finds energy-sufficient as well as energy-efficient paths and, as a result, prolong the lifetime of the networks. Further, DEAR is scalable in the number of sensors and robust to the dynamics of event generation due to its decentralized nature. 2) Maximum Energy Welfare Routing (MaxEW): A new metric, Energy Welfare, based on a social welfare function from social science or economics, is proposed to measure how energy balanced a sensor network is. The metric considers the average and inequality of sensors remaining energies at the same time. This metric gives rise to the design of the Maximum Energy Welfare Routing (MaxEW) algorithm, which can achieve simultaneously energy efficiency and energy balance of sensor networks. To our best knowledge, this is the first application of social welfare functions for an engineering problem. 3) Network structure-aware ant-based Routing: Ant System is well known for its adaptivity and robustness for dynamic changes of environment. Capturing this feature of the Ant System, we proposed a new Ant System for Routing in wireless Sensor Networks (AS-RSN). In addition, considering heterogeneity in node degree, an advanced version of the ant-based routing scheme, Structure-aware Ant System for Routing in wireless Sensor Networks (AS-RSN II), is also proposed. A comparison with the original Ant System shows the effectiveness of the ant-based routing through numerical experiments. The research undertaken utilized distributed control methodologies encompassing economics-oriented control, swarm intelligence, and complex network theory, in order to develop distributed energy-balanced routing algorithms. These control methodologies can be extended to solve any other optimization problem or control any dynamic system. iv

5 Table of Contents List of Figures List of Tables Acknowledgments ix xii xiii Chapter 1 Introduction Wireless sensor network(wsn) Routing in wireless sensor networks Research motivation Research Objectives Uniqueness and Contributions Organization of the Thesis Chapter 2 Models and preliminary Network Topology Energy Consumption Model Lifetime of Sensor Network Event Generation Functions Shapes of target areas and positions of base stations Chapter 3 Related Work Routing in Wireless Sensor Networks Inequality Indices and Social Welfare Functions Inequality Indices in Social Sciences v

6 3.2.2 Welfare Functions in Social Sciences Ant System (AS) and Ant Colony System (ACS) Chapter 4 Mathematical Models for Routing in Wireless Sensor Networks IP Model for Maximum Lifetime Routing Traffic Equations Energy Constraint IP Formulation IP Model for Energy Balanced Routing Energy Constraint IP Formulation Fully Connected Network (FCN) and Partially Connected Network (PCN) Numerical Analysis Neighbor Distance Node density Event Generation Patterns Conclusions Chapter 5 Distributed Energy Adaptive Routing (DEAR) Introduction Distributed Energy Adaptive Routing (DEAR) Example Steps in the DEAR algorithm Algorithm Characteristics Experimental Results Lifetime of Sensor Network Energy Balancing Different Event Generation Functions Neighbor Distance Position of the base station Density of Sensors Initial Energy Distribution Conclusion and Future works vi

7 Chapter 6 Maximum Energy Welfare (MaxEW) Routing Introduction Energy Equality and Energy Welfare Energy Equality (EE) Energy Welare (EW ) Alternative Energy Welfare Metrics Maximum Energy Welfare (MaxEW) Routing Neighbor Distance and Neighbors Routing Table Routing Algorithm An Example No-loop Property of MaxEW Experimental Results Lifetime Energy-balancing Alternative Energy Welfare Metrics Random and Repeated Event Generation Patterns with Different Parameter Values Effects of Neighbor Distance Conclusions and Future Work Chapter 7 Ant-based Routing in Wireless Sensor Networks Ant System (AS) Ant System - Routing in Wireless Sensor Networks (AS-RSN) An example Algorithm Details Structure-Aware Ant Colony System - Routing in Sensor Networks (AS-RSN II) Node goodness Transition probability An Example Algorithm Details Experimental Results Lifetime Distributed AS-RSN Determining of τ Conclusions and Future work vii

8 Chapter 8 Conclusions and Future Research Research summary Contributions Future Research Appendix A The results of IP routing problems with neighbor distance (20 sets) 113 Appendix B Algorithm of Ant System - Routing in Wireless Sensor Networks 115 Bibliography 119 viii

9 List of Figures 1.1 Wireless micro sensor A wireless sensor network Energy imbalance sensor networks with Direct communication (DC) and Minimum Transmission Energy (MTE) Energy imbalance sensor networks with Repeated Event Generation Function Research road map and thesis organization Limitation of transmission capability Best candidate selection problem Repeated event generation from (a) a rectangle area and (b) a circle area Shapes of target areas and positions of base stations The configurations of experimental sensor networks: (a) 100m 100m square and (b) 100m-radius sensor networks Lorenz curve for inequality A tradeoff between energy balance and energy efficiency Neighboring Distance Lifetime with neighbor distance Computational time with neighbor distance Lifetimes and computational time of RP-FCN and RP-RPN(20m) with different node densities Lifetime of RP-FCN and RP-RPN(20) with uniform, random, and repeated event generation functions Distributions of residual energies of sensors after 3 rounds: Imbalance and balance An example scenario An example routing path in DEAR A tradeoff between energy balance and energy efficiency ix

10 5.5 Lifetimes of sensor networks Lifetimes of sensor networks with random and repeated event generation patterns Remaining energy distributions of sensors with uniform events for DC, MTE, SOR, and DEAR after 150 Rounds Remaining energy distributions of sensors Routing paths by Direct, MTE, SOR, and DEAR with repeat events on the region from (0,0) to (50,50) Number of neighboring nodes and number of rounds with neighboring distance (a) Number of neighbor nodes against neighboring distance and (b) Number of rounds against neighboring distance for the square sensor network Number of rounds with neighboring distance: (a) 100 nodes, (b) 150 nodes, and (c) 200 nodes Remaining Energy Distribution with Direct at time (a) 0 (b) 50R, (c) 100R, and (d) 150R Remaining Energy Distribution with MTE at time (a) 0 (b) 50R, (c) 100R, and (d) 150R Remaining Energy Distribution with SOR at time (a) 0 (b) 50R, (c) 100R, and (d) 150R Remaining Energy Distribution with DEAR at time (a) 0 (b) 50R, (c) 100R, and (d) 150R An explanatory example for Energy Welfare Routing algorithm An example routing path in Energy Welfare Routing algorithm An example of MaxEW algorithm No-loop Property of MaxEW MaxEW under concurrent transmission The number of active sensors over time under three event generation patterns The energy population at 150 th round under uniform event generation pattern Routing paths by Direct, MTE, SOR, and MaxEW (a) Lifetime (L 1 ) as a function of random rate α Number of active sensors over time for repeated event generation pattern in a 20m-radius circle area Lifetime as a function of neighbor distance Transition probabilities at node An example: Tabu list of ant k x

11 7.3 An example: the basic idea of AS-RSN II An example: AS-RSN II The number of active sensors over time under uniform event generation patterns The number of active sensors over time under random event generation patterns The number of active sensors over time under repeated event generation patterns Lifetime of AS-RSN, AS-RSN II, and Distributed AS-RSN L 1, L 10, and L 20 for AS-RSN, AS-RSN II, and Distributed AS-RSN L 1, L 10, and L 20 with l 0 = τ xi

12 List of Tables 5.1 Lifetime (L 1, L 10, L 20 ) for Direct, MTE, SOR, and DEAR-20m with Uniform, Random, and Repeat Events Lifetime (L 1, L 10, L 20 ) of 100 m 100 m square sensor network with different positions of the base station Lifetime (L 1, L 10, L 20 ) for Direct, MTE, SOR, and DEAR-20m with 100, 150, and 200 nodes Alternative Energy Welfare Metrics MaxEW routing algorithm Expected Energy Residuals and Energy Welfare of sensors {A, B, C} Lifetime (L 1, L 10, L 20 ) driven by Atkinson s, Sen s and Dagum s welfare functions Lifetime (L 1, L 10, L 20 ) for repeated event generation pattern with various radii Routing table of node 1 before routing data k Routing table of node 1 after routing data k Routing table of node 1 for data packet k Lifetime (L 1, L 10, L 20 ) with Direct, MTE, SOR, AS-RSN, AS-RSN II A.1 Lifetimes of FCN and PCN with neighbor distance (from 10m to 50m) B.1 Ant System - Routing in Sensor Networks: ACS-RSN B.2 Structure-aware Ant System - Routing in Wireless Sensor Networks: AS-RSN II B.3 Distributed Ant System - Routing in Wireless Sensor Networks: Distributed AS-RSN xii

13 Acknowledgments I would like to express my deepest appreciation to my thesis advisor, Professor Soundar R. T. Kumara for his patience, encouragement, and guidance. I would also like to thank my committee members, Professor A. Ravi Ravindran, Tao Yao, and Prasenjit Mitra for their insightful commentary and enlightening discussions on my work. My thanks to all my student colleagues, particulary to the Laboratory for Intelligent Systems and Quality (LISQ) members, for being so friendly, supportive and helpful in several ways. Especially, I would like to give a special thanks to Dr. Seokcheon Lee of the school of industrial engineering at Purdue university and Dr. Jindae Kim. Family is one of my strongest supports that helped me through these years. I would like to thank my mother, Hyungja Jeong and mother-in-low Kyunghee Kim in Korea for their love and encouragement. Also, I would like to thank my three precious kids, Lynn (Chaelynn), Bryan (Chaehoon), and Claire (Chaewon). I could not have done this without them. I appreciate and love them from the bottom of my heart. Finally, I wish to express my deep love and gratitude for my wife, Nayoung Song, whose love and encouragement enrich all the facts of my life and will always inspire me. xiii

14 Chapter 1 Introduction 1.1 Wireless sensor network(wsn) The advances in wireless communication and electronics technologies has lead to wireless sensors becoming smaller, less expensive, and more powerful [1, 2, 3] (Figure 1.1). These tiny sensors have sensing, data processing, and wireless communication capabilities. Each sensor monitors its own sensing territory for some predetermined events or changes of environmental parameters, and the sensor reports the event to a sink node or base station in a multi-hop communication fashion. Even though each sensor only can cover a small sensing range and communicate in a short distance, they together are capable of achieving a big task through a coordinated effort. Figure 1.1. Wireless micro sensor

15 2 A wireless sensor network (WSN) consists of a large number of wireless sensors which are randomly and uniformly distributed over a target area. If an event occurs in the target area, sensors detecting the events report events to sink nodes or the base station for further analysis (Figure 1.2). These WSNs can be utilized for risky or difficult tasks, such as military, environmental, health, home, and other commercial applications[1, 4, 5, 6, 7]. For example, in a battle field, a commander can be aware of the status of friendly troops or the availability of equipment by using the sensor networks [4]. Critical terrains, approach routes in the battle field also can be monitored for the activities of the opposing forces. Another application is forest fire early detection system [5]. Smoke or temperature sensors can be deployed into a fire-susceptible forest area to detect a forest fire on its early stage. Lastly, the technology of WSN also can be used in health applications [6]. The physiological data collected by wireless sensors are stored for a long period and used for medical exploration. Figure 1.2. A wireless sensor network

16 3 In wireless communication, network topology and routing policy are necessary for wireless devices to communicate with each other or to a gateway node 1. Similarly, in WSNs, topology control and routing algorithms are required to determine a path for data to be sent to a sink node or base station. Although many algorithms have been proposed for traditional wireless ad-hoc networks, they are not capable of considering the unique features of WSNs. The features are (1) the number of sensors in a WSN can be extremely high, (2) sensor are limited in power, (3) sensors mainly use broadcasting communication scheme, and (4) the network topology of a sensor network can change frequently. Therefore, the implementation of the WSN applications demands for a new network topology and routing algorithm considering the features of WSNs. 1.2 Routing in wireless sensor networks A fundamental objective of WSNs is to report events of predetermined nature or transmit sensed data to sink nodes or the base station for further analysis [1, 2, 3]. Proper routing algorithms help in achieving this objective by determining proper data flow paths. While considering this basic requirement, the design of the routing algorithm should incorporate the following factors: Efficient use of battery power: Sensors are battery-powered and their batteries cannot be replaced because the sensors are unattended after being deployed in the target area. Therefore, the operational time of the sensors is limited and, consequently, the lifetime of the network is also finite. To prolong the operational period of the network a routing algorithm for WSNs must have a design that seeks energy-efficiency, i.e. transmitted data must be via minimum energy-consuming paths. Distributed control: A WSN can consist of a large number of nodes with which central control architectures are not appropriate, due to overhead costs 1 In this thesis, both a sink node and base station can be considered as a gateway node which has no limitation in energy and communication resources. All sensed data are sent to the gateway node and a remote user can access to the gateway node to retrieve the sensed data for further analysis.

17 4 of computation and communication. Therefore, the routing algorithm should adopt a distributed control architecture to distribute the burdens of control. Dynamic networks: WSNs are highly dynamic with the following two reasons. 1) Frequent changes to the network topology due to the introduction of new sensors, failure of sensors, and movement of sensors and 2) events to be detected by the sensors have uncertainties in their positions and frequencies. Therefore, the routing algorithm should be capable of self-organization and/or sufficiently robust for the situational dynamics without requiring any global adjustment. A routing algorithm for WSNs should be able to respond to the considerations discussed above. In other words, an energy-efficient, distributed, and robust routing algorithm is necessary for WSNs. 1.3 Research motivation Most routing algorithms [8, 9, 10] for sensor networks focus on finding energy efficient paths to prolong the network s lifetime. As a result, the power of sensors on efficient paths depletes quickly and sensor networks become incapable of monitoring events from regions where all sensors are non-functioning. Figure 1.3 shows that this problematic situation occurs with Direct Communication (DC) and Minimum Transmission Energy (MTE) schemes, which are typical routing algorithms for wireless ad-hoc networks and applicable to WSNs. In DC, since every sensor simply transmits data directly to the base station without considering any energyefficient indirect path, the sensors far away from the base station get depleted quickly (Figure 1.3(a)). While, for MTE schemes, the sensors close to the base station drain quickly because all sensors consider indirect routing to save their power (Figure 1.3(b)). Thus, in designing routing algorithms for sensor networks, energy balance is a consideration to prevent the sensors from early depletion. On the other hand, in many sensor network applications, the events that must be tracked occur at random locations and have non-deterministic event generation patterns. The events could occur randomly over the target area, or repeatedly at a specific part of the target area [11, 12]. Event patterns can change from one type

18 5 (a) Direct Communication (b) Minimum Transmission Energy Figure 1.3. Energy imbalance sensor networks with Direct communication (DC) and Minimum Transmission Energy (MTE). to another over time. For example, in the case of the repeated event generation function, only the sensors within region, R, where events happen repeatedly, have data to be sent to the base station as shown in Figure 1.4. With DC or MTE, the sensors in region, R, lose their power quickly while other sensors have sufficient energy. Consequently, the network becomes unable to detect upcoming events from region, R. To prevent this situation, a routing algorithm should be able to distribute the data traffic and/or balance the energy of the network. In fact, the routing algorithm should be sufficiently robust for diverse event generation functions and the robustness of routing algorithm for diverse event generation functions can be obtained by balancing the energy of the network. To obtain the goal a routing algorithm for WSNs should consider not only energy efficiency but also the amount of energy remaining in each sensor to distribute the traffic over the whole network, avoid non-functioning sensors due to early power depletion, and finally achieve an energy balance of the network. The primary motivation of this research is that energy balance induces maximum lifetime and robustness of sensor networks and, accordingly, a routing algorithms is necessary to achieve the energy balance. This research investigates

19 6 Figure 1.4. Energy imbalance sensor networks with Repeated Event Generation Function. decentralized routing algorithms to realize sensor networks with maximum lifetime and robustness to network dynamics. 1.4 Research Objectives The main research objective is to develop a decentralized energy-balanced routing algorithm for WSNs. The routing algorithm should be capable of (1) achieving energy balance of network in an energy-efficient way, (2) adopting a decentralized decision making scheme, and (3) being robust for several dynamics in WSNs. The presented work first identify desirable features of energy balance and propose decentralized routing algorithms to achieve the energy balance by distributed control methodologies encompassing economics-oriented control, swarm intelligence, and complex network theory. The following tasks have been conducted to attain the main research objective: Identify a new network topology which is suitable for decentralized routing algorithms. The network topology reduces the solution spaces which sensors should consider for their routing decision while minimizing the loss of solution quality.

20 7 Define several event generation functions to evaluate routing algorithms for WSNs. These event functions enable to implement dynamics in WSNs. Define a routing problem with the proposed topology and event generation functions. This routing problem can be interpreted as a best node selection problem. Build a mathematical model, Integer Programming Model, which obtains the optimal solution of the defined routing problem. The results of the model provide a performance guideline for heuristic routing algorithms. Devise a heuristic metric to evaluate how sufficient energy a path has as well as how energy efficient the path is. Using this metric, a Decentralized Energy-Adaptive Routing (DEAR) algorithm is developed. Introduce the concept of social welfare, which is devised to consider the average and inequality of utilities of member in a society simultaneously, in design of a energy-efficient and energy-balanced routing algorithm for WSNs. Develop and implement a network structure-aware Ant System which considers heterogeneity of nodes to advance a basic Ant System. In this routing algorithm, node degree, a metric from complex network theory, is used to evaluate heterogeneity of nodes in WSNs. 1.5 Uniqueness and Contributions The uniqueness of this research is envisioned in several ways, firstly considering energy balance to obtain maximum lifetime and robustness of sensor networks. Indeed, it utilizes several areas of economics, swarm intelligence, and complex network theory to develop decentralized energy-balanced routing algorithms. The specific contributions of this research are as follows: 1. Energy balance is a direct consideration in the design of routing algorithms that maximizes the lifetimes of sensor networks and achieves robustness for dynamics of sensor networks.

21 8 2. A new network topology for WSNs, to which decentralized control mechanisms are applicable, is proposed. 3. Although most existing routing algorithms assume that events are generated uniformly at each sensor [9, 10, 8], events could occur randomly [12], or repeatedly [11] at a specific part of the target area. This research utilizes the diverse event generation functions in evaluation of routing algorithms for WSNs to consider a more realistic problem. 4. A proposed heuristic criterion, called Energy Cost, considers energy balance and efficiency simultaneously. Using this metric results in the design and implementation of the Distributed Energy Adaptive Routing (DEAR) algorithm. 5. This research proposes the first application of the social welfare function to an engineering problem and this approach can be extended to many other multi objective optimization problems as a general purpose heuristic algorithm. 6. A Network Structure-aware Ant System reinforces the original Ant System with complex network theory. This is the first trial to integrate complex network theory with swarm intelligence algorithm. 1.6 Organization of the Thesis Chapter 2 discusses specifications in WSNs. Network topology, energy consumption model, network lifetime, event generation functions, and other network parameters are discussed. Especially, a new network topology applicable to decentralized routing algorithms is proposed. Chapter 3 reviews the related background literature on Routing in WSNs, Social Welfare Function, and Ant Colony Optimization. Chapter 4 presents a mathematical model for a routing problem considered in this thesis. The result of this model gives a upper bound for the performance of proposed routing algorithms. Also, with the network topology discussed in Chapter 2, a method to reduce the computational time of the routing algorithm is discussed. Chapter 5 proposes a new heuristic metric, called Energy Cost (EC), to consider energy sufficiency as well as efficiency. Using this characteristic of this

22 9 metric, a localized routing algorithm, the Distributed Energy Adaptive Routing (DEAR), is proposed to accomplish energy balance of sensor networks in an energy efficient and decentralized manner. Chapter 6 presents a new heuristic metric, called Energy Welfare, to achieve the efficiency and balance of energies of sensors simultaneously. Based on this metric, a localized routing algorithm, the Maximum Energy Welfare (MaxEW) routing, provided to sensors, allows the sensors to maximize the energy welfare of their own local society. The maximization of energy welfare in local societies leads to an energy balance of the whole network. Chapter 7 presents two ant-based routing algorithms. The first algorithm, Ant System for Routing in Wireless Sensor Networks (AS-RSN), applies the characteristics of Ant Colony Optimization techniques to the routing problem discussed in this dissertation. The second algorithm, Structure-aware Ant System for Routing in Wireless Sensor Networks (AS-RSN II), advances AS-RSN by considering the heterogeneity of the network with a metric from complex network theory. Finally, conclusions, contributions, and possible extensions of this research work are the subject of Chapter 8. Figure 1.5 summarizes the road map of the research and the organization of this dissertation.

23 Figure 1.5. Research road map and thesis organization 10

24 Chapter 2 Models and preliminary With n homogenous sensors randomly and uniformly distributed over a target area, all sensed data must be routed to the base station. The sensors, are limited in power, can control their respective transmission power for minimal consumption to transmit to a destination [9, 10, 13, 14, 15, 16]. This is the minimum requirement for allowing routing algorithms to maximize sensor networks operational times. This chapter discusses a wireless sensor network model, which is used to design and implement a mathematical model and routing algorithms, including network topology, energy consumption model, lifetime of sensor network, and shapes of target areas and positions of base stations. Especially, a new network topology applicable to decentralized routing algorithms is presented. The details of the sensor network model considered are: 2.1 Network Topology Each sensor uses a fixed transmission power for communicating with its neighboring sensors; whereas, it transmits data to the base station with the minimum transmission power. The neighboring distance is the maximal reachable distance with the fixed transmission power for neighboring sensors. For a given sensor the sensors within its neighboring distance are its neighboring sensors or neighbors. In this scheme, each sensor can be aware of the current energy level of its neighbors or energy required to transmit from its neighboring sensors to the base station by anticipating and/or eavesdropping for data from its neighbors [17]. A sensor s

25 12 neighboring sensors can receive all the messages the sensor transmits, since every node has the same neighbor distance. When a sensor transmits a message to one of its neighboring nodes or the base station, the sensor adds its available energy after transmission to the data so that all of its neighbors can update their routing table for the sender s energy level. This updating process guarantees that information from neighboring sensors for the routing decision is available for sensors [17]. On the other hand, one of the typical methods to save energy in sensor networks is to consider a duty-cycle of sensors in the design of the Medium Access Control (MAC) layer [17, 18, 19, 20]. Although sensors turn their radios off during idle periods to save their energy, these MAC schemes guarantee synchronization of the awake/sleep schedules of all sensors or, at least, neighboring nodes. Therefore, sensors can be aware of the current energy levels of their neighboring nodes regardless of the design of the MAC layer. (a) Figure 2.1. Limitation of transmission capability: (a) All sensors can communicate with the base station directly (b) Only sensors close to the base station can communicate with it directly. (b)

26 13 Many applications [8, 9, 10] assume that all sensors have an ability to communicate with the base station directly, as shown in Figure 2.1(a). In some other applications [21, 22], only a small portion of sensors can communicate with the base station directly due to their limited transmission capabilities. In Figure 2.1(b), the sensors located in area A can only transmit data to the base station directly. In this scenario, the sensors in area A use the power in their batteries more quickly than the other sensors, because they need to transmit the other sensors data as well as their own data. Since no method exists to transmit data to the base station when all sensors in A expend their energies completely, the energies of the sensors in A should be more efficiently and effectively used. In other words, the data transmission capacity of area A determines the lifetime of the overall sensor network [22]. In fact, area A in Figure 2.1(b) can be considered a different network on its own. This work considers the sensor networks in which all sensors can communicate with the base station directly. Figure 2.2. Best candidate selection problem

27 14 With the network topology explained, a routing problem can be a one node or one-hop path selection problem (Figure 2.2). Once built, the selection problem can apply any metric to evaluate alternatives. The selected alternative can be interpreted as the next node to which a data packet is routed. Based on the evaluation of alternative paths with some metrics, the node routes data to achieve an energy balance of a local society (neighboring nodes and the node itself). The energy balance of the whole network can be achieved using this local energy balance approach. 2.2 Energy Consumption Model Each sensor uses a fixed transmission power for communicating with its neighboring sensors while each sensor transmits data to the base station. The neighboring distance is the maximum reachable distance with the fixed transmission power for neighboring sensors. For a given sensor, the sensors within its neighboring distance are its neighbors. This scheme reduces the operational complexity because it does not require sensors to be aware of the positions of their neighbors as long as the neighbors are within the neighboring distance. Also, each node can be aware of the current energy level of its neighbors or energy required to transmit from its neighboring nodes to the base station by anticipating and/or eavesdropping on data from the neighbors. Generally, sensors consume energy when they sense, receive and transmit data. However, the amount of energy consumption for sensing is unaffected by the routing algorithm and only a small difference exists between the power consumption for idle and receiving modes [23]. Therefore, this work considers only the energy consumed while transmitting messages. According to the radio model [9], energy consumption (E) for transmitting data is proportional to the transmission distance as well as the square of the amount of data. By normalization of the amount of sensed data, the energy consumption model simplifies to E = d 2, where E and d are the required energy and the transmission distance, respectively [8].

28 Lifetime of Sensor Network The effectiveness of the proposed routing algorithms is measured by the proposed metric, network s lifetime. A sensor network s lifetime is the time until the first node or a portion of nodes become incapable, due to energy depletion, of sending data to its neighbors [8, 10, 16, 24, 25]. The portion (number of depleted nodes) can vary depending on the context of the sensor networks. In this thesis, the lifetime of a sensor network is the number of rounds until the first (L 1 ), 10% (L 10 ), or 20% (L 20 ) of node(s) expend all their energy [24, 16]. L 1 also can be considered the full functioning period of the sensor network. 2.4 Event Generation Functions Many previous studies of routing algorithms assumed that all sensors have uniform data or event generation rates [8, 9, 10]. In infrastructure monitoring applications, each sensor performs a sensing task for every fixed time and has a homogeneous event generation function or the same event generation rate. However, in many sensor network applications, this assumption becomes unrealistic. When monitoring the migration of a herd of animals, the animals might move along a path in the target area repeatedly [11]. In the case of forest fire detection, events occur rarely and randomly over the target area [12]. Therefore, evaluating the robustness of a routing algorithm is more reasonable when considering the diverse potential event generation patterns. This work considers three event generation functions: Uniform event generation: Every sensor has a data packet to be reported during a fixed time or round. Random event generation with random rate α : Every sensor has a data packet to be reported with probability α during a fixed time or round. The probability α is the random rate. Repeated event generation from a local area A: Only the sensors in local area A have data packets to be reported during a fixed time or round. The shape of the area can be a point, a circle, a square, or any other configuration. (Figure 2.3)

29 Base Station A (a) 100 Base Station 50 A (b) Figure 2.3. Repeated event generation from (a) a rectangle area and (b) a circle area

30 2.5 Shapes of target areas and positions of base stations Wireless sensors can be deployed according to diverse target area shapes and the positions of the base station or sink nodes can vary depending on the objectives of sensor network or the nature of the target. As shown in Figure 2.4, the shape of a target area can be linear [26], circle [8], or square [9, 10], and the position of the base station can be inside or outside of the target area. These two factors affect the performance of routing algorithms in general [8, 10]. Intuitively, the center of the sensor network is the best position for the base station with respect to energy efficiency, because the average distance from sensors to the base station is minimal. However, in some sensor network applications in hostile or inaccessible environments, it is impossible that the base station is located at the center of the sensor network [1]. In such cases, the base station must be outside of the target area. Previous research has used two different shapes of sensor networks (see Figure 2.5) with adjusted scales [8, 10]. The first is a sensor network with 100 nodes randomly, uniformly deployed in a 100m 100m square area with the base station located at (50, 150). The other example has 100 sensors, randomly deployed, in a 100m-radius with the base station at (0, 0). 17

31 18 (a) (b) (c) Figure 2.4. Shapes of target areas and positions of base stations: The shape of a target area can be linear, a circle, or a square, and the base station can be located inside or outside the sensor network.

32 Base Station (a) Base Station (b) Figure 2.5. The configurations of experimental sensor networks: (a) 100m 100m square and (b) 100m-radius sensor networks.

33 Chapter 3 Related Work This chapter surveys routing in wireless sensor networks, social welfare functions, and ant colony optimization. Firstly, Section 3.1 reviews previous research efforts on routing for wireless sensor networks, and discusses the pros and cons of the existing routing algorithms. This research is the first application of social welfare function to tackle an engineering problem. Secondly, Section 3.2 presents several social welfare functions to be incorporated in our routing algorithms instead of surveying previous works. Lastly, Section 3.3 summaries previous ant systems for routing in data communication networks and wireless sensor networks. 3.1 Routing in Wireless Sensor Networks Significant efforts have attempted to develop routing algorithms to extend the lifetime of sensor networks. Hierarchical routing considers data aggregation and fusion in order to reduce the number of transmissions to the base station [9, 10, 27, 28]. Through clustering and cluster header selection rules, these hierarchical approaches spread energy usages over the whole network to extend operational time of sensor networks. These hierarchical routings always accompany dynamic topology control to build clusters and choose cluster heads for the clusters. Heinzelman et al. [9] proposed LEACH (Low-Energy Adaptive Clustering Hierarchy), a clustering-based protocol that utilizes a randomized rotation of local cluster-heads to evenly distribute the energy load among the sensors in the network. In LEACH, to enhance

34 21 system lifetime, each sensor has data fusion capability to reduce the amount of data transmitted to the base station. Forming clusters and the randomized rotation of cluster-heads incur high overhead and complexity. PEGASIS (Power-Efficient GAthering in Sensor Information Systems) [10] introduces a new metric, energydelay which simultaneously minimizes energy and delays cost for data gathering from sensor networks. In this routing scheme, all sensors form a chain and communicate with the base station through a leadersensor, selected randomly for each round. Also, this routing algorithm uses data fusion to reduce the amount of data to be transmitted. However, one requirement is that sensors have global information about the whole network and apply a greedy algorithm to build the chain. HEED (Hybrid, Energy-Efficient, Distributed Clustering Approach) [28] balances energy usage of sensors and improves network scalability and lifetime by topology control. In every clustering period, sensors become a cluster-head with a probability proportional to its residual energy. To prevent sensors from having more than one cluster-head, this algorithm introduces an inter-cluster communication energy cost, and sensors choose a cluster-head to minimize the energy cost. However, to balance residual energies of sensors, HEED requires frequent reclustering causing a high, overhead cost, synchronization problem among sensors. TEEN (Threshold sensitive Energy Efficient sensor Network protocol) [27] was devised for reactive networks which have sudden and drastic changes in the sensed attributes. Based on a hierarchical grouping where closer nodes form clusters, sensors send the sensed data to their cluster-head when this sensed value reaches a threshold value. The main drawback of TEEN is the necessity for high overhead and complexity involved with forming clusters at multiple levels. Even though these hierarchical routings produce good results in some applications with high redundancy in their data, no evidence exists that the algorithm works well with the applications in which all sensed data should be sent to the base station. Some routing algorithms [8, 24, 29] focus on finding good paths to maximize lifetime of sensor networks with a given network topology. Shah et al. [29] proposed an energy-aware routing which uses a set of top-k optimal paths in turn to prevent data traffic from concentrating on a optimal path. This routing scheme distributes data traffic over the sub-optimal paths. However, the setup cost for building the set

35 22 of suboptimal paths for each node is very high and still one path can be depleted quickly when many sensors choose at path as one of their suboptimal paths. Chang and Tassiulas [24] proposed a shortest cost path routing algorithm called the Flow Augmentation (FA) algorithm. This algorithm chooses a path which consumes less energy and does not include a node with small residual energy for a given data packet. Applying this heuristic rule to each data, the FA algorithm finds the shortest cost path and achieves a balance of residual energy over the entire network. This algorithm assumes that sensors have global information about the topology of networks to find the path with sufficient energy. In spite of the superiority of this algorithm with diverse configurations of sensor networks, this algorithm is not adequate for large scale networks and is not adaptive to dynamic network environments. To extend the lifetime of sensor networks in which all sensed data should be reported in its original form, Rogers et al. [8] proposed a self-organized routing (SOR) algorithm. In this algorithm, a sensor saves its energy by hiring another sensor as a mediator. To make sensors act willingly as mediators, Rogers et al. introduced a delicate payment scheme. Sensors earn different payments depending on whether they transmit their own data or mediate other sensors data. If a sensor can obtain more payment, it is willing to be a mediator for other nodes. This algorithm has several desirable properties. Energy-efficiency and energy-balancing are pursued together through selfish behaviors; sensors make local decisions based on local information, and solution space has no limit. The result section directly compares the SOR algorithm with proposed algorithms proposed in this study.

36 3.2 Inequality Indices and Social Welfare Functions This section surveys inequality indices and social welfare functions in social science. The inequality indices and social welfare functions can be used to evaluate alternatives in selection problems or routing paths in routing problems Inequality Indices in Social Sciences Several approaches exist for measurement of inequality in social sciences mostly with respect to income. A summary of those inequality indices are: Gini Index [30]: The Gini index is one of the most commonly used indicators of income inequality. It derives from Lorenz curve, which plots the cumulative proportion of income earned by people ranked from bottom to top as shown in Figure 3.1. In perfect equality the Lorenz curve follows a 45 o line. As the degree of inequality increases, the area between the curve and 45 o line becomes larger. If the area between the curve and the 45 o line is A and the whole area below the 45 o line is B, then the Gini index, I G (t), is computed as in Equation (3.1). I G (t) = A A + B = i S j S P i(t) P j (t), (3.1) 2n 2 P (t) where S is a set of individuals, and P i (t) denotes the utility of individual i at time t. Robin Hood Index [31]: The Robin Hood index, as in Equation (3.2), is the maximum vertical distance between Lorenz curve and 45 o line as shown in Figure 3.1. I R (t) = R. (3.2) Atkinson Index [32]: The general form of the Atkinson index, as in Equation (3.3), includes ε, the so-called inequality aversion parameter. The pa-

37 24 Figure 3.1. Lorenz curve plots the cumulative proportion of income earned by people, ranked from bottom to top. As the degree of inequality increases, the area A between the Lorenz curve and a 45 line becomes larger. rameter ε reflects the strength of society s penalty for inequality, and can take values ranging from zero to infinity. When ε equals zero, no penalty accrues for inequality. As ε rises, society imposes more penalty for inequality. The values of ε typically used, include 1.5, 2.0, and 2.5 [33, 34]. ( ) I A(ε) (t) = ε P i (t) n P (t) i S 1 1 ε. (3.3) Welfare Functions in Social Sciences In the social sciences such as economics or politics, considerable efforts have attempted to define welfare functions to compare welfare between space and time. Average is still the most widely used welfare function despite its well-known shortcomings. However, a broad range of philosophical approaches suggests that high inequality reduces aggregate welfare [35]. Welfare of society S at time t, W S (t), is defined as follow: Sen welfare function [36]: The Sen welfare function, as in Equation (3.4), has a simple form of weighting the average by the Gini index. In fact, Amartya Sen received the Nobel Prize in Economic Sciences in 1998 for his

38 25 contributions to the research on fundamental problems in welfare economics including the definition of this welfare function ( W S (t) = P (t) (1 I G (t)), (3.4) where P (t) is the average of individuals utilities at time t. Atkinson welfare function [37]: Replacing the Gini index with the Atkinson index in the Sen welfare function results in the Atkinson welfare function appearing in Equation (3.5). Two cases are studied explicitly, ε = 2 and ε = 1 [35]. In the latter case, the general form of the Atkinson welfare function is not defined and the function is transformed into Equation (3.6). W S (t) = P (t) (1 I G (t)); (3.5) W S (t) = e 1 n j S lnp j(t). (3.6) Dagum welfare function [38]: The Dagum welfare function, as in Equation (3.7), imposes more penalty for inequality on the Sen welfare function by the denominator. W S (t) = P (t) (1 I G(t)) (1 + I G (t)). (3.7) The social welfare functions discussed above are used to design the Maximum Energy Welfare Routing and alternative routing algorithms in Chapter 6.

39 Ant System (AS) and Ant Colony System (ACS) In 1992, Dorigo [39] devised the Ant System (AS) as a meta-heuristic to solve the Traveling Salesman Problem (TSP). In the TSP the objective is to find a minimum length tour connecting n given cities. The AS provides a good solution within a reasonable time only for small-size problems. To improve the performance of the AS for large-size problems Dorigo and Gambardella [40, 41] introduced the Ant Colony System (ACS) algorithm. The ACS modified the transition rule, pheromone trail update rule of the AS and used a candidate list to reduce the solution search space. As a general purpose meta heuristic, the AS and ACS have many applications such as the Quadratic Assignment Problem (QAP) [42], Job-shop Scheduling Problem (JSP) [43], Graphic Coloring Problem (GCP) [44], Vehicle Routing Problem (VRP)[45], and other NP-hard problems [46, 47]. Even though extensive research has considered the static optimization problems, mentioned earlier, relatively less efforts have contributed to solutions of dynamic optimization problems such as the network routing problem. In fact, one favorable characteristic of the and-based approach is adaptiveness to and robustness for changes of environment, over time. Therefore, AS and ACS are suitable for dynamic optimization problems. Schoonderwoerd et al. [48] first tried to tackle a dynamic problem, a routing problem in telecommunication networks with AS. In this work, ants launch, periodically, from any node in the network at any time. With a given destination the ants travel over the network. Each node updates its routing table with information from the launched ants. Di Caro and Dorigo [49] proposed an ant-based adaptive routing algorithm, AntNet, to traffic conditions. Different from the Schoonderwoerd s work, the AntNet, designed for data communication networks, adaptability of routing algorithm for data traffic becomes the most important. The experimental results of this work show that AntNet performed better than NSFNET and NTTnet which are well-known, existing, routing algorithms. White et al. [50] proposed an ant-based algorithm for routing in circuitswitched networks. This work has principles similar to this study s ant-based

40 27 routing algorithm. This routing scheme is built by Point-to-Point(PTP) request. For a each pair of starting points and destinations, an ant launches at the starting point to look for the best path to the destination, given a cost function. Zhang et al. [16] proposed an ant-based routing algorithm designated for wireless sensor networks. This work proposed Cost-aware ant routing, based on AntNet. In the routing algorithm, sensors are aware, from their neighbors, of the costs to arrive at the destination. Using this information, the transition probability at sensor i to one of neighboring nodes, j, is determined by Equation (3.8). P ij = C j k N i C k, (3.8) where P ij and C j are the transition probability for node j at node i and the cost or distance from node j to a destination. Apparently, less cost leads to greater probability. Even though this feature enables finding energy efficient paths, the routing algorithm does not consider energy balance over the network. Some sensors in this algorithm are forced to deplete quickly. In [51], energy sufficiency is a consideration in the calculation of transition probability, as Equation (3.9) where η ij = P k ij = τij α η β ij l N i,l / M τ α k il, (3.9) ηβ il E j l N i E l. η ij is a heuristic metric to measure energy sufficiency of node j and E j is the current energy of node j. η ij and M k are the amount of pheromone on link (i,j) and a tabu list of ant k, respectively. Since a node having more energy has a greater probability, an energy balance of network might be achieved by this ant routing algorithm. However, the performance of the routing system improves by considering how good nodes are for reaching to a destination. Chen et al. [52] introduced a new type of ant, a search ant, which provides network information to the following ants to improve the original ant system. However, the role of the search ant is not different from normal ants, and the search ant requires a considerable amount of network resource. These existing algorithms require high overhead costs for updating routing

41 28 tables of nodes or finding the best path for every pair of starting point and destination. In addition, these algorithms do not consider heterogeneity of nodes in networks. For example, nodes in the network are heterogeneous in node degree which is the number of links. This metric, node degree, can be used to evaluate goodness of path. With these considerations, this study proposes a network structure-aware Ant System for routing in wireless sensor networks.

42 Chapter 4 Mathematical Models for Routing in Wireless Sensor Networks Chang and Tassiulas [24] used LP(Linear Programming) modeling to determine routes that maximize the lifetime of sensor networks. This model is useful for calculating a upper bounds for performances of routing algorithms. However, this model has a limitation. In many applications of telecommunication and sensor networks, non-integer values for nodes are not applicable for their routing policies. Therefore, the result of a mathematical model for routing problem should be integer to be applicable. This chapter presents two IP(Integer Programming) problems, which are maximum lifetime routing and energy-balanced routing problems. The first problem is involved in maximization of the periods which no sensor is depleted with given a network topology and event generation function (Section 4.1). While, the second IP model maximizes the minimum residual energy of sensor at a certain time with given a network topology and event generation function (Section 4.2). Even though these two IP problems guarantee the optimal routing policy, the complexity of the models drastically increase as the number of sensors increases. Therefore, Section 4.3 defines a new IP problem having a reduced solution space. The new IP model is evaluated in terms of solution quality and computational time though numerical analysis (Section 4.4) and the solution is compared with the original IP model.

43 IP Model for Maximum Lifetime Routing Consider a sensor network where n sensors are deployed randomly and uniformly in a target area, and the sensors transmit all sensed data to the base station. N and B denote the set of sensor nodes and the base station. Sensor i, i N has a set of neighbor nodes, N i, according to the network topology. E i and D i (T ) are the battery capacity of sensor i and the data traffic generated by sensor i during any time interval [0, T ]. Lastly, e ij and x ij represent the required energy for a transmission and the number of transmissions from node i to j, respectively. Given D i (T ), i N, the IP problem involves maximizing the lifetime, T, of sensor network Traffic Equations Figure 4.1. A tradeoff between energy balance and energy efficiency. Since all sensed data should be sent to the base station, the incoming and outgoing data traffic at a sensor are the same. As shown in Figure 4.1, the incoming traffic at node i consists of data traffic from nodes, j, which have node i as their neighbors and data generated at node i during the time interval [0, T ]. On the other hand, the outgoing traffic is the sum of the traffic sent by a sensor i to its neighboring nodes, N i,and the base station, B. Therefore, the traffic equation for each node is:

44 31 x ji + D i (T ) = j:i N j j N i +{B} x ij for all i N. (4.1) Constraints (4.1) guarantees that all data are transmitted to the base station. By summing all equations in (4.1) for all i the following equation can be obtained: x ib = D i (T ). (4.2) i N i N The incoming traffic to the base station is equal to the data traffic generated by all sensors during [0, T ]. According to Uniform, Random, and Repeated event generation functions, D i (t) can be defined as Equation (4.3). k T D i (t) = α k T k T if x i A for Uniform for Random for Repeated (4.3) where k is an event generation rate for a unit time Energy Constraint Based on our energy consumption model, sensors use their power to transmit data to neighbors and the base station by e ij where j N + {B}. Since the energy consumed at node i should be less than or equal to the initial energy of sensor i, the following energy constraint is obtained: e ij x ij E i for all i N. (4.4) j N i +{B}

45 IP Formulation Now, the routing problem can be formulated as an IP problem. The objective function is to maximize the time T or the full functioning period, and the constraints are Equations (4.1), (4.2), and (4.4). Therefore, the problem is: Maximize T s.t. x ji + D i (T ) = j:i N j j N i +{B} e ij x ij E i for all i N. j N i +{B} x ij for all i N (4.5) x ij : non-negative integer for all i and j. If D i (T ) is a linear function of T, the objective function, Maximize T is equivalent to Maximize i D i(t). Since D i (T ) = k i T, i D i(t) = ( i k i) T. Therefore, the objective function, Maximize T can be replaced by Maximize i D i(t ) and the routing problem is also a maximum throughput routing problem for a given time T. The result of this problem provides routing policies (x ij ) for sensors so that make the given sensor network energy balanced at time T. Even though this IP problem can be used to obtain the routing policy, this mathematical model can be also used to obtain an upper bound for the lifetime of sensor networks for different routing algorithms. Therefore, we transform the IP problem (4.5) to a LP problem with two following assumptions. D i (T ) is a linear function of T All x ij are non-negative real number. We solve the LP problem to derive the upper bound of the performance, to evaluate the algorithm proposed in the next chapters.

46 IP Model for Energy Balanced Routing The second IP problem is related to energy balanced routing. Given a time interval [0, T ] and event generation function, D i (T ), i N, the IP problem involves maximizing the minimum residual energy of sensors at time T. For building this IP model the energy constraints and objective functions are changed while the traffic constraints are the same as Equation (4.1) Energy Constraint The residual energy of sensor i at time T is the initial energy of sensor i minus the total energy consumed to transmit data to neighbors and the base station. Equation (4.6) guarantees that the residual energies of all sensors are greater than and equal to the minimum residual energy of sensors, E min. E i e ij x ij E min for all i N. (4.6) j N i +{B} IP Formulation We have an IP formulation maximizing the the minimum residual energy of sensors. The objective is to maximize the minimum residual energy of sensors, E min, with the constraints of Equations (4.1), (4.2), and (4.6). Therefore, the problem is: Maximize E min s.t. x ji + D i (T ) = j:i N j j N i +{B} E i e ij x ij E min for all i N j N i +{B} x ij for all i N (4.7) x ij : non-negative integer for all i and j.

47 34 By replacing the objective function with Maximize T and letting E min = 0, the IP in Equation (4.7) is the same as the IP in Equation (4.5). 4.3 Fully Connected Network (FCN) and Partially Connected Network (PCN) According to the set of neighboring nodes, wireless sensor networks can be classified into a fully connected network (FCN) and a partially connected network with a neighboring distance, d, (PCN(d)). FCN and PCN(d) can be defined as follow: Definition (Fully Connected Network). If all sensors can communicate with any other sensor in a sensor network, the sensor network can be called fullyconnected. In other words, N N i, i. Definition (Partially Connected Network with neighboring distance d)). Each sensor can communicate with only the sensors within distance d from itself. The sensor network is partially connected with distance d. N N i, i. In FCN, the transmission distance of sensors is a long enough to reach any other sensor in the network (Figure 4.2(a)). In this case, the set of sensor i s neighboring nodes, N i, become to the set of all nodes N and, consequently, the complexity of the IP problem in Equation 4.1 is extremely high. To reduce the number of variables we consider a neighboring distance which is much shorter than the maximum transmission distance of sensors (Figure 4.2(b)). Let the IP problems for the fully connected network and partially connected network with neighbor distance d m be RP-FCN (Routing Problem - Fully Connected Network) and RP- PCN(d) (Routing Problem Partially Connected Network with d m). Apparently, RP-FCN gives better performance than RP-PCNs in terms of network lifetime. However, RP-PCN(d) provides a big benefit on computational time by considering the smaller set of neighboring nodes than RP-FCN. As d increases in RP-PCN(d), the result and complexity of the IP problem are close to ones of RP-FCN. The numerical analysis section discusses a trade-off between complexity and quality of solution.

48 35 (a) (b) Figure 4.2. (a) Fully connected Network (b) Partially connected network with a neighboring distance. 4.4 Numerical Analysis As explained earlier, the size of IP problem in Equation (4.5) heavily depends on the size of neighboring node set for each sensor. If a sensor has a big neighboring distance, then the sensor has a bigger neighboring node set and, consequently, the solution space of the IP problem also increases. Apparently, the increase in the problem size leads to increase solution time as well as improvement in the solution quality. In this section, a guideline for a tradeoff between the size of the problem and solution quality is provided through some numerical experiments. The experiments use a sensor network in which 100 nodes have random and uniform deployment in a 100m 100m square area with the base station located at (50, 150) as shown in Figure 2.5(a). Sensors are initially endowed with 250,000 energy units. The initial energy endowments are established such that the farthest

49 36 node from the base station is capable of transmitting data 100 times under Direct communication scheme. To demonstrate the effects of different event generation patterns, simulations are performed using uniform, random, and repeated event generation patterns we have defined. In case of random generation, the random rate α is set to 0.25, i.e. the probability that each sensor has an event in a round is While, for the repeated event generation, sensors located in a square area from (0, 0) to (50, 50) incur repeated events. Since a sensor network is generated randomly, 20 experiments are repeated for each condition and an average of the results is taken. We coded a program to generate a set of LP and IP problems described in Subsection and solved the problems using commercially available LP solvers CPLEX [53]. In the case of IP problems, for computational convenience, we stopped running the IP solvers when we found feasible IP solutions which have solution gaps less than 0.5% 1 from the optimal. The empirical analysis consists of three parts. We evaluate the lifetime by a fully connected network and partially connected networks with different neighbor distances in Subsection Subsection and demonstrates the effects of node density and several event generation patterns, respectively Neighbor Distance Figure 4.3 shows the effects of neighbor distance on the lifetime and computational time of LP and IP problems. The results show that the solution quality and computational time depend on the neighbor distance. Figure 4.3(a) and (b) shows that the increase in neighbor distances results in an increase in average lifetime. The quality of solution was stable from 20m neighbor distance. While, such an increase lead to a monotonic increase of the computational time(figure 4.4(a) and (b)). In this experiment, 20m neighbor distance is the best tradeoff between lifetime and computational time. Therefore, this value of the neighbor distance is used for experiments in the following chapters to evaluate the proposed routing algorithms in this thesis. Table A.1 in Appendix A presents specific numbers for the results of IP problems with diverse neighbor distances. 1 CPLEX provides this value as a solution gap

50 Lifetime 200 RP FCN = Lifetime 200 RP FCN: RP PCN(20m) RP FCN Neighbor Distance (m) (a) With RP-FCN and RP-PCN(20) 150 RP PCN(20m) RP FCN Neighbor Distance (m) (b) With RP-FCN and RP-PCN(20) Figure 4.3. Lifetime with neighbor distance Computational Time (sec) * RP FCN: 0.35 sec RP PCN(20m) Computational Time (sec) * RP FCN: sec RP PCN(20m) Neighbor Distance (m) (a) With RP-FCN and RP-PCN(20) Neighbor Distance (m) (b) With RP-FCN and RP-PCN(20) Figure 4.4. Computational time with neighbor distance Node density Figure 4.5 presents the effect of node density on the lifetime and computational time. The lifetimes of RP-FCN and RP-PCN(20) are almost the same where the number of nodes, or equivalently node density, is greater than or equal to 100 nodes (Figure 4.5 (a)). In the case of computational time, difference between RP-FCN and RP-PCN(20) increases exponentially as the number of nodes does (Figure 4.5 (b)). This result implies that RP-PCN(20) can be considered instead of RP-FCN to solve routing problems in wireless sensor networks with savings in computational time without sacrificing the quality of solutions.

51 38 Lifetime RP FCN RP PCN(20m) Computational time (sec) RP FCN RP PCN(20m) Number of nodes Number of nodes (a) Lifetime (b) Computational time Figure 4.5. Lifetimes and computational time of RP-FCN and RP-RPN(20m) with different node densities Event Generation Patterns Figure 4.6 lists lifetimes of RP-FCN and RP-RPN(20) with uniform, random, and repeated event generation functions which are , , and for RP-FCN and 282.2, , and for RP-RPN(20), respectively. No big difference between the optimal values of RP-FCN and RP-PCN(20) exists regardless of event generation functions. Therefore, instead of RP-FCN, RP-PCN(20) can be used to investigate the optimal solution for the proposed routing problem with less computational efforts. 4.5 Conclusions With global information about network topology and event generation function, routing problems in wireless sensor networks can be modeled as Linear Programming (LP) and Integer programming (IP) models. Even though LP can provide good approximate solutions and many good IP solvers are available, the approximate solutions are not applicable and the complexity of the IP problems are extremely high. A way to reduce complexity of the IP problems is desirable. Therefore, this chapter introduces a new network topology in which sensors only consider other sensors within their neighbor distances instead of all sensors (discussed in Chapter 2) to reduce the solution space of IP routing problems. Through

52 RP FCN RP PCN(20) 800 Lifetime Uniform Random Repeated Event generation pattern Figure 4.6. Lifetime of RP-FCN and RP-RPN(20) with uniform, random, and repeated event generation functions several numerical results we showed that this approach reduces the computational time drastically while keeping the qualities of solutions. The results of the numerical experiments gives a validation for using neighbor distance in designs of three proposed routing algorithms in the following chapters.

53 Chapter 5 Distributed Energy Adaptive Routing (DEAR) Most routing algorithms for sensor networks focus on finding energy efficient paths to prolong the lifetime of sensor networks. As a result, the power of sensors on efficient paths depletes quickly, and consequently sensor networks become incapable of monitoring events from some parts of their target areas. In many sensor network applications, the events that must be tracked occur at random locations and have non-deterministic generation patterns. Therefore, ideally, routing algorithms should consider not only energy efficiency, but also the amount of energy remaining in each sensor, thus avoiding non-functioning sensors due to early power depletion. This paper introduces a new metric, Energy Cost, devised to consider a balance of sensors remaining energies, as well as energy efficiency. This metric gives rise to the design of the Distributed Energy Adaptive Routing (DEAR) algorithm devised to balance the data traffic of sensor networks in a decentralized manner and consequently prolong the lifetime of the networks. DEAR is scalable in the number of sensors and also robust to the variations in the dynamics of event generation. 5.1 Introduction The primary idea of this work is that sensor networks can respond properly to events that have uncertainty in their position and generation rates and maximize

54 41 Figure 5.1. Distributions of residual energies of sensors after 3 rounds: Imbalance and balance. the period when they function fully through energy balancing. In Figure 5.1, a sensor network has three sensors and the sensors send their messages to the base station sequentially and repeatedly. Each sensor has 9 units of an initial energy 1 and the numbers above arrows indicate the amounts of energy required to the corresponding transmissions. If all sensors use only energy efficient paths, sensor 1 becomes depleted after each sensor transmits its message to the base station three times (Figure 5.1 (a)). Since the events have uncertainties in their positions and generation rates, this sensor network might not respond properly to upcoming events after a period of time during which sensors become inactive from energy depletion. However, an energy-balanced sensor network with alternative paths remains event-ready after a similar period because all sensors remain active (Figure 5.1 (b)). To capture the advantages of energy balance, this study proposes a new heuristic metric, called Energy Cost (EC), to establish energy sufficiency as well as efficiency. Since the EC is transmission energy cost relative to available energy, its value is low when required energy for transmission is low and available energy is high. Using this characteristic of this metric, a localized routing algorithm, 1 Generally, a batter power is measured in Joule(J). To simplify the explanation, we just remove the specific power unit.

55 42 the Distributed Energy Adaptive Routing (DEAR), is proposed to accomplish energy balance of sensor networks in an energy efficient manner. Individual sensors forward messages to neighbors that the originating sensors consider the best route to the base station. The determination of the globally optimal route is difficult because the individual sensors do not have dynamic topology information for the entire network and the dynamic energy balances of each node in the network. Thus, locally optimal decisions need to be made at the nodes. The organization of the rest of the chapter is as follows. In Section 5.2, we present the details of the Distributed Energy-Adaptive Routing (DEAR) algorithms. Section 5.3 contains extensive simulation results, and conclude in Section Distributed Energy Adaptive Routing (DEAR) The proposed routing algorithm uses a path with energy sufficiency as well as energy efficiency to pursue energy balance for the sensor network. Energy sufficiency depends upon the available energy, and energy efficiency depends upon the required energy. By using a composite of both quantities, a good path that achieves energy balance can be found. Only one of them, by itself cannot indicate the goodness of a path because of the dual objectives of not depleting the energy reserves of popular paths and of sending messages through energy efficient paths to ensure the total energy needed to route the messages are kept to a minimum. The definition of the composite measure, Energy Cost(EC i ) for a transmission from node i to j is: EC ij = Required energy from node i to j Available energy at node i (5.1) The basic idea of the proposed routing algorithm is to use a path having the minimum EC. When a sensor i sends data to the base station, it can transmit data to the base station directly or route the data to one of its neighbors (N i ). In other words, the sensor determines which sensor is the best candidate for direct communication with the base station among its neighbors and itself. For evaluating

56 43 these alternatives, sensor i considers the total required energies to the base station via neighboring nodes. The Total Energy Cost (T EC ik ) of a neighboring node k at senor i is simply the sum of the energy costs from node i to k and from node k to the base station: T EC ik = EC ik + EC k,bs (5.2) This measure is the composite quantity that indicates the goodness of a path including a neighboring node. Based on this metric, sensor i can select the best candidate, node K, for direct communication with the base station: K = ArgMin(T EC ij ) (5.3) j N i +{i} If the best candidate node is the node i itself, it sends data to the base station and completes the routing process for the data. Otherwise, it forwards the data to the best candidate among its neighboring nodes and that node then repeats the same routing process. This process continues until a node selects itself as the best candidate and sends directly to the base station. This localized decision-making process results in a monotonic decrease of energy cost over time because the best candidate can have an indirect path that is better than direct transmission. Each sensor makes its decision with the assumption that one of its neighboring nodes sends data to the base station directly. Sensors do not care if the receiving node sends data to the base station or passes data to one of its neighboring nodes. This characteristic makes the proposed algorithm different from the Dijkstra algorithm [54] and the Distance vector algorithm [55], which consider the best path from the next node. Through this local decision making process, a sensor network can achieve energy balance and prolong the lifetime of the sensor network. We show an example of the running of the DEAR algorithm, and then discuss the details and the characteristics of the proposed algorithm.

57 Example In Figure 5.2, node n 1 has three alternative routes to the base station, which are two indirect routes via neighboring nodes and one direct route. E i and e ij represents the currently available energy of node i and the required energy for transmission from node i to j, respectively. The node n 1 calculates TEC value for each alternative route as in Figure 5.2(c). The second column shows the energy cost for direct transmission to the base station from an alternative node, and the third column for the transmission to a neighboring node. The energy cost to each neighbor is the same because the transmission power for neighbors is fixed. By totaling these two columns, the total energy cost for each route is shown in the last column. The computational results indicate that route 3 is the least energyexpensive one with T EC 3 = However, this cost can further decrease if the node n 5 has more cost-effective routes than direct transmission. Node n 1 chooses n 3 as the best candidate and sends data to n 3. At this moment, the node adds its available energy, after transmission and destination, to the data so that all of its neighbors can update their EC tables accordingly. A node needs only the information of its neighbors for the routing decision and this updating process guarantees it since every node has the same transmission power for its neighbors. After receiving this data from node n 1, node n 3 starts a routing process again. This routing process continues until the base station receives the data Steps in the DEAR algorithm Each sensor keeps a small EC table. The EC table contains node identification number, minimum transmission power to the base station, and available energy for each neighboring node. The steps of the algorithm are: 1. Initialize EC table: During the setup period, each sensor finds its minimum transmission power to the base station. Then, each sensor broadcasts a setup message to neighboring nodes using a pre-set transmission power. This setup message includes node identifier, minimum transmission power to the base station, and available energy. Every node receiving this broadcast message registers the transmitting node as one of its neighbors. Since all nodes

58 45 Figure 5.2. An example scenario: (a) node n 1 needs to send data to base station and two nodes locate within its neighboring distance; (b) three alternative routes for transmission are available; (c) n 3 is the best candidate with the least total energy cost. have an identical neighbor distance, two nodes within the neighbor distance are neighbors to each other. After the setup period, all sensors initialize their EC tables. 2. Update EC table: The routing table reflects changes of neighbors energy levels. When a sensor transmits data, all of its neighbors receive this data and get the current battery level of the transmitting sensor. As a result, whenever a sensor s battery level changes, all routing tables, including the corresponding sensor information, are updated. 3. Decentralized routing decision: Based on their EC table, all nodes make a local routing decision. Based on Equation (5.3), node i selects K as the best candidate for transmitting data to the base station without considering whether K sends data directly to the base station or not. For tie breaking, if a direct path and an indirect path result in the same EC, the direct path

59 46 is selected to reduce the number of transmissions or hops. In the case of two indirect paths having the same EC values, any path of them is selected randomly. Figure 5.3. An example routing path: n i sends data to n j, n j to n k, then n k sends to the base station directly. Figure 5.3 shows how the DEAR algorithm operates over a sensor network. For a given data, n i chooses n j among several possible routes. After the data passes to n j, energy level of n i changes and the EC table of n j also changes. n j performs the same process sequentially. In the figure, n k sends data to the base station directly because n k, itself, has the minimum energy cost compared to other indirect routes Algorithm Characteristics This section discusses the characteristics of the DEAR algorithm. Observation 1 : DEAR occasionally prevents sensors from using the most energy efficient path to achieve an energy balance of sensors. As described in Figure 5.4, even though e 1,BS < e 12 + e 2,BS, sensor 1 sends data to sensor 2 instead of to the base station directly because e 1,BS E 1 > e 12 E 1 + e 2,BS E 2. As a result, sensor 1 having relatively low energy can conserve its energy by passing the data to sensor 2 with relatively higher energy. Through this characteristic DEAR can achieve an energy balance over the entire network. Observation 2 : DEAR guarantees elimination of loops in any routing path. After

60 47 sensor A sends data to sensor B located on the minimal energy cost path, sensor B also considers sensor A as one of the candidates for data transmission. However, sensor B never routes data to sensor A, because the energy cost of using sensor A is greater than that of direct transmission from sensor B to the base station. In DEAR, a sensor routes data to a neighbor only if the neighbor incurs less energy cost than the sensor itself. As this routing mechanism continues, the energy cost of the original node is apparently greater than that of the next down-stream node. Therefore, DEAR always assures finding a routing path to the base station without loops. Observation 3 : The performance of the proposed algorithm heavily depends on the neighboring distance. As the neighboring distance increases, the number of neighbors also increases and each sensor has a better chance to find less costly energy paths. However, an increase in neighboring distance also implies an increase in energy required to reach neighboring nodes. Therefore, an optimally desirable neighbor distance exists that balances these two competing criteria. This distance also depends upon the density of sensors. Figure 5.4. A tradeoff between energy balance and energy efficiency.

61 Experimental Results In this section, we provide several experimental results to validate the effectiveness of the DEAR algorithm. The comparison of the algorithm is with three other algorithms discussed in [9, 8]: Direct Communication (DC), Minimum Transmission Energy (MTE), and Self-Organized Routing (SOR). We coded the four routing algorithms in C programming language while solving the mathematical model using a commercially available LP solver [56]. Two different shapes of sensor networks are used (see Figure 2.5). The first example is a sensor network with 100 nodes randomly uniformly deployed in a 100m 100m square area with the base station located at (50, 150). The other example has 100 sensors randomly deployed in a 100m-radius with the base station at (0, 0). In the square and circle sensor networks one sensor has an assigned initial battery level of 250,000 and 100,000, respectively. The initial energy levels are established by determining the amount of energy needed for the farthest node to transmit data to the base station 100 times with DC [8]. Because the sensor networks are randomly generated, 100 repeated experiments for each condition provides an average for the results. The empirical analysis consists of three parts. First, we compare the lifetime of DC, MTE, SOR, and DEAR. The second part provides the effects of neighbor distance on the proposed algorithm. Finally, the third part demonstrates how the DEAR algorithm is robust for diverse event generation patterns Lifetime of Sensor Network This experimentation evaluates the performance of the DEAR algorithm with 20m neighboring distance, DEAR-20m, of the square sensor network. Figure 5.5(a) plots the number of active sensors against the number of rounds for each algorithm. We call it a round that every sensor sends its data to the base station once. This graph shows that DEAR-20m has better performance than DC, MTE, and SOR algorithms until 50(%) of nodes die. Also noticeable is that the DEAR algorithm has similar patterns to the Optimal. Sensors in DC, MTE, and SOR algorithms depleted their energies gradually with time. However, in the DEAR algorithm, the majority of sensors is alive up to 200 rounds and deplete simulta-

62 49 Number of active sensors Direct MTE SOR DEAR 20m Optimal L 1 L Time (a) L 20 Number of active sensors Direct MTE 20 SOR DEAR 20m Optimal Time Figure 5.5. Performance results: the number of active sensors against the number of rounds and the lifetime for each algorithm with (a) square and (b) circle sensor network, respectively. (b) L 1 L 10 L 20 neously, thus indicating good energy balancing throughout the network. Similarly, Figure 5.5(b) provides the performance result for the four routing algorithms with the 100m radius sensor network. Although the superiority of performance is reduced, still, DEAR shows better performance than the other three algorithms until 40(%) of nodes drain. Also, Figure 5.5(a) and (b) show the lifetimes of the sensor networks (L 1, L 10, L 20 ) according to the definitions in the Chapter 2. DEAR-20m is dominantly better than the three other routing algorithms for all various lifetime definitions, with 2.5, 2, and 1.7 times for DC, 20, 5, and 2.5 times for MTE, and 10, 2, and 1.5 times for SOR. Number of Active Sensors Direct MTE SOR DEAR 20m LP Time (a) Number of Active Sensors Direct MTE 20 SOR DEAR 20m LP Time Figure 5.6. The number of active sensors over time under (a) random and (b) repeated event generation patterns with the square sensor network. (b)

63 50 Similar observations can be found even for random and repeated event generation patterns as shown in Figures 5.6(a) and (b), respectively. Especially, the performance of DEAR in repeated generation is dominantly better than others in all different definitions of the lifetime. With these findings, we can conclude that our algorithm is superior to other routing algorithms regardless of event generation patterns, thus robust. Direct Uniform 150R MTE Uniform 150R Remaining Battery x Y (a) 40 X SOR Uniform 150R Remaining Battery x Y (b) 40 X DEAR Uniform 150R Remaining Battery x Y Remaining Battery x X Y (c) (d) Figure 5.7. Remaining energy distributions of sensors with uniform events for DC, MTE, SOR, and DEAR after 150 Rounds. X Energy Balancing Figure 5.7 shows how well DEAR achieves the energy balance of sensors over the network. As discussed in [9], in DC (Figure 5.7(a)), MTE (Figure 5.7 (b)) and SOR(Figure 5.7(c)) schemes, sensors far away and close to the base station depleted their energies about round 150. While, in DEAR, all sensors remain live and even have sufficient energy for responding to upcoming events (Figure 5.7 (d)).

64 51 Also notable is that DC, MTE, and SOR missed some events during the first 150 rounds. However, DEAR guaranteed that all data was transmitted to the base station for the same period. x 10 6 DEAR Uniform 150R Optimal: 1.2 x Y Figure 5.8. Remaining energy distributions of sensors with their distances to the base station at (50, 150) with uniform events for DEAR after 150 Rounds. Figure 5.8 shows the result of the IP problem in Chapter 4 and residual energy distribution of sensors according to their y-axis distance in DEAR. In IP, all sensors have the same residual energy, , after 150 rounds. On the other hand, in our algorithm, the residual energy of sensor increases as the distance to the base station does. In fact, DEAR pursues an energy balance over sensor network in terms of direct communication capacity instead of the amount of energy. This is a desirable property of our routing algorithm because all sensors are guaranteed to have the same capability to deliver their data to the base station with time. Figure 5.9 shows the routing paths for four algorithms with repeated events in the regions from (0, 0) to (50, 50). In the case of Direct, MTE, and SOR, data traffic concentrates in specific sensors which have location in the region or on the efficient path. On the other hand, DEAR tries to disperse energy usage over the whole network to achieve energy balance. As a result, DEAR can keep all sensors operating for as long as possible.

65 Direct 150 MTE BS BS Y Y X (a) SOR BS X (b) DEAR BS Y Y X (c) Figure 5.9. Routing paths by Direct, MTE, SOR, and DEAR with repeat events on the region from (0,0) to (50,50). (d) X Different Event Generation Functions To identify the effect of different event generation types on the lifetime of a sensor network, performed simulations use uniform, random, and repeat event generation functions. In the case of the random distribution, 25% of sensors have events randomly occurring in each round. While, for the repeat events, the assumption is that sensors from (0, 0) to (50, 50) observe repeated events. Table 1 gives the results of the lifetime of sensor networks (L 1, L 10, L 20 ) for Direct, MTE, SOR, and DEAR algorithms with three different event generation types. As shown in

66 53 Table 5.1. Lifetime (L 1, L 10, L 20 ) for Direct, MTE, SOR, and DEAR-20m with Uniform, Random, and Repeat Events. Uniform Random Repeated L 1 L 10 L 20 L 1 L 10 L 20 L 1 L 10 L 20 Direct MTE SOR DEAR-20m LP Table1, DEAR shows a dominant performance compared with Direct, MTE and SOR over the time. Especially, in the case of L 1, DEAR gives approximately two to eight times better performance than the others. Average number of neighor nodes Neighboring Distance (a) Number of rounds Neighboring distance Figure Number of neighboring nodes and number of rounds with neighboring distance (a) Number of neighbor nodes against neighboring distance and (b) Number of rounds against neighboring distance for the square sensor network. (b) L 1 L 10 L Neighbor Distance Figure 5.10 shows the effects of neighbor distance on the lifetime of the square sensor network. The results show that the performance of the DEAR algorithm depends on neighbor distance or equivalently the number of neighbor nodes. Figure 5.10(a) shows that the increase in neighbor distances results in an increase in the number of neighbor nodes. However, Figure 5.10(b) shows that such an increase

67 54 not lead to a monotonic increase of the lifetime. This phenomenon is due to the following two reasons; (1) the increased distance requires more transmission power between neighbors and (2) sensors have to expend the same transmission power for its neighboring nodes regardless of the actual distances to neighboring nodes. In this experiment, the best neighboring distance for the DEAR algorithm is 22m, 17m, and 16m (ranging between 8-12 neighbors) for L 1, L 10, L Position of the base station To examine the effect of the location of the base station, we used 5 different positions of the base station. The base station is located at either of (50, 50), (50, 150), (50, 200), (50, 300), or randomly within the target area. Table 5.2 summarizes the results of each algorithm. DEAR is several times better than Direct and SOR over diverse BS locations. As the base station is far away from the target area, the performance our approach is more close to the optimal solution Density of Sensors In Subsection 5.3.4, we observed that DEAR gives the best performance where the neighbor distance is approximately 22m. Though there is no evidence that the neighbor distance 22m is still valid when the density of sensors changes, we can conjecture that the number of neighbors, 8 corresponding to 100 nodes, might be valid under varying densities. So, by setting the transmission power to have one the average 8 neighbors, we made experimentation with different densities. In our simulation, average numbers of neighbors are 8.17, 9.2, and 8.77 for 100, 150, and 200 nodes respectively. Table 5.3 shows that DEAR is superior to Direct, MTE, and SOR with consistent performance regardless of the density of the sensors. This insensitivity indicates that the optimal number of neighbors might be an invariant of the density of sensors. In general, the increase in the density gives more chance to find a better route but on the other hand results in increased traffics. DEAR algorithm may neutralize both effects in some way. This observation can reduce the efforts of determining appropriate transmission power. Given the size of target area and the number of sensors, one can decide the best transmission power to achieve the optimal number of neighbors.

68 55 Table 5.2. Lifetime (L1, L10, L20) of 100 m 100 m square sensor network with different positions of the base station. (50,50) (50,150) (50,200) L1 L10 L20 L1 L10 L20 L1 L10 L20 Direct SOR DEAR-17.5m LP (50,300) Random L1 L10 L20 L1 L10 L20 Direct SOR DEAR-17.5m LP

69 56 Table 5.3. Lifetime (L 1, L 10, L 20 ) for Direct, MTE, SOR, and DEAR-20m with 100, 150, and 200 nodes. 100 nodes 150 nodes 200 nodes L 1 L 10 L 20 L 1 L 10 L 20 L 1 L 10 L 20 Direct MTE SOR DEAR-20m Figure 5.11 plots number of rounds over neighboring distance with different sensor densities Initial Energy Distribution Figure 5.12, 5.13, 5.14, and 5.15 show the remaining energy distribution for Direct, MTE, SOR, and DEAR with time. For this experiment, we randomly and uniformly assigned a value between 125,000 and 375,000 to each sensor as it initial energy level. In Direct, MTE, and SOR, some sensors are already drained out around the 50 rounds while other sensors have sufficient energy. However, DEAR achieves an energy balance of sensors. Even though sensors have different initial battery levels at time 0, DEAR keeps all sensors alive with the same direct transmission capability as time goes on. 5.4 Conclusion and Future works Sensor networks should be able to achieve energy balance as well as energy efficiency to prolong their lifetimes and prepare for the uncertainties of event generation. Most energy aware routing algorithms are only concerned about energy efficiency. This chapter presents a heuristic criterion, called Energy Cost, to consider energy balance and efficiency simultaneously. Using this metric, we have designed and implemented the Distributed Energy Balanced Routing (DEAR) algorithm. The designed algorithm demonstrates its superiority to Direct Communication (Direct), Minimum Transmission Energy (MTE), and Self Organized Routing (SOR)

70 With 100 nodes 300 With 150 nodes Number of Round L 1 Number of rounds L L L 10 L Neighboring Distance L Neighboring Distance (a) 300 With 200 nodes (b) 250 Number of rounds L 1 L 10 L Neighboring Distance (c) Figure Number of rounds with neighboring distance: (a) 100 nodes, (b) 150 nodes, and (c) 200 nodes. with a lifetime metric, generally accepted for evaluation of routing algorithms. Additionally, from the experimental results, the conclusion is that DEAR is robust for several event generation functions. In summary, the proposed algorithm has several desirable properties. First, it is simple and localized, supporting scalability. Second, the algorithm maintains energy efficiency for networks while keeping an energy balance. Third, the algorithm is robust to diverse event generation patterns. The lifetime of sensor networks is one of the most popular measurements to evaluate routing algorithms. Although this work defines the lifetime of sensor network as L 1, L 10, L 20, the definition of lifetime can vary according to the objective and nature of sensor network. Therefore, one can investigate the use of more delicate measurements which could be generally accepted. Also, in this work, three

71 58 types of event generation function are the bases for evaluation of the routing algorithm. Future work will involve development of more diverse and detailed event generation functions. In addition, although this study considers a general multihop communication scenario, where only a few sensors can communicate with the base station, a more specific problem definition and routing algorithm for this scenario is required. To apply the proposed algorithm to the general case, additional routing policies for sensors not able to communicate with the base station directly is necessary. In other words, sensors far from the base station need a different routing scheme to send their data to one of sensors in the area where sensors can communicate with the base station. Future work will advance the DEAR to apply to the general scenario and investigate how well the new DEAR works in the scenario.

72 59 Initial Energy Distribution (at Round 0) Direct Uniform 50R x 10 6 x Initial Energy Y X 100 Remaining Energy Y X 100 (a) Direct Uniform 100R (b) Direct Uniform 150R Remaining Energy x Y 0 0 (c) X Figure Remaining Energy Distribution with Direct at time (a) 0 (b) 50R, (c) 100R, and (d) 150R. Remaining Energy x Y 0 0 (d) X

73 60 Initial Energy Distribution (at Round 0) MTE Uniform 50R x 10 6 x Initial Energy Y X 100 Remaining Battery Y X 100 (a) MTE Uniform 100R (b) MTE Uniform 150R x Remaining Battery Y X x Remaining Battery Y X (c) (d) Figure Remaining Energy Distribution with MTE at time (a) 0 (b) 50R, (c) 100R, and (d) 150R.

74 61 Initial Energy Distribution (at Round 0) SOR Uniform 50R x 10 6 x Initial Energy Y X 100 Remaining Battery Y X 100 (a) SOR Uniform 100R (b) SOR Uniform 150R Remaining Energy x Y 0 0 (c) X Figure Remaining Energy Distribution with SOR at time (a) 0 (b) 50R, (c) 100R, and (d) 150R. Remaining Battery x Y 0 0 (d) X

75 62 Initial Energy Distribution (at Round 0) DEAR Uniform 50R x 10 6 x Initial Energy Y X 100 Remaining Battery Y X 100 (a) DEAR Uniform 100R (b) DEAR Uniform 150R Remaining Battery x Y 0 0 (c) X Figure Remaining Energy Distribution with DEAR at time (a) 0 (b) 50R, (c) 100R, and (d) 150R. Remaining Energy x Y 0 0 (d) X

76 Chapter 6 Maximum Energy Welfare (MaxEW) Routing Since sensors have limited power, the power should be used in an efficient way. However, this approach drives sensors on the efficient paths being depleted quickly, and consequently the sensor networks become incapable of monitoring events from some parts of their target areas. In many sensor network applications, the sensed events have uncertainties in positions and generation patterns. Therefore, routing algorithms should be designed to consider not only energy efficiency, but also the amount of energy left in each sensor to avoid sensors losing power, early. This chapter introduces a new metric, called Energy-Welfare, which considers average and balance of sensors remaining energies at the same time. Using this metric, we design the Maximum Energy Welfare Routing (MaxEW) algorithm, which achieves simultaneous energy efficiency and energy balance of sensor networks. 6.1 Introduction We assume that sensors can obtain information about the energy left in each neighbor and the energy required to transmit to the base station from that neighbor (See Section 2). Individual sensors forward messages to neighbors that they think are on the best route to the base station. The determination of the optimal route is difficult because the individual sensors do not have the information about the dynamic topology of the entire network and the dynamic energy balances of

77 64 Figure 6.1. An explanatory example for Energy Welfare Routing algorithm. Node 1 routes data to a path to maximize an Energy Welfare (Average Equality) of sensor 1 and 2. The equality is a proposed metric in this chapter to measure how even residual energies of sensors are. The values of equality are calculated by Equations (6.1) and (6.2). each node on the network. This study proposes a new heuristic metric, called Energy Welfare, to achieve the efficiency and balance of energies of sensors simultaneously. Based on this metric, we propose a localized routing algorithm, the Maximum Energy Welfare (MaxEW) routing, to accomplish the two objectives. Figure 6.1 shows a simple example of the MaxEW routing. E i and e ij represent the residual energy of sensor i and energy required to transmit from node i to node j, respectively. Sensor 1 has two paths for reaching to the base station. Path 2 is more energy efficient than path 1. However, if Sensor 1 keeps using path 2, sensor 2 will completely dissipate its power while sensor 1 has sufficient energy. In MaxEW, sensors can avoid the traffic concentration to a sensor by using the metric, Energy Welfare (Average Equality), as a decision criterion. Based on the metric, sensor 1 chooses path 1 which causes higher energy welfare. The remainder of this chapter is organized as follows. Section 6.2 defines energy equality and energy welfare metrics and Section 6.3 presents maximum energy welfare routing algorithm. Extensive simulation results are provided in Section 6.4 and finally we conclude our work in Section 6.5.

78 Energy Equality and Energy Welfare To prolong the lifetime of sensor networks robustly to diverse event generation patterns, the routing algorithm must be designed to achieve energy-efficiency and energy-balancing together. For this purpose, Energy Welfare (EW ) metric is introduced in this section, based on which the MaxEW routing algorithm is designed in the following section. The MaxEW utilizes this metric as a goodness measure for energy populations. The energy welfare, which is originally used to compute income welfare in social sciences, combines average and equality of an energy population. We define first energy equality and then energy welfare Energy Equality (EE) To measure how well energy-balanced a set of sensors is, the Energy Equality (EE) is computed according to Equations (6.1) and (6.2). The input data to these equations are energy residuals of a sensor population at a certain time. EE(t) = 1 I A (t, ε) (6.1) ( ) I A(ε) (t) = ε E i (t) n E(t) i N 1 1 ε (6.2) EE(t) denotes energy equality at time t and I A (t, ε) is an inequality index at time t (details of this index will follow). N is a set of sensors and n the number of sensors. E i (t) denotes the energy residual of sensor i at time t and E(t) the average of energy residuals at time t. The I A (t, ε), known as Atkinson inequality index [32], imposes different penalties on inequality through inequality aversion parameter ε. This parameter takes values ranging from zero to infinity. When equals zero, no penalty for inequality accrues and I A is zero. As ε increases, the inequality is more penalized and I A converges to one. Therefore, 0 I A 1 and hence 0 EE 1. The aversion parameter provides a flexibility to apply this metric to diverse sensor network applications.

79 Energy Welare (EW ) In addition to the equality, which depicts energy-balancing, the goodness measure for energy populations should also consider average of energy residuals. If a routing algorithm only pursues energy-balancing without considering energy-efficiency, sensors energy would be depleted rapidly. Energy Welfare (EW ) combines average and equality by simply weighting the average by energy equality as in Equation (6.3). EW (t) = E(t) EE(t) = ( 1 n i N E i (t) 1 ε ) 1 1 ε (6.3) The EW has the exactly same form as so-called Atkinson welfare function [37]. It increases with the increase of average and equality, and trades off between them through aversion parameter ε. It is desirable to have high EW at any given time, since then the sensors are achieving energy-efficiency as well as energy-balancing simultaneously Alternative Energy Welfare Metrics In addition to Atkinson s, there exist other welfare functions that can be used to compute energy welfare, such as Sen [36] and Dagum [38] welfare functions. These two welfare functions are derived from Gini index [30]. The Gini index is derived from the Lorenz curve, which plots the cumulative proportion of income earned by the people ranked from bottom to top as shown in 3.1. In perfect equality the Lorenz curve follows the 45 o line. As the degree of inequality increases, the area between the curve and 45 o line becomes larger. If the area between the curve and 45 o line is A, and the area below the curve is B, then the Gini index I G is computed as follows: I G (t) = A A + B = i N j N E i(t) E j (t) 2n 2 E(t) (6.4) By replacing the inequality index IA in (6.1) with I G, Sen welfare function is formed as in Equation (6.5). Dagum welfare function as in Equation (6.6) is

80 67 similar to Sen s but it imposes more penalties on inequality by the denominator. EW (t) = E(t) (1 I G (t) (6.5) EW (t) = E(t) 1 I G(t) 1 + I G (t) (6.6) Table 6.1 summarizes alternative energy welfare metrics that will be investigated in our experimental study. Note that the routing algorithm designed in the following section can use any of these welfare metrics without any change of algorithm structure. Table 6.1. Alternative Energy Welfare Metrics. EE(Energy Equality) EW(Energy Welfare) 1 I A (t, 1.5) E(t) (1 I A (t, 1.5)) Atkinson 1 I A (t, 2.0) E(t) (1 I A (t, 2.0)) 1 I A (t, 2.5) E(t) (1 I A (t, 2.5)) Sen 1 I G (t) E(t) (1 I G (t)) Dagum 1 I G (t) E(t) (1 I G (t))/(1 + I G (t)) 6.3 Maximum Energy Welfare (MaxEW) Routing In the MaxEW routing algorithm designed in this section, sensors make local routing decisions by utilizing the energy welfare metric as a goodness measure. This routing algorithm pursues globally efficient energy-balancing through maximizing the energy welfares of overlapped local societies.

81 Neighbor Distance and Neighbors Every sensor uses one of two transmission distances. One is direct distance to the base station and another neighbor distance common to all sensors. For a given sensor the sensors within its neighbor distance are called neighboring sensors or neighbors. Since every node has the same neighbor distance, sensors are neighbors each other. Therefore, a sensor s neighboring sensors will receive all the messages the sensor transmits and hence a sensor will receive all the messages its neighbors transmit. When the direct distance is less than the neighbor distance, a sensor uses the neighbor distance so that all of its neighbors can receive the messages from the sensor. The neighbor structure is important to keep the routing tables updated based on which the routing decisions are made. While, one of the typical methods to save energy in sensor networks is to consider a duty-cycle on sensors in the design of the Medium Access Control (MAC) layer [18, 17, 19, 20]. Although sensors turn their radio off during idle period to save their energies, these MAC schemes guarantee that the awake/sleep schedules of all sensors or, at least, neighboring nodes are synchronized. Therefore, sensors can be aware of the current energy levels of its neighboring nodes regardless of the design of the MAC layer Routing Table Each sensor keeps a routing table only for its neighbors. The routing table contains identification number, distance to base station, and current energy residual, for each neighbor. 1. Initialization of the routing table: During initial setup period, each sensor finds its direct distance to the base station. Then, each sensor broadcasts a setup message to its neighbors with a pre-set transmission power for the neighbor distance. This setup message includes identification number, distance to base station, and current energy residual, of the transmitting sensor itself. Every sensor receiving this setup message registers the transmitting sensor as one of its neighbors. Since all sensors have an identical neighbor distance, every sensor will get the setup messages from all of its neighbors. After the setup period, all sensors initialize their routing tables.

82 69 2. Updating of the routing table: When a sensor transmits data, it also transmits a control message composed of its identification number, designated sensor (or base station) identification number, and current energy residual. Only the designated sensor (or base station) further processes the data and all the neighbors update their routing tables by using this control message. Also, if a sensor does not get any message from a neighbor in a round, the sensor removes the neighbor from the routing table. This could happen when the neighbor becomes inactive due to energy depletion or moves out of the neighbor distance due to some environmental forces. Therefore, the routing table keeps updated information adaptive to topological changes Routing Algorithm Based on the routing table, a sensor makes a routing decision such that the energy welfare of its local society is maximized. A sensor i considers alternative paths as if the paths have at most two hops to the base station: transmitting directly to the base station or transmitting to the base station indirectly through one of its neighbors (N i ). In other words, the sensor determines which sensor is the best candidate for direct communication with the base station among its neighbors and itself. Note that a sensor considers only feasible paths with the limitations of available energy. To evaluate the alternative paths, the sensor calculates expected EW of its local society consisting of its neighbors and itself, for each alterative path. A path results in a population of energy residuals of the local society and a social welfare function is used to compute the local energy welfare from the energy population. After computing the energy welfare for each alternative path, a path is selected if the path gives the highest local energy welfare. To calculate the expected EW, the sensor i anticipates an energy population as in Equation (6.7), resulting from each decision D i (t) = k N i + {i} which represents the candidate for direct communication with the base station. Note that E j (t) denotes the energy residual of sensor j at time t and Êik j (t+1) expected energy residual of sensor j resulting from the decision D i (t) = k.

83 70 {E j (t) : j N i + {i}} D i(t)=k {Êik } j (t + 1) : j N i + {i} where k N i +{i} (6.7) Specifically, for direct transmission or D i (t) = i, the expected energy residuals of sensor i and its neighbors are computed as in Equation (6.8), in which T EB i represents the required transmission energy from the sensor i to the base station. In this case, only the energy residual of sensor i changes. Ê ii i (t + 1) = E i (t) T EB i, Ê ii j (t + 1) = E j (t), j N i (6.8) For the indirect transmission through a neighbor k or D i (t) = k N i, the expected energy residuals of sensor i and its neighbors are as in Equation (6.9), where TEN is required transmission energy for the fixed neighbor distance. Different from direct transmission, energy residuals of sensors i and k change in this case. Ê ik i (t + 1) = E i (t) T EN, Ê ik k (t + 1) = E k (t) T EB k, Ê ik j (t + 1) = E j (t) j N i {k} (6.9) Using the expected energy residuals from Equations (6.8) and (6.9), sensor i can calculate the expected EW ik for each decision k by Equation (6.10) which is based on the Atkinson welfare function. By comparing these expected EWs, the sensor routes data to sensor K allowing the maximum EW of the local society N i + i, as described in Equation (6.11). For tie-breaking, if a direct path and an indirect path result in the same EW, the direct path is selected to reduce the number of transmissions or hops. In case of two indirect paths having the same EW value, a path can be selected randomly. ÊW ik (t + 1) = 1 n j N i +{i} j (t + 1) 1 ε Ê ik 1 1 ε (6.10)

84 71 ) ik K = ArgMax (ÊW (t + 1) k N i +{i} (6.11) The table 6.2 below gives a high-level description of the routing decision of MaxEW algorithm. In essence, this description is the same as the one we have discussed. Table 6.2. MaxEW routing algorithm Algorithm 6.1. MaxEW routing algorithm at node i and time t For all k N i + {i} do If k = i then For all j N i + i do If j = i then E j (t + 1) = E j (t) T EB j Else E j (t + 1) = E j (t) End If End For Else For all j N i + {i} do If j = i then E j (t + 1) = E j (t) T EN Else If k = j then E j (t + 1) = E j (t) T EB j Else E j (t + 1) = E j (t) End If End For End If Compute EW ik by Equation (6.10) End For Choose K = ArgMax(EW ik ) and route data. k N i +{i} Figure 6.2 shows how the MaxEW algorithm operates over a sensor network. For a given data packet, sensor 5 chooses sensor 9 among several possible paths. After the data is passed to sensor 9, the energy residual of sensor 5 changes

85 72 and the routing table of sensor 9 also changes. Sensor 9 performs the same process sequentially. Once a sensor 12 evaluates the direct transmission results in the maximum energy welfare of its local society, it sends to the base station and the process terminates. Every data packet in a round is sent to the base station following the same process. Since local societies are overlapped, local efforts to minimize energy consumption and maximize equality would lead to globally efficient energy-balancing. Robustness to diverse event generation patterns is also supported by the preparedness resulting from this emergent property. Figure 6.2. An example routing path: sensor 5 sends data to sensor 9, sensor 9 to sensor 12, then sensor 12 sends to the base station directly An Example This section provides an example to clarify the mechanism of the MaxEW algorithm. In Figure 6.3(a) sensor A has a data packet to be sent to the base station. Since it has two neighbors, there are three alternative paths to the base station, which are two indirect paths (A B BS, A C BS) and one direct path (A BS). Figure 6.3(b) lists E j, T EB j and T EN for each sensor of the local society {A, B, C}, which are composed from the routing table and used to make the routing decision. At current time t, for each alternative path, sensor A computes the expected energy residuals of itself A and neighbors B and C at next time t+1. The second column of Table 6.3 shows these expected energy residuals for each alternative