The Impact of Base Station Mobility Patterns on Wireless Sensor Network Lifetime Omer Cayirpunar, Esra Kadioglu Urtis, and Bulent Tavli TOBB University of Economics and Technology, Ankara, Turkey {ocayirpunar,ekadioglu,btavli}@etu.edu.tr Abstract—Maximization of network lifetime is one of the most important design goals in Wireless Sensor Networks (WSNs). In WSNs with static base stations, sensor nodes close to the base station dissipate most of their energies for relaying other sensor nodes’ data. Although cooperation among the sensor nodes results in longer network lifetimes in comparison to greedy approaches, there is an inherent limit on the achievable network lifetime due to the limited energy of the sensor nodes in close proximity of the base station acting as relays. Base station mobility is proposed as a remedy for the WSN hot spot problem. As the base station relocates, the burden of relaying the data coming from all sensor nodes can be shared by a larger set of nodes. To take advantage of base station mobility to maximize the network lifetime, determining the optimal mobility pattern is of utmost importance. In this study, we investigate the impact of using three base station mobility patterns which are random mobility, grid mobility, and spiral mobility. To avoid the shadowing effects of specific protocols or algorithms we build a novel Mixed Integer Programming (MIP) framework which enables us to explore the design space under optimal operating conditions. Index Terms—wireless sensor networks, sink mobility, mobility patterns, optimal sink location, mobile robotics, mixed integer programming, energy efficiency. I. I NTRODUCTION A Wireless Sensor Network (WSN) consists of multiple small form factor sensor nodes capable of sensing, data processing, and wireless communication. Sensor nodes which perform sensing tasks such as monitoring a region have limited battery energy, and hence, a limited lifetime [1]. It is a widely accepted WSN research assumption that the base station operates without energy limitation [1]. In a typical WSN deployment, a single base station performs the data collection while anchored at a stationary position which is usually chosen as the network’s geometric center of gravity [2]. One of the most important design criteria in WSNs is the maximization of network lifetime. As the sensor nodes have limited energy, they become nonfunctional after their energy is depleted. Since it is not practical to replace the batteries of sensor nodes in the field, development of efficient network strategies that optimize the network lifetime by optimizing the energy dissipation is imperative [1]. Location of the base station in WSNs directly affects the network lifetime because the base station is in communication with all the other nodes in the network directly (single-hop) or indirectly (multi-hop). In single-hop communications (i.e., sensor nodes transmit their data to the base station, directly), sensor nodes which are farther from the base station dissipate more energy than the closer nodes to the base station and drain their batteries faster. On the other hand, in multi-hop communications (i.e., data packets reach the base station via sensor nodes acting as relays), sensor nodes closer to the base station are burdened with the task of relaying the data coming from further nodes in addition to transmitting their own generated data. Such flow patterns cause the sensor nodes closer to the base station to drain their energies more rapidly than the other sensor nodes, which is known as the hotspot problem in WSN literature [3]. Repositioning the base station helps mitigating the hotspot problem in WSNs [4]. Depending on the availability and feasibility, employing a mobile base station (e.g., a mobile robot acting as a base station [5]) can improve the network lifetime significantly [6], [7] when compared to a network with a static base station. The important research problem in this case is the determination of the base station mobility pattern. Nevertheless, it is shown that even random mobility of the base station can result in significant network lifetime gains [8]. For a given WSN topology, the base station repositioning problem can be converted into an equivalent graph theory problem and can be solved by using various mathematical pro- gramming approaches. There is a rich literature on base station repositioning optimization through Linear Programming (LP) and Mixed Integer Programming (MIP) [3], [9]. Furthermore, the base station repositioning problem is investigated by using various heuristic approaches such as Particle Swarm Optimization (PSO) [10], [11] and Genetic Algorithms [5], [12]. There is a tradeoff in using the exact and approximate (heuristic) optimization approaches. Heuristic approaches do not guarantee optimality. Indeed, in general, it is not known how good is the solution found by a heuristic approach (what is the optimality gap?). On the other hand, exact methods do not scale. It is shown that the solution of the optimal base station repositioning problem is NP-complete [4] and it is not possible to find a solution in reasonable time for large networks. In this study, we propose a novel optimization framework to investigate the effects of base station repositioning by using three mobility patterns (random, grid, and spiral). In fact, we integrated an exact mathematical programming model (MIP) with a heuristic search space (the mobility patterns) to characterize the impact of mobility patterns on WSN lifetime.