Efficient scheduling of a mobile charger in large-scale sensor networks

Highlights

• We give the definition of problem MBA and prove the NP-hardness of the problem.

• We consider the MBA problem in three aspects and propose three approximation algorithms corresponding to these three cases.

• We conduct extensive simulations to validate our algorithms. The results show the effectiveness of our algorithms.

Abstract

Schedule a mobile charger to replenish energy to sensor nodes for the wireless sensor networks has attracted great attention recently, due to its efficiency and flexibility. Some existing works study the mobile charger scheduling problem by considering that only the depot can recharge or replace the battery for the mobile charger. However, for large-scale wireless sensor networks, the mobile charger is energy inefficient or even may run out of energy during the travel for charging. In this paper, we consider the scenario that there are some service stations in the network area which can be used to replace the battery for the mobile charger, and we study the problem of minimizing the number of used batteries for a mobile charger to charge a wireless sensor network (MBA). We first consider a special case of the MBA problem, in which the depot is the only service station, and we present an approximation algorithm to address it. Then we propose an approximation algorithm for the MBA problem with the assumption that the distance of any two service stations is limited. And finally, we consider the general MBA problem and propose an approximation algorithm. We validate the performance of our algorithms by extensive simulations, and the results show that our proposed algorithms are promising.

Introduction

In the past few decades, using Wireless Sensor Networks (WSNs) to monitor the physical world has been widely used [1], [2]. The sensor nodes in a wireless sensor network are usually powered by batteries, and can only operate for a limited time due to the limited energy capacity of the on-board batteries. Therefore, it's a critical task to prolong the lifetime of a wireless sensor network. Many approaches have been proposed to extend the wireless sensor network lifetime, such as battery replacement [3] and energy harvesting [4], [5]. However, battery replacement is not suitable for large-scale wireless sensor networks as it is very time-consuming and costly [6]. Energy harvesting sensor nodes harvest ambient energy from their surroundings such as solar [5] and wind [7] energy, these environmental energy sources are time-varying and not stable in nature, besides, this approach requires sensor nodes to be equipped with some expensive equipments, and therefore, the energy harvesting approach remains limited benefits for WSNs in practice.

The recent breakthrough in wireless power transfer technology provides a new approach to replenish energy to sensor nodes [8]. As a promising way to prolong the lifetime of WSNs, wireless charging guarantees the continuous power supply for sensor nodes and is insensitive to surroundings. Some researchers study the problem of replenishing energy to sensor nodes in WSNs with a mobile charger (MC) [9], [10], [11] so that sensors can achieve continuous operation. In these studies, they consider that there is a depot for maintaining the MC, and the MC will be periodically dispatched to traverse the sensor nodes in the network area and charge them one by one. However, for large-scale wireless sensor networks, it's energy inefficient and time consuming for the MC if there is only one depot, as the MC consumes lots of energy on the traveling, and it may take multiple rounds to charge all the sensor nodes. Even worse, for some wireless sensor networks with extremely large-scale areas, the MC may not be able to reach the sensor nodes that are very far from the depot, and thus cannot finish the charging task. To overcome the time consuming problem of using single MC to charge large-scale sensor networks, some researchers investigate the problem of charging a wireless sensor network with multiple mobile chargers [12], [13], [14], [15], [16], in which they schedule multiple wireless chargers from the depot to charge sensor nodes, but they did not solve the energy inefficient problem.

In this paper, we consider that there is a set of service stations in the network area which can replace battery for the MC with the help of some mechanical equipments. In such a scenario, the depot dispatch a MC to traverse and charge each sensor node one by one, when the MC is going to run out of it energy, it will move to a nearby service station to replace a new battery and then continue to traverse and charge the remaining sensor nodes. These service stations will recharge these replaced batteries and used for the next charging tour. The total cost of a charging tour is directly related to the number of used batteries of the MC during a charging cycle. Design a charging tour for the MC to fully charge all the sensor nodes with the minimum number of used batteries, therefore, is a realistic and crucial problem in this scenario.

To reduce the cost of maintaining the continuous operation of a sensor network with a MC, in this paper, we study the charging tour design problem for achieving minimize the number of used batteries during a charging cycle. The main contributions of our work are as follows.

• We consider the scenario that a network area has a set of service stations and give the definition of the MBA problem. We also prove that the MBA problem is NP-hard.

• We design approximation algorithms for the MBA problem. Particularly, we first solve the special case of the MBA problem where there is only one service station in the network area. Then we consider the MBA problem with the assumption that the distance between any two service stations is limited by $U/\eta$, where U is the energy capacity of the MC, and η is the energy consumption rate of the MC for traveling. And finally, we address the general MBA problem.

• We evaluate our algorithms by conducting extensive simulations. The simulation results show the effectiveness of our algorithms.

The remainder of this paper is structured as follows. In Section 2, we introduce the related works of this paper. In Section 3, we formally define the MBA problem to be addressed, and prove the NP-hardness of problem MBA. In Section 4, we present an approximation algorithm for a special case of the MBA problem (S-MBA). In Section 5, we address the limited MBA problem (L-MBA) and design an approximation algorithm for it. In Section 6, we propose an approximation algorithm for the general MBA problem and conduct the performance analysis. In Section 7, we conduct extensive simulations to evaluate our algorithms. And finally, we conclude this paper in Section 8.