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Top1. Introduction
Wireless sensor networks (WSNs) consist of a large number of tiny sensors deployed in specific areas for event monitoring. Such networks can be used for military, aerospace, disaster relief, environmental, medical, industrial, and many other applications.
Energy is critical to a WSN because sensor node is usually powered by battery with limited capacity due to its small size. Sometimes it is not easy or even impossible to extend the life of the wireless sensor by replacing the battery, which limits the application of the wireless sensor (Xie, Shi, Hou, & Sherali, 2012). Some of the previous energy savings studies are based on balanced power consumption (Tarng et al., 2011), mobile sensors (Butler & Rus, 2004), mobile collectors (Yao, Li, & Wu, 2006) and so on. However, these methods only reduce the rate of energy consumption and do not extend the life of the WSNs infinitely.
Recently, much progress has been made in the field of wireless energy transmission. Kurs has demonstrated the feasibility of wireless energy transfer through strongly coupled magnetic resonances (Kurs, Karalis, Moffatt, Joannopoulos, Fisher, & Soljačić, 2007). This technology inspires new ideas for wireless sensor networks. Previous studies have suggested that wireless chargers equipped with coupled coils can use this new technology to replenish energy to sensor nodes within some certain distance. Furthermore, when these chargers are bundled with vehicles (will be referred to as wireless charging vehicles, WCVs) moving within a wireless rechargeable sensor network (WRSN), all nodes in the WRSN may be recharged. Extending the life of a WRSN infinitely is thus possible and scheduling of the WCVs to achieve this goal has become an essential issue addressed by many researches.
Related studies generally consider charging scheduling problems by using deterministic or non-deterministic methods (Bouakaz, Gautier, & Talpin, 2014; Xu, Cheng, & Wu, 2018). The deterministic methods assume that the WCV or Base Station (BS) is capable of recording some necessary information (such as position and energy state) of the sensor node. On the other hand, in the non-deterministic method, the node itself actively monitors its remaining energy and sends a recharging request to the WCV / BS when the energy level falls below a certain threshold. In either case, The WCV / BS then bases on the recorded information or received requests to determine the order of charging according to some scheduling policy.
At present, most of the charging path scheduling methods consider time, distance or both at the same time, and greedily generate a charging path by selecting nodes one by one (Bouakaz et al., 2014; Lin, Wang, Han, Wu, Yu, & Wu, 2016). However, other factors, such as data delivery rate and network availability, were usually not taken into consideration. In terms of message transmission, in addition to the information generated by the node itself, the node must also forward data from other nodes that are located farther away from the base station. Accordingly, nodes close to the base station need to bear more communication responsibilities than the other. Therefore, nodes near the base station tend to lose battery power quicker. In case that BS is located at the center of a WSN, death of nodes in the lower tier (nodes closer to the BS) may prevent data transmission from higher tier nodes to the base station and thus results in a bottleneck area (Wang & Zhang, 2009) or form the so-called “doughnut effect” (Padmanabh & Roy, 2006). The consequence would be a lower packet delivery rate overall.