# Recharging Schedule for Mitigating Data Loss in Wireless Rechargeable Sensor Network
## 1 Introduction  
Wireless Sensor Network (WSN) is widely used in many applications, such as environmental monitoring, target tracking, security surveillance, etc. [1]. As nodes in a network are powered by energy-limited batteries, the network lifetime is always limited by nodes' energy [2]. Owing to recent advances in Wireless Power Transfer (WPT) technology [3], a novel application named Wireless Rechargeable Sensor Network (WRSN) provides a promising approach to make sensor nodes work perpetually and has drawn growing attention from the research community [4; 5; 6; 7; 8]. In WRSN, when the battery of a node is depleted, a wireless charging vehicle called a mobile charger, which is equipped with an energy transceiver and high capacity battery, can move close to thenode and charge it for a period of time. The maximal travel distance of the mobile charger is bounded due to its limited fuel capacity. After charging a number of nodes, the mobile charger has to return to the base station for refueling. Thus, due to the mobile charger's refueling time and limited traveling speed, not every node which needs to be charged is serviced in time. In such a scenario, it is necessary to make a route plan for the mobile charger to determine which nodes should be charged first within the limited travel distance. In WSN, a node usually behaves as both a data source and a data router [9; 10; 11]. The sensory data traffic follows a many-to-one pattern, where relay nodes tend to be congested as they are not only collecting and processing but also relaying data from nodes farther away. A node can be called critical node if it plays an irreplaceable role as a relay node in some routing paths. When a critical node depletes its energy, some other nodes that send their sensory data to the base station via this node can't find an alternative routing path and become disconnected from the base station, which will make the network suffer data loss. In practical WSN, although the critical nodes are rare due to the dense deployment of nodes, there still exist some nodes that have a potential to be critical nodes, which are referred to as high criticality nodes in this paper. For example, as shown in Figure 1, there are the two paths A-B-C-E and A-B-D-E from node A to node E. Obviously, node B is a critical node that is irreplaceable in two paths. Node C and Node D are the high criticality nodes which will become critical node when the other is inactive. Thus, the high criticality node can also play a 'bridging' role in keeping the network connected, and the higher the criticality of a node is, the greater possibility to become critical node it owns. In order to decrease the risk of data loss, for the mobile charger, it is vital to charge as many high criticality nodes include critical nodes as possible before their batteries are depleted. To realize this, there is a question needed to be answered: How to quantify the criticality of nodes that the mobile charger can be scheduled to charge them effectively? Betweenness centrality metric [12] is one of most commonly used direct measurement to characterize the criticality of nodes, by estimating the node's contribution to the shortest routing paths construction. A node that participates in most of the shortest path is considered to be the highest criticality node. Since the betweenness centrality is computed by counting all of the paths through each node in the network, its computation is too costly to be adopted in the large network. Besides, the betweenness centrality of an edge node in the network is zero, which can't determine the source node's contribution. In the existing studies [13; 14], to schedule the mobile charger, the node's energy consumption rate is used as an indirect measurement of the node's criticality. However, it is hard to accurately estimate node's energy consumption rate in the practical WSN. Unlike previous metrics, a simple metric named criticality index is introduced in our work to quantify the criticality of nodes.