# Adaptive Energy Balanced Routing Strategy for Wireless Reschargeable Sensor Networks
## 4 Routing Strategy  
In WRSN, nodes transmit information to sink nodes in the form of multi-hop, during which the WCV provides energy for them. The charging process will change the energy state of nodes, which greatly influences their next hop selection. When the source node \(i\) selects the node close to it as the next hop, it is beneficial to avoid the node \(i\) consuming too fast. However, the choice may cause a long transmission chain from the source node to sink node, increasing the total energy consumption on the chain. Similarly, if the node \(i\) selects the node closer to the sink node, its own energy consumption will increase, but other network performance indicators may be optimized, such as reducing the hop count and total energy consumption. Meanwhile, as shown by Equation (8), nodes that consume energy quickly tend to obtain more charging time. For nodes with high charging efficiency, more charging time means more charging energy; thus, appropriately increasing the energy consumption speed of those nodes is beneficial to utilize the charging energy effectively. Additionally, for nodes with low charging efficiency, the energy they obtained in charging part may not be able to compensate for their energy loss in the routing process. For a long run of high consumption in routing, they will gradually decline residual energy until death. Therefore, the routing strategy needs to be adjusted according to the impact of the charging process. Different routes should be selected based on nodes' residual energy and charging characteristic. For nodes with high charging efficiency, the energy consumption rate can be increased appropriately to improve the network performance. For nodes with low residual energy and low charging efficiency, the energy consumption should be reduced to prolong their lifetime. Based on this, this section proposes a routing strategy adaptive to the node charging characteristics,  
Figure 2: Schematic diagram of charging points location. which takes the energy of node \(i,j\) and the relevant charging characteristics as the deciding factors of the routing cost \(U(i,j)\). In this strategy, \(U(i,j)\) can be calculated as:  
\[U(i,j)=\alpha_{i}\frac{C_{ij}}{\hat{E}_{i}}+(1-\alpha_{i})\frac{C_{js}}{\hat{E}_ {j}},j\in NF(i) \tag{9}\]  
where \(\hat{E}_{i}\), \(\hat{E}_{j}\) are the energy of node \(i\), \(j\) after being charged, \(C_{ij}\) is the energy consumption of node \(i\) sending unit data packet to node \(j\), and \(C_{js}\) is the forward energy consumption of node \(j\). Considering from the perspective of node \(i\), \(C_{ij}\) is smaller when node \(j\) closer to node \(i\) is selected, which is beneficial to extend the life of node \(i\). However, the forward energy consumption will be larger for node \(j\). From the point of view of the next hop node \(j\), when node \(j\) is closer to sink node, the forward energy consumption will be smaller. It is conducive to prolong the lifetime of node \(j\). However, the long transmission distance from node \(i\) to node \(j\) will increase the energy consumption of node \(i\). Therefore, the selection of the next hop node needs to adjust the two parts to achieve a balance, reducing the total energy consumption and optimizing the network performance indicators. In WRSN, the node energy is obtained by the joint influence of node energy consumption stage and charging stage. From the previous analysis, the charging energy obtained by nodes with the same distance to the charging path can be adjusted to a basic balance by charging strategy; however, the charging efficiency of the nodes closer to the charging path is still higher than that of the nodes away from the charging path, so that more energy can be obtained by those nodes in the same charging time. For convenience of description, \(\alpha_{i}\) is used to characterize how much energy node \(i\) gets in a certain charging time.