# Joint Energy Supply and Routing Path Selection for
## 4 Simulation Results and Analysis
As a major part of the nodal energy consumption, the transmission energy consumption in this paper is positively correlated with the square of the single-hop distance, and the average hops is inversely related to the single-hop distance in the case of the same network deployment. Therefore, when the number of nodes is constant, as the fusion index \(\partial\) increases or decreases, the average hops presents a variation trend in Figure 3, at the same time, a similar trend in the average energy consumption with varying fusion index is found in Figure 4.  
### The Impact of Fusion Index on Network Performances  
In order to explore the effect of harmonic coefficient \(\alpha\) under different charging durations, we vary the value of \(\alpha\) from 0.1 to 0.9 with a fixed step length, and set the fusion index to 1 and the network size to 100. The simulation results are shown in Figures 5-7. As shown in Figure 5, the network lifetime increases slightly with the increase of \(\alpha\) in [0.1, 0.4], but drops sharply with the increase of \(\alpha\) in [0.4, 0.9]. This is because we take into account the transmission energy consumption from node \(i\) to node \(j\), the forward energy consumption of node \(j\) and the estimated residual energy of both nodes, and the harmonic coefficient determines the degree of influence of the above factors on the next-hop node selection process. When the value of \(\alpha\) is in [0.1, 0.4], with the increase of the harmonic coefficient, the selection of the next-hop node \(j\) is more and more focused on the state of node \(i\) itself, seeking the least transmission energy consumption and the largest estimated residual energy of node \(i\), at this point, the forward distance of next-hop node may increases, but from Figure 7, it can be seen that the average energy consumption increases but the magnitude is not large when the charging duration is 1, basically unchanged or even reduced when the charge duration is 2-5, so the network lifetime can be extended. When the value of \(\alpha\) is in [0.4, 0.9], as the harmonic coefficient continues to increase, the state of node \(j\) is excessively ignored when selecting the next-hop node \(j\). As a result, the hop count of node \(i\) to sink increases greatly, resulting in greater energy consumption and making the network lifetime gradually reduced. Figures 6 and 7 show the variation of the average hops and the average energy consumption with different harmonic coefficients. Same as the Section 4.1, these two figures share a similar trend. Obviously, compared to the case of non-charging, charging the network allows the nodes to have enough energy and select the next-hop node with farther transmission distance, which can send data back to the base station as soon as possible, so there are less average hops after executing the charging  
Figure 5: Network lifetime with varying harmonic coefficient. strategy. Moreover, energy replenishment from the WCD results in less energy depletion per round, greatly extending the network lifetime. In addition, it can be observed that the average hops and the average energy consumption increase with the increase of the harmonic coefficient when the charging duration is 0 (i.e., no charging occurs). This is reasonable as the fact that the value of the harmonic coefficient characterizes the importance of node \(i\) in routing selection at some extent. When \(\alpha\) is increased, the forward distance of the next-hop node becomes larger and the average hops increases naturally. At the same time, nodes closer to the sink usually consume more energy, so the average energy consumption increases accordingly. When the charging duration is 2-5 and the harmonic coefficient belongs to [0.1, 0.4], the average hops increases slightly with the increasing of harmonic coefficient.