# Joint Energy Supply and Routing Path Selection for
## 4 Simulation Results and Analysis
### The Impact of Charging Duration on Network Performances  
In this section, for purpose of studying the impact of charging duration \(T_{c}\) more intuitively, we present Figures 8-10 which are different visualisations of the data in Figures 5-7. Figure 8 shows the network lifetime with varying charging duration under different harmonic coefficients. There is no doubt that the survival time of network will increase accordingly when we extend the total charging time. However, just like what has been presented in these three figures, the network lifetime with varying charging duration has different tendencies when the harmonic coefficient is in [0.1, 0.4] and [0.5, 0.9], and the best performance exists when it is 0.1. This is because, as it has been pointed out above, the minimum energy consumption routing is detrimental to the network performances. Besides, as it grows, metrics are increasingly biased towards energy consumption, so there is a trade-off between how we value the harmonic coefficient.  
As it can be seen from Figure 9, the average hops decrease with the increase of the charging duration, thereinto, the average hops decrease significantly when the charging duration \(T_{c}\) is in [0, 2],  
Figure 8: Average hops with varying charging duration.  
Figure 9: Average hops with varying charging duration.  
but the trend of decreasing is getting smaller and smaller when \(T_{c}\) is in [2; 5]. This is because when the network is replenished with energy, the more the charging duration is, the more energy the sensor nodes can obtain. After getting enough energy replenishment, the routing can consider a forward distance of the next-hop node as small as possible, so the average hops decrease with the increase of the charging duration. However, since the maximum communication radius is \(d_{0}\), the effect that the average hops decreases with the allowable communication range is obvious, but when \(T_{c}\) continues to increase, constrained by the communication range and other routing decision factors, it is impossible for node \(i\) to pursue the single hop furthest indefinitely, and eventually the average hops change slowly.  
Figure 10 shows the effect of charging duration under different harmonic coefficients on the average energy consumption of the network, whose trend is very similar to Figure 9. Compared with the charge duration of 0, the decay rate of the network energy has been greatly improved due to the energy supplement of WCD. However, same as the Figure 9, the average energy consumption decreases with the increasing of the charging duration and the amplitude is not consistent. Specifically, on the one hand, it is related to the average hops, on the other hand, the limited energy supply capacity of WCD also plays an important role. In the early stage of network operation, the nodal energy loss is not serious, and the charging scheme can reduce the attenuation of the network energy well, but as the working time continues, more and more nodes lack energy, then the limited energy supply capacity can play a smaller role, and cannot significantly reduce the average energy consumption.