# Joint Energy Supply and Routing Path Selection for
## 4 Simulation Results and Analysis
### The Impact of Fusion Index on Network Performances  
This section examines the impact of the fusion index on network performances by setting the network size to 100 and the harmonic coefficient to 0.4 and keeping them constant. Figures 2-4 are the graphs of network lifetime, average hops and average energy consumption under varying fusion index and different charging durations \(T_{c}\), respectively, where \(T_{c}=0\) indicates that the network is not charged. From the simulation results in Figure 2, the charging strategy presented in this paper significantly prolongs the network lifetime compared to the method of not using wireless charging for nodes, and in the late period of network, as the \(\partial\) decreases, WCD charges nodes with low remaining energy more and more, that is, the closer the node to death, the more energy the node gets, so the effect of delaying node energy attenuation is more obvious, which further increases the network lifetime. For example, when the charging duration \(T_{c}\) is 5, if the fusion index \(\partial\) decreases from 15 to 1, the network lifetime increases by about 177%. In addition, it can be found that the impact of fusion index \(\partial\) on the network lifetime is different. This is because the charge duration \(T_{c}\) determines the total amount of energy that the network can obtain after one round of charging when the WCD's charging rate has been determined, i.e., the size of the energy supply capacity, and the fusion index \(\partial\) is able to concentrate energy and give priority to rapidly consuming nodes. However, when the charging duration is 1, the WCD's supply capacity is so small that the energy gain of the node is very limited. Therefore, the decrease of the fusion index only makes the network lifetime slightly increase, which cannot achieve the fundamental change. But with the increase of \(T_{c}\), the energy of WCD is relatively high, and the fusion index is more and more effective in optimizing the distribution of energy, accordingly, the network survival time is also longer. Figure 3 shows the variation of average hops with the fusion index \(\partial\). It can be seen that as the fusion index \(\partial\) decreases, the limited energy can be more rationally distributed, and the node energy loss caused by data transmission can be replenished by WCD in time. Thus, in order to transmit the data packet to the sink node at a faster speed, the node will strive to maximize the single-hop forward distance so that the average hops of the network gradually decrease to ensure a tolerable network delay. Of course, we can see that with the increasing of fusion index, the growth rate of average hops is gradually decreasing and will eventually tend to be flat, because this paper not only considers the nodal energy, but also integrates the transmission energy consumption. Therefore, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Definition** & **Notation** & **Value** \\ \hline Simulation area & \(S\) & \(100\times 100\) m\({}^{2}\) \\ \hline Network size & \(n\) & \(100\sim 300\) \\ Nodal original energy & \(E_{0}\) & 0.5 J \\ \hline Maximum communication range & \(R\) & 30 m \\ Data rate & \(r\) & 8000 bit/h \\ \hline Buffer size & \(BF\) & 20 packets \\ \hline Sink & \((sink.x,sink.y)\) & \((50\) m, 50 m) \\ \hline Charging rate & \(\Lambda_{c}\eta\) & 0.0045 J/h \\ Charging duration & \(T_{c}\) & 0 \(\sim 5\) h \\ Fusion index & \(\partial\) & 1 \(\sim 62\) \\ Harmonic coefficient & \(\alpha\) & 0.1 \(\sim 0.9\) \\ Flight velocity of mobile charger & \(v_{m}\) & 30 m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Parameters. From Figure 4, the charging obviously slows down the energy consumption rate of each node, moreover, it can be found that Figures 3 and 4 have similar trends, because the average energy consumption refers to the sum of average energy consumption of all sensor nodes in each data transmission cycle over a period of time.