## 6 Performance Evaluation
### Evaluation with Different Parameters  
To evaluate the influence of \(\varphi_{0}\), \(\beta_{1}\) and \(\beta_{2}\), we simulate the variance of residual energy and the average latency of each packet as these values change. \(\beta_{1}\) and \(\beta_{2}\) are the weights of the sum of delay-related cost and energy-related cost for successful and failed transmission respectively. \(\varphi_{ij}\) is the delay sensitivity. \(\varphi_{0}\) is the coefficient to modify \(\varphi_{ij}\). Higher \(\beta_{1}\) and \(\beta_{2}\) can distribute energy more evenly because the residual energy is more important in routing decision. Higher \(\varphi_{0}\) means delay is more important so that the detouring routing is restricted.  
In the simulation, \(\varphi_{0}\), \(\beta_{1}\) and \(\beta_{2}\) vary between 0.1 and 0.9 with a step of 0.2. Comparing the variance of residual energy in Figure 3 with varying parameters, we can conclude that with larger \(\beta_{1}\), \(\beta_{2}\) and smaller \(\varphi_{0}\), the residual energy distributes more uniformly. When \(\beta_{1}=\beta_{2}=0.9\) and \(\varphi_{0}=0.1\), the residual energy variance is about 18, less than 1/3 of that with \(\beta_{1}=\beta_{2}=0.1\) and \(\varphi_{0}=0.9\). That is to say less nodes will drain the energy early. Thus, the network lifetime can be prolonged.  
However, as shown in Figure 4, the end-to-end delay is increased. When \(\beta_{1}=\beta_{2}=0.9\), \(\varphi_{0}=0.1\), the delay is 42 s, about 25% longer than that with \(\beta_{1}=\beta_{2}=0.1\), \(\varphi_{0}=0.9\). This is because that the path detours to avoid nodes close to the sink node but with relatively lower energy. On one hand, higher \(\beta_{1}\) and \(\beta_{2}\) mean higher weight of the energy-related cost. Nodes with more residual energy cost less to communicate. Therefore, they are more favorable to packet forwarding, making the variance of residual energy lower. On the other hand, as \(0<\varphi_{0}<1\), \(\varphi_{0}\) indicates that the sink node attaches less importance to delay during the routing decision. Although a node is far away from the sink node, it  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Values** \\ \hline Transmission power & 10 W \\ Receiving power & 3 W \\ Idle power & 30 mW \\ Data packet size & 300 B \\ Transmission rate & 3 kbps \\ Transmission range & 500 m \\ Preamble signal length & 0.49 s \\ Simulation time & \(10^{4}\) s \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation parameters.  
Figure 3: Variance of the residual energy with different values of \(\varphi_{0}\), \(\beta_{1}\) and \(\beta_{2}\).  
can be the next hop as long as the residual energy is high enough. As a result, detour routing with more residual energy and longer latency is chosen as the routing path. Furthermore, as \(\varphi_{0}\) increases, the rates of the incremental variance and decreasing average latency reduce. The reason is that, when \(\varphi_{0}\) increases to a certain degree, the sink node determines routing path with the lowest latency thereafter, paying little attention to the residual energy. However, when \(\varphi_{0}\) is too small, the average latency increases significantly because of the detour routing. Thus, \(\varphi_{0}\) can not increase or decrease infinitely. In the following evaluation, we set \(\varphi_{0}\) to 0.3, 0.5 and 0.7 respectively and set \(\beta_{1}\), \(\beta_{2}\) to 0.7.