# An Equilibrium Strategy-Based Routing Optimization Algorithm for Wireless Sensor Networks
## 4 Simulation Results and Analysis
### The Impact of Parameter \(\beta\) on Network Performance  
In order to compare the influence of different parameters on the algorithm itself, in the simulation, we value the \(\beta\) under different network sizes, and the interval and step size are [0, 1] and 0.2 respectively.  
(1) Impact of parameter \(\beta\) on average hops under different network sizes  
It can be seen from Figure 3 that, under the same network size, when the parameter \(\beta\) increases from 0 to 0.6, the average hops gradually decreases. This is because as \(\beta\) increases, the forward energy consumption of node \(j\) has an increasing influence on the selection of the next hop, that is, the source node will focus on selecting the forward neighbor node closer to the sink as next hop, thus the number of path hops is gradually reduced. When \(\beta\) is in [0.6, 1], the path hops tend to be stable as \(\beta\) increases further. In addition, when \(\beta\) remains the same, as the network size expands, the node distribution becomes denser, so that the average hops increases continuously.  
(2) Impact of parameter \(\beta\) on average energy consumption under different network sizes  
As shown in Figure 4, when \(\beta\) is the same, as the network size increases, the average hops increases gradually (Figure 3), so the energy consumed on the path increases, resulting in the increasing of the average energy consumption of the entire network. When the network size remains the same and \(\beta\) increases in [0, 0.6], the average energy consumption gradually decreases. This is because as \(\beta\) increases, on the one hand, the hops have an increasing influence on the link cost in Equation (4). On the other hand, as shown in Figure 3, the average hops gradually decreases in [0, 0.6]. Thus, the overall energy consumption of the network will gradually decrease. When \(\beta\) is in the range of [0.6, 1], the average hops basically remains the same, but since the selection of the next hop neglects the influence of single-hop energy consumption, the average network energy consumption has a slowly increase in this range.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Definition** & **Value** \\ \hline Simulation area & 100 \(\times\) 100 m\({}^{2}\) \\ Network size & 150–300 \\ Maximum communication range & 30 m \\ Packets size & 1024 bits \\ Buffer size & 20 packets \\ Sink & (50, 50) \\ Data generation rate & 1024 bits/round \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation Parameters.  
(3) Impact of parameter \(\beta\) on packets loss rate under different network sizes  
Figure 5 shows the trend of packet loss rate PLR with parameter \(\beta\) at different network sizes. When the network size is the same, the packet loss rate decreases as \(\beta\) increases in [0, 0.4], this is because the value of \(\beta\) is small at this time, and the hops do not dominate the selection of the path.  
Meanwhile, after using the edge-cutting strategy, the load of each node in the minimum routing graph is balanced, thereby reducing the packet loss rate of the node. However, as \(\beta\) continues to increase, the node near the sink will be the priority node, that is, the path with less hops is selected to forward the data as much as possible, which will cause the nodes close to the sink to be over-selected and exceed the their capacity, resulting in packet loss. Then, the packet loss rate will increase slightly and tend to be stable. When \(\beta\) remains the same, as the network size \(N\) increases, the forward neighbor nodes in the inner layer gradually increase. By utilizing the edge-cutting strategy, excess load will be shared to other nodes with fewer loads in advance, thus effectively reducing the packet loss rate.  
Figure 4: AEC varying with \(\beta\) at different network sizes.  
Figure 3: AH varying with \(\beta\) at different network sizes.