## 6 Test and Analysis of Results  
We conducted simulation experiments using Python to verify the effectiveness of the proposed method. Additionally, we compare the routing protocol proposed with the classical routing protocols LEACH, E-LEACH, and EEUC under identical conditions. In our experiments, we randomly deploy 200 sensor nodes within a 600 m \(\times\) 30 m monitoring area, with the sink node located at the center of the left edge of the region. To validate the robustness and reliability of the method, we set up two scenarios for the experiment: in Scene I, the sink is located at \((0,15)\), and in Scene II, the sink is located at \((650,15)\). The results in both scenarios are similar, so we use Scene I as an example for the explanation. Table 2 provides detailed parameter settings for the experiments. After the topology discovery phase, the network enters the clustering stage. Figure 9 presents the flowchart of nodes participating in the cluster head competition by using the timing Formula (12). When the timer starts, nodes will enter the receiving state. If they receive a broadcast from other nodes becoming cluster heads before the timer ends, they will decide whether to join the cluster based on whether those nodes are their neighboring nodes. If no broadcasts are received by the end of the timer, the node will send out a broadcast to become a cluster head. \begin{table}
\begin{tabular}{c c} \hline \hline
**Mark** & **Describe** \\ \hline \(CH_{i}\) & ID of the cluster head \(i\) \\ \(d_{sink}(CH_{i})\) & Distance from the cluster head to sink \\ \(E_{R}(CH_{i})\) & Residual energy of the cluster head \\ \(PreCH(CH_{i})\) & Number of load cluster heads of the cluster head \\ \(NextCH(CH_{i})\) & Candidate cluster heads of the cluster head \\ \(select(CH_{i},CH_{j})\) & Selection value of candidate cluster head of the cluster head \\ \(Nexthop(CH_{i})\) & Next hop nodes of the cluster head \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Cluster head information. Figure 9: Clustering through the timing mechanism. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Node distribution \((W\times H)\) & 600 m \(\times\) 30 m \\ Sink node coordinates & (0, 15)/(650, 15) \\ The total number of network nodes \(n\) & 200 \\ Distance threshold \(d_{0}\) & 87 m \\ Packet length & 2000 bit \\ Packet length for control & 100 bit \\ The maximum communication radius \(R_{max}\) & 70 m \\ The initial energy of nodes \(E_{0}\) & 0.3 J \\ Timing coefficient & \(0.5+0.1+0.4=1\) \\ Time adjustment factor \(k\) & 0.95 \\ Circuit consumes energy coefficient \(E_{ec}\) & \(5.0\times 10^{-8}\) J/bit \\ Data fusion energy Ech.C & \(5.0\times 10^{-9}\) J/bit \\ Energy coefficient of channel & \(\varepsilon_{fs}\): \(1.0\times 10^{-11}\) J/bit \\ propagation model & \(\varepsilon_{amp}\): \(1.3\times 10^{-15}\) J/bit \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental parameter settings. In the cluster head election process, we set each node's timer duration \(T(N_{i})\) according to Formula (12). In this equation, the timer duration \(T(N_{i})\) is influenced by the node's remaining energy, node degree, and the distance to the sink, where \(\alpha\), \(\beta\), and \(\gamma\) represent their respective impact coefficients on \(T(N_{i})\). The more residual energy the nodes have, the higher node degrees the nodes have, the greater the competition radius is, the shorter the set time is, it is more likely to become a cluster head. Timing began, and some nodes successively became cluster heads. In the early stages of the network's operation, the energy levels between nodes are relatively balanced, and the timer duration is mainly determined by the distance from the node to the sink. After the network has been operating for a while, the nodes consume some energy, leading to an uneven energy distribution. At this point, the energy coefficient \(\alpha\) is dominant.