## 3 The Clustering Protocol
### Node Dormancy Mechanism
To get the optimal routing factor \(\alpha\), we conduct related simulations, including \(\alpha\) is taken from 9 numbers between 0.1 and 0.9 and the \begin{table}
\begin{tabular}{l c} \hline \hline  & **Parameter** & **Value** \\ \hline \(E_{elc}\) & 50 nJ/bit \\ \(E_{DA}\) & 5 nJ/bit/message \\ \(\varepsilon_{\beta}\) & 10 pJ/bit/m\({}^{2}\) \\ \(\varepsilon_{amp}\) & 0.0013 pJ/bit/m\({}^{4}\) \\ The diameter of monitoring area, \(M\) & 200 m \\ Initial number of nodes, \(N\) & 100 \\ Size of message, \(e\) & 4000 bits \\ Initial energy & 0.4–0.8 J \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 8: Node dormancy diagram of a cluster. #### 4.1.3 The Optimal Routing Factor

Although the network has the longest lifetime in the case of \(\alpha=0.1\) compared with other cases, its first node death time is too early, which means that the energy consumption distribution of the nodes is rather uneven in this case. In homogeneous networks, the first node's death round in the case of \(\alpha=0.2\) is 1018, it is too small. Although the first node's death rounds in the case of \(\alpha=0.4\)-0.9 are very close, the last node's death round in the case of \(\alpha=0.4\) is the largest among them. The first node's death round in the case of \(\alpha=0.3\) is less than that in the case of \(\alpha=0.4\), but the last node's death round in the case of \(\alpha=0.3\) is more than that in the case of \(\alpha=0.4\). Thus, the optimal routing factor \(\alpha\) in homogeneous networks is 0.3 or 0.4. In heterogeneous networks, the first node's death rounds in the case of \(\alpha=0.2\)-0.9 are very close, but the last node's death rounds in the case of \(\alpha=0.2\) and 0.3 are both the largest among them. Thus, the optimal routing factor \(\alpha\) in heterogeneous networks is 0.2 or 0.3. In summary, we can determine the optimal routing factor (\(\alpha=0.3\)) in the protocol. ### Comparison of the Death Round of the First Node

In WSNs, network performance tends to decline with the nodes' death, and the network is in a stable period before the first node dies. The death of the first node indicates that the network enters an unstable period and its performance starts to decline. The clustering protocol in this paper balances the energy consumption of the network by cyclically selecting the CHs and considers the remaining energy and location of the node in the process of the CHs selection. Figure 13 shows that in the homogeneous networks (0.4 J and 0.8 J), the round of the first node's death in the three protocols LEACH, SEP, and DEEC is not substantially different. In comparison, our protocol has an advantage in delaying the round of the first node's death. In the heterogeneous networks (0.4-0.8 J), our protocol can still maintain good performance in this respect. At this time, the DEEC performance is the best among the other three protocols, the LEACH performance is second, and the SEP performance is poor. It is not difficult to understand that in heterogeneous networks, the energy gap between nodes is large. But regardless of the energy of the nodes in the network, the same probability that LEACH gives these nodes is elected as the CH. SEP only considers the initial energy of the node that will cause the high-energy node to have less energy but maintain a high probability of being selected as the CH after multiple rounds of iterations, so that it increases the death

Figure 12: The network lifetime comparison in heterogeneous networks (routing factor = 0.2, 0.4, 0.6 and 0.8). rate of the node and causes the first node to die the earliest. DEEC comprehensively analyzes the initial energy and residual energy of the node, which can ensure the probability that the node with high initial energy is elected as the CH can be lowered after multiple rounds of data iterations, so that other nodes with high remaining energy have higher probability to be elected as the CH.