## 4 Simulations and Results  
The simulations assume that 10 percent of sensor nodes are super nodes, which have twice the energy of normal nodes, and 20 percent of sensor nodes are advanced nodes, which have 1.5 times the energy of normal nodes. In practice, the communication range of sensors is 20-30 m. So, the experiment randomly deployed 100 nodes in a square area of 100 \(\times\) 100 square meters to simulate the actual scene. The sink node is located at the center of the sensing area. We use '+' for the super node, '\(\diamond\)' for the advanced node, 'o' for the normal node, and '\(\times\)' for the base station. The network model of this experiment is shown in Figure 2a. The optimal probability of each node to become a cluster head is set as 0.1. The initialized energy of the normal node is 0.5 Joules, the initialized energy of the advanced node is 0.75 Joules, and the initialized energy of the super node is 1 Joule. This proposed protocol is simulated using MATLAB. The parameters of the simulations appear in Table 1.  
Figure 2b shows the number of live nodes in each round of the network. It can be seen from Figure 2b that the nodes start to die at 1200 rounds when using SEP, M-SEP, and TSEP, but they start to die at 1400 rounds when using the proposed method. The nodes completely died at 1800 rounds, 2000 rounds, and 2500 rounds, respectively, when using SEP, M-SEP, and TSEP. However, at 2500 rounds, there still are about 40 surviving nodes for the proposed method. Therefore, this proves that the proposed method prolongs the network's lifetime.  
Figure 3a shows the residual energy of all nodes for SEP, M-SEP, TSEP and the proposed method. From Figure 3a, we can see that the residual energy decreases with the increasing of rounds for all methods, but the proposed method has more residual energy than the others. The residual energy of the super nodes, advanced nodes, and normal nodes are shown in Figure 3b. From Figure 3b, we can see that the speed of residual energy decreases faster for super nodes as compared with the others. This shows that the super node has a high probability of being elected as the cluster head. Therefore, in the initial stage and data transmission stage, the super node consumes more energy than the advanced node. The super nodes have more energy than the others, and they also consume more  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameters** & _do_ & \(\varepsilon_{fs}\) & \(\varepsilon_{mp}\) & \(E_{dec}\) & \(E_{DA}\) & \(l\) \\ \hline
**Values** & 87 m & 10 pJ/bit/m\({}^{2}\) & 0.0013 pJ/bit/m\({}^{4}\) & 50 nJ/bit & 5 nJ/bit & 4000 bit \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation Parameters.  
Figure 2: (a) Network model; (b) The number of alive nodes. ITSEP: Improved Threshold-Sensitive Stable Election protocol; TSEP: Threshold-Sensitive Stable Election Protocol; SEP: Stable Election Protocol; MSEP: Modified Stable Election Protocol.  
energy. This balances the energy consumption of all the nodes in the network and also prolongs the network's lifetime.  
Figure 4 displays the number of packets sent to the base station from the cluster heads with respect to the number of rounds. If there is a higher number of surviving nodes, there will be a higher number of selected cluster heads, resulting in a longer network lifetime. With the increase of the network's lifetime, the number of packets received by the base station also increases correspondingly. From Figure 4, we can see that the number of packets for the proposed method is more than that of the other methods, and its network lifetime is also longer than that of the other methods.