## 5 Simulation and Results  
In this section, the performance of the proposed protocol is evaluated in both of its aspects: the static scenario (EDMR-S) and the dynamic scenario (EDMR-D). The experimental results are compared with those achieved using the DMR protocol. The comparison is further extended to include the EDMHT-LEACH and the LEACH protocols. To verify the effectiveness of the proposed protocol, a number of experiments were performed using MATLAB R2023a. These experiments were conducted in different deployment areas to simulate various scenarios typically faced in WSN environments. The sensor nodes were stationary and randomly distributed across the deployment region, whereas the BS was placed outside this area (Figure 9). In the first experiment, 200 sensor nodes were randomly scattered across three deployment areas, while the BS was positioned at the coordinates (150, 480). Table 2 contains a list of common parameters used in the assessment of these protocols, whereas the elementary components of the first experiment are presented in Table 3.  
Figure 8: Updated case of the dynamic sleeping scenario shown in Figure 7.  
Figure 9: The experimental deployment region. Figure 10 demonstrates the network lifetime, measured in rounds, of the EDMR-S and the EDMR-D protocols compared with the other protocols. Generally, the simulation results showed that the network lifetime was extended across all deployment areas through the use of the proposed protocols. For example, in the (350 \(\times\) 350) m\({}^{2}\) deployment area, the EDMR-S protocol attained a maximum number of rounds (2230 rounds), while the EDMR-D protocol achieved 1945 rounds. In comparison, the DMR protocol reached only 1671 rounds. As a result, the proposed sleeping mechanism led to remarkable results in the network lifetime compared with the DMR protocol. Similar results were observed in the other two deployment areas. Furthermore, it was noted that the EDMR-S protocol showed a relative advantage over the EDMR-D protocol. This advantage is attributed to the static sleeping mechanism applied in the EDMR-S protocol, which effectively reduced energy consumption by deactivating unnecessary clusters for the remainder of the round. Notably, in the 350 \(\times\) 350 m\({}^{2}\) deployment area, the vertical distance between the node deployment region and the BS is shorter than in the other experimental regions. This proximity minimizes the average transmission distance, which in turn lowers energy consumption and contributes to extending the network lifetime. The second experiment focused on studying the effect of the number of sensor nodes on the network lifetime. The deployment area (350 \(\times\) 350) m\({}^{2}\) was selected; the BS was placed at (150, 480), whereas the number of nodes was varied. Table 4 contains the parameters of the second experiment. Figure 11 shows the impact of varying the number of nodes on the network lifetime. It was observed that the EDMR-S and the EDMR-D protocols outperformed all other protocols for different numbers of nodes used in the experiment. For instance, when 300 sensor nodes were used, the EDMR-S protocol recorded 2327 rounds, the EDMR-D protocol reached 2162 rounds, while the DMR, EDMHT, and LEACH protocols attained 1815, 936, and 236 rounds, respectively. As the number of nodes decreased in the \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Values** \\ \hline BS coordinates (X1, \(Y1\)) & (150 m, 480 m) \\ \hline Initial energy (\(Eo\)) & 0.5 \\ \hline The percentage of CH (\(p\)) & 0.2 \\ \hline \(E_{dac}\) & 50 nJ/bit \\ \hline \(\varepsilon_{fs}\) & 10 pJ/bit/m\({}^{2}\) \\ \hline \(T_{min}\) & 0.03 \\ \hline Relative weight (\(\alpha\)) & 100 \\ \hline Data aggregated energy (\(E_{DA}\)) & 5 nJ/bit \\ \hline \(\varepsilon_{mp}\) & 0.0013 pJ/bit/m\({}^{4}\) \\ \hline TH & 0.03 \\ \hline Data packet size & 6400 bit \\ \hline Control packet size & 200 bit \\ \hline \end{tabular}
\end{table} 
Table 2: Standard simulation parameters.