## 5 Results and Discussion  
The proposed algorithm aims to increase the heterogeneity of the clustering algorithms and extends the three-tier structure to a four-tier structure. There are two intermediate node structures proposed in this study. Additionally, the performance comparison of various energy-efficient clustering-based protocols has also been presented. The performance of the standard DEC and MDEC [5; 20] is compared with the proposed method of NR-MDEC protocol for the WSN application. The standard energy parameters, deployed for performance and node analysis in the simulation, are presented in Table 3.  
Figure 8: Algorithmic flowchart of proposed NR-MDEC protocol. The simulation results of comparisons between MDEC and DEC are presented in Figures 9-11. Figure 9 illustrates the performance comparison between DEC and MDEC protocols. Here, the \(x\)-axis denotes the number of rounds i.e., number of continuous steps of data transmission from nodes to base station, while the \(y\)-axis denotes the number of live nodes survived so far. In this simulation, 100 nodes were considered, and message transmission initiated. After nearly 1920 rounds, all the nodes of MDEC died; however, for DEC, this figure is 2068 rounds. This showed that, in this simulation, DEC's efficiency was slightly better than MDEC. A comparison of energy levels MDEC versus DEC is given in Figure 10. This graph compares DEC and MDEC based on energy levels after each iteration of data transmission. The \(x\)-axis represents the number of rounds and the \(y\)-axis represents the energy levels. The graph displays a slightly better energy performance by live MDEC nodes at the end of 100 rounds compared to live DEC nodes. It was found out that, when it comes to the rate of energy drain, MDEC outperforms DEC in the initial stage. This is one of the reasons this factor is utilized, and it balanced the network throughout the data transmission in WSN. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Description** & **Symbol** & **Value** \\ \hline Energy used by the amplifier for short-range transmission & \(E_{s}\) & 10 pJ/bit/m\({}^{2}\) \\ Energy consumed for long-distance transmission by the amplifier & \(E_{l}\) & 0.0013 pJ/bit/m\({}^{4}\) \\ The energy required to send or receive the signal in the electronics loop & \(E_{e}\) & 50 nJ/bit \\ Energy used for the formation of beams & \(E_{bf}\) & 5 nJ/bit \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Standard energy parameters used in the simulation. Figure 9: Performance of DEC vs. MDEC for 100 nodes. A comparison of residual energy levels of the nodes for MDEC versus DEC is given in Figure 11. The \(x\)-axis represents the number of rounds and the \(y\)-axis represents the residual energy. The graph displays a slightly better Residual energy performance by live MDEC nodes at the end of 2000 rounds compared to live DEC nodes. This also supports the facts of Figure 10, which was performed for 100 steps. It can be observed that MDEC gives slightly better energy levels while all the nodes are live and residual energy levels are slightly better with MDEC compared to DEC. Similarly, the simulation results of comparisons of dead nodes for different methods are presented in Figure 12.  
Figure 11: Comparison of residual energy of the nodes for standard DEC and MDEC protocol. Figure 10: Comparison of energy level for DEC and MDEC. In this figure, Blue, Green, and Red colored bars denote the number of rounds of DEC, MDEC, and NR-MDEC algorithms respectively. Precise values of the round number of First Node Dead (FND), Last Node Dead (LND), and 60% Dead are mentioned, and their graphical illustration is given. For DEC, the first node was dead after 1823 rounds, while 60% of all the nodes died after 1950 rounds. DEC completely shuts off at the end of 2068 rounds. For MDEC, the first node died after 1723 rounds, 60% of all the nodes died after 1880 rounds, and, after 1920 rounds, the network ran out of energy.