# Clustering for Lifetime Enhancement in Wireless Sensor Networks
## 4 Simulation Results
### Second Scenario: The Base Station (BS) Is Located at the Center of the Area (100, 100)  
In this scenario, we first replicate the tests from the initial scenario, where nodes either transmit data individually or are grouped into clusters of two or three. We then conduct additional tests, incorporating our study's findings on the relationship between distance from the base station (BS) and node performance. Specifically, individual transmission is more effective for nodes located less than 83 m from the BS, clusters of two nodes are better for nodes between 83 and 123 m from the BS, and clusters of three nodes are most effective for nodes between 123 and 149 m, which includes the area's diameter of 141 m, representing the maximum distance within the area. Figures 12-14 show the topologies for individual nodes, clusters of two nodes, and clusters of three nodes, respectively. Figure 12: Topology of the second scenario with individual nodes and BS at (100, 100). Figure 13: Topology of the second scenario with pair nodes and BS at (100, 100). The lifetime and throughput for these topologies are shown in Figures 15 and 16, respectively. Table 4 provides the values for the FDN, MDN, and LDN parameters. According to the results shown in Figures 9 and 10, a cluster with a density of 2 nodes is the most effective for prolonging lifetime, indicating better conservation of node energy. This is followed by the individual topology, then the Cluster-3 topology. However, in terms of throughput, the individual topology outperforms the others, followed by Cluster-2 and then Cluster-3. This is because individual nodes send packets to the base station more frequently than when they are part of pairs or trios. Figure 14: Topology of the second scenario with trio nodes and BS at (100, 100). Figure 15: Lifetime for individual nodes, Cluster-2, and Cluster-3 topologies with BS at (100, 100). Regarding the FDN, which defines the network's lifetime (Figures 15 and 16), Cluster-2 performs the best, lasting 477 rounds before the first node dies. This is followed by the individual topology with 302 rounds, and finally, Cluster-3 with 264 rounds. Note that there are other definitions of network lifetime, such as until the last node dies or until the application can no longer function. For MDN, the results show that Cluster-3 performs the best, followed by Cluster-2 with 1084 rounds, and then the individual-based topology with 1056 rounds. Finally, for LDN, both the Cluster-2 and individual topologies have the same value, lasting 2477 rounds, while the Cluster-3 topology achieves 2187 rounds. The conclusion drawn from the simulation highlights that different distances yield optimal efficiency for each topology. For distances less than 83 m, the individual node topology is more efficient. For distances between 83 and 123 m, the cluster with a density of two nodes performs better, and for distances between 123 and 141 m, the cluster with three nodes is more effective. However, the overall simulation results indicate that the Cluster-2 topology outperforms the others, followed by the individual node topology, with the Cluster-3 topology being the least effective. In the following simulations, we implement the findings from our study. First, we use a topology divided into two zones: nodes within 83 m transmit individually, while nodes farther than 83 m transmit in pairs. For the final topology, we divide the WSN into three zones: the first for nodes within 83 m, the second for nodes between 83 and 123 m, and the third for nodes beyond 123 m. \begin{table}
\begin{tabular}{c c c c} \hline
**Topology** & **FDN** & **MDN** & **LDN** \\ \hline Individual & 302 & 1056 & 2477 \\ \hline Cluster-2 & 477 & 1084 & 2477 \\ \hline Cluster-3 & 264 & 1121 & 2187 \\ \hline \end{tabular}
\end{table} 
Table 4: FDN, MDN, LDN for individual nodes, Cluster-2, and Cluster-3 topologies. Figure 16: Throughput for individual nodes, Cluster-2, and Cluster-3 topologies with BS at (100, 100). Figures 20 and 21 display the lifetime and throughput for these topologies.