## 4 Proposed Algorithm
### Cluster Head Selection
Furthermore, we discovered that, similar to LEACH, most of the nodes in FEHCA were operational for the majority of the time, as shown in Figure 9, whereas this is not the case in many proposed algorithms [36], where the nodes' batteries start to become depleted immediately, as shown in Table 2b; after a certain number of communication rounds, this forces a decision to be made on the data received from limited regions only. Furthermore, FEHCA lasted 50 percent longer than LEACH, with over 90% of nodes still alive. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**(a)**} & \multicolumn{2}{c}{**(b)**} \\ \hline \multirow{2}{*}{**No. of Rounds**} & **No. of Alive Nodes** & **No. of Alive Nodes** & **No. of Alive Nodes** & **No. of Alive Nodes** & **No. of Alive Nodes in** \\  & **in LEACH** & **in FEHCA** & **in FEHCA** & **in ESO- LEACH**[36] & **FEHCA:H_energy_UD** \\ \hline



\hline \end{tabular}
\end{table} 
Table 2: (**a**) Network lifetime comparison of LEACH and FEHCA; (**b**) network lifetime comparison of ESO-LEACH and FEHCA:H_energy_UD. Figure 9: Performance of FEHCA and LEACH in terms of operational nodes per round when base station is positioned inside the deployment area. The Fault-tolerant Energy-efficient Hierarchical Clustering Algorithm (FEHCA), similarly to LEACH, operates at nearly full strength for the majority of its lifespan, which is critical for reliable networks. It achieves minimum energy dissipation variation due to the determination of optimum number of cluster heads and then by focusing on cluster head placement at or near the centroids, as opposed to LEACH, which elects cluster heads at random. The fault-tolerant behaviour of cluster heads has been also demonstrated by FEHCA. In the event of a cluster head failure, secondary cluster heads (sCHs) take over the task. As shown in Figure 12, failed packet transmissions have been handled and re-transmitted. In addition, the paper compares FEHCA: H_energy_UD to ESO-LEACH [36] with the same parameters. FEHCA: H_energy_UD uniformly distributes high energy nodes with twice the energy of normal nodes (i.e., 1) initial energy) in each cluster. High energy nodes are contained in the set of N-normal nodes; thus, normal node count = N- high energy nodes. FEHCA: H_energy_UD, on average, keeps 90% of the network alive for more than 80% of the network life time, while ESO-LEACH keeps around 50% of the network alive for approximately 40% of the network life time, as shown in Table 2b. ### Experimental Evaluation for Scenario 2

In Scenario 2, the deployment area (x, y) is 100 m \(\times\) 100 m, 100 sensor nodes are randomly deployed and the base station is placed in position (50, 200), i.e., far away from the deployment area, as in hostile environments such as inaccessible border regions, wildlife monitoring, etc., as shown in Figure 13.

Figure 14 shows the clustered network after the optimal clusters have been determined, with the CHs chosen by the BS near or at the centroids. Each cluster communicates directly with the BS with the help of the elected CH, as depicted by Figure 15.

In Figure 16, a typical scenario involving the distance between the BS and the communicating CHs is illustrated, in which three CHs with 0.5 J of initial energy communicating directly with the BS are located at 117 m, 151 m and 185 m distances from the BS. When considering multipath propagation \(\varepsilon_{\mathrm{mp}}\), we can see that the CH furthest from the BS is functional for 80 rounds, while the CHs closer to the BS are able to communicate for 173

Figure 13: Random deployment of 100 sensor nodes in an area of 100 m \(\times\) 100 m with BS positioned outside the deployment area at position (50, 200). Figure 16: Effect of distance of cluster heads (CHs) from BS on the network lifespan. Figure 14: Network clustering using k-means algorithm. Figure 15: Depiction of network clusters along with respective centroids (each cluster communicates directly with the BS).