## 4 Proposed Algorithm
### Cluster Head Selection
Due to different energy requirements, cluster heads that are far away from the base station tend to lose energy at a much faster rate than cluster heads that are close to the base station. As a result, after a few rounds of communication with the base station, the network is left with only nearby cluster heads that are communicating with the base station and are responsible for increasing the network lifetime. The simulation results validate this, and is shown in Figure 17.

Based on the distance from the BS and the initial energy known, the lifetime of the nodes closer to the BS and the farthest nodes in terms of number of rounds can be calculated. Furthermore, in accordance with Lemma 2, the ratio of high energy nodes to be deployed as the distance from the BS increases has been determined, and the results are presented in Figure 18, which presents data from distant clusters for the majority of the network lifetime. Compared to the result of uniform distribution of high energy nodes as shown in Figure 17, the induction of high energy nodes in an increasing manner shows promising results, and the base station is able to receive data from a larger area rather than only from the nearby region, as shown in Figure 18, for a prolonged period of time. This assists in making practical decisions that are much more reliable than decisions made solely on the basis of nearby region cluster heads. The simulation results depicted in Figure 19, also shows that the proposed FEHCA, with the help of controlled energy dissipation variations due to (a) optimal number of cluster selection, (b) better positioning of cluster heads and (c) energy conservation by

Figure 17: Placement of alive nodes when the count is less than 10 with uniform distribution of high energy nodes. Figure 9:0 Placement of alive nodes when the count is less than 10 with incremental distribution of high energy nodes. delaying the new cluster head election procedure in the case of CH failures, helped in almost doubling the performance as compared to LEACH for the same parameters. As shown in Figure 19, the proposed algorithm has been tested with high energy nodes that are uniformly distributed (FEHCA: H_energy_UD) and incrementally distributed (FEHCA: H_energy_ID). When comparing FEHCA and its variants to LEACH, Figure 20 shows the energy consumption variations per transmission, which are again minimised in the case of FEHCA and its variants. ## 6 Conclusions

Energy conservation and fault tolerance are two major aspects when it comes to wireless sensor networks. This paper presents a centralised clustering mechanism with an energy-efficient data dissemination scheme that can cope with a certain number of faulty cluster heads. We simulated the proposed Fault-tolerant Energy-efficient Hierarchical Clustering Algorithm (FEHCA) for the scenarios with the base station inside as well as outside the monitored area and found the results encouraging. The energy consumption per transmission was much better as compared to LEACH. The proposed FEHCA demonstrated, on average, a 70 percent increase in network performance in terms of the number of rounds as compared to LEACH when the base station was positioned inside the deployment. FEHCA surpassed LEACH in keeping most of the nodes alive for the majority of the time, unlike many well-known proposed schemes with the proper energy management; in fact,

Figure 9:1 Performance of FEHCA and LEACH in terms of operational nodes per round when BS is positioned outside the deployment area. Figure 9:2 Energy dissipation per round in LEACH and FEHCA when BS is positioned outside the deployment area. FEHCA lasted for 50 percent more rounds than LEACH with more than 90 percent of nodes alive. The proposed algorithm was also compared with ESO-LEACH in terms of common parameters and it succeeded in keeping more than 90 percent of the nodes alive for more than 80 percent of the network lifetime, as compared to ESO-LEACH, where almost 50% of the network was down within approximately 40% of the network lifetime.