## 8 Simulation
### Experimental Results
#### 8.2.3 Average Network Lifetime  
Several works define the network lifetime as the period from network initialization to the round when the last node dies [9; 46]. This parameter is important because it shows how long network nodes are able to run the protocol. Moreover, the early death of nodes can lead to a disconnection of some part of the network. Therefore, to evaluate the lifetime of the network, we considered the round at which the first node die (FND) and last node die (LND). Figure 15 shows the time at which the first node died according to different level of density. Typically, when the density increases, the connectivity among nodes increases, which reduces the CHs cardinality and balances the energy consumption among CMs. In MH-LEACH nodes die quickly because the protocol does not consider the residual energy of nodes. According to Figure 15, when the density is greater than 200 (\(\delta\geq 200\)) the FND round of MH-LEACH tends to stabilize between 1400 and 1600 rounds. Mezghani protocol reveals better performance compared to MH-LEACH (improved by 45.2%) due to the reduced number of generated CHs (Figure 12) and to the usage of Khalimsky theory [34] to elaborate an energy efficient cluster topology. According to Figure 15a, DC2 HC shows the highest durability, where the FND node reached 2876 round, whereas, in Mezghani and MH-LEACH it only reached 2591 and 1565 rounds, respectively. When increasing the maximum hop constraint (\(k>1\)), the performance of the three simulated protocols increase due to the usage of the multi-hop clustering, which reduces the energy consumption. The curve allure of DC2 HC in Figure 15b shows an improvement in performance compared to the other approaches. Indeed, the proposed scheme generates a low cardinality of dense clusters based on the neighborhood \(TCR\) value. DC2 HC uses the two hop neighbors information to favor nodes located in a well-connected region to be elected as a CH, it uses a multi-hop routing tree inside each cluster to improve the intra-cluster communications. Figure 14: Average number of exchanged messages during the clustering process (**a**) \(k=1\), (**b**) \(k=2\), (**c**) \(k=3\). Therefore, the connectivity among clusters is improved which reduces the waste of energy devoted to wireless transmission. Consequently, D2 MHC achieves a gain factor of 13.3% and 58.5% compared to Mezghani and MH-LEACH respectively. Figure 16 shows the round at which all network nodes died versus the network density (\(\delta\in[40,1300]\)) considering \(k\in\{1,2,3\}\). In MH-LEACH, the role of CHs is rotated randomly and periodically which reduces the number of setup messages, therefore, MH-LEACH behaves better than Mezghani protocol. However, using DC2 HC allows a further extension of nodes lifetime since it minimizes the set of cluster heads and, thus, it reduces the waste of energy devoted to long range communications. Moreover, it limits the number of CH rotation which reduces the clustering messages and the overall energy consumption offering the network a longer lifetime. Our proposed protocol outperforms Mezghani and MH-LEACH protocols in terms of network lifetime by 26.3% and 13.3% respectively. Figure 17 depicts the total number of nodes that remain alive over execution time considering the number of deployed nodes \(\delta=1000\). Although the performances of the three protocols initially look similar, we observe that DC2 HC has more alive nodes than the other algorithm with the growth of rounds. MH-LEACH selects the set of CHs based on random probabilities and does not consider nodes residual energy, which results in a faster death of network nodes. At the end of the clustering process only few nodes are remaining alive. Nevertheless, using our protocol allows network nodes to last for longer period. Whereas with the other protocols, nodes died faster. Table 7 summarizes the gains obtained by DC2 HC when compared to Mezghani and MH-LEACH in terms of energy consumption.