# An Efficient Model-Based Clustering via Joint Multiple Sink Placement for WSNs
## 5 Simulation and Evaluation
### Simulation Results
#### 5.2.1 Statistical Results over The Lifetime Based on Various Methods  
In this study, we defined the first node's energy consumption (\(\text{FE}_{\text{C}}\)) that ultimately reaches their initial energy (\(\text{FE}_{\text{I}}\)) while transmitting the data as a metric to measure the network lifetime t as follows:  
\[\text{t}=\text{t}_{\text{f}}-\text{t}_{\text{i}} \tag{19}\]  
where \(\text{t}_{\text{f}}\) is the instance t when \(\text{FE}_{\text{C}}-\text{FE}_{\text{I}}=0\), and \(\text{t}_{\text{i}}\) is the instance when the network starts. The LEACH, HEMP, DP clustering and the proposed approach were used to investigate the effect of a variable number of sensor nodes on the network's lifetime. The network's lifetime was evaluated according to the number of sensors, which ranged from 200 to 1500, as shown in Figure 5(a). It is worth noting that the network's lifetime diminishes as the overall number of sensors grows; this phenomenon occurs mainly because by increasing the number of sensors in the same cluster, the considered sink covers a significant number of nodes' packets. Our proposed approach shows two possible sink placements: the barycentre of the weighted cluster and the barycentre of the neighbours' clusters, the Cp factor, and the data routing technique; all of these factors improve the network's lifetime. The network's lifetime obtained by LEACH, HEMP, and DP clustering, in addition to our proposed approach, is between 114 s and 95 s, 130 s and 118 s, 145 s and 124 s, and 160 s and 132 s, respectively, as the total number of sensors grows between 200 and 600. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Approach**} & **Number of Nodes with** & **Number of Nodes with** & **Number of Nodes with** & **Number of Nodes with** & **Number of Nodes with** \\  & **1-Hop (\%)** & **2-Hop (\%)** & **3-Hop (\%)** & **4-Hop (\%)** & **5-Hop (\%)** \\ \hline LEACH [57] & 87.2 & 4.8 & 3.5 & 2.5 & 2 \\ \hline HEMP [39] & 92.5 & 3.5 & 2.5 & 1.5 & 0 \\ \hline DP clustering [61] & 93.5 & 3.5 & 2.8 & 0.2 & 0 \\ \hline Our proposed & 96.5 & 2 & 1.5 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of the efficiency of sensors affectations for different clustering algorithm. The network's lifetime decreases as the number of sensors grows for all of the compared algorithms. Nevertheless, in all cases, our proposed method has achieved a more extended network lifetime than the other techniques. Furthermore, in Figure 6a, we note that by increasing the number of sensors, the lifetime lowers (the first node depletes its energy). We can relate that to different assumptions, e.g. that which nodes are depleted first depends on a set of parameters, such as the initial energy (the energy consumption will increase by increasing the number of sensors, and nodes that have lower initial energy probably deplete its energy first), the location (direct or indirect to sinks), the degree (number of sensors in communication range increases by increasing number of sensors), etc. Using the experimental parameters shown in Table 4, the influence of a variable number of clusters on the network's performance is investigated in this scenario. The number of clusters increases from 10 to 50. The results are depicted in Figure 6b, where it is clear that the network's lifetime extends as the number of clusters grows, causing each cluster's size to diminish. Hence, the number of intracluster communications is reduced. On the other hand, the network's number of CHs increases as the distance between nodes decreases. Therefore, each CH sends its measurements via a shorter link. This criterion, according to the suggested model, indeed increases the network's lifetime. The proposed approach, with all of the algorithms, efficiently balances the residual energy among the sensors of each cluster by increasing the number of groups and decreasing their sizes. Thus, the network's lifetime is increased. Above all, our proposed approach notably provides the best results.