## 6 Performance Evaluation
### Simulation Results
#### 6.2.4 Network Lifetime  
Network lifetime can be defined as the time interval between the start of network simulation and when the first sensor node dies, all sensor nodes die, some percentage of sensor nodes die, loss of coverage occurs or network is partitioned such that path from source to sink does not exist [26]. According to [26], network lifetime can also be evaluated in terms of the dead node ratio in the network. The time when 25%  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Schemes**} & \multicolumn{6}{c}{**Number of Rounds**} \\ \cline{2-9}  & **500** & **1000** & **1500** & **2000** & **2500** & **3000** & **3500** \\ \hline SEP-E & \(-1.47\) & \(2.78\) & \(13.64\) & \(68.75\) & \(600\) & \(328.57\) & \(233.33\) \\ DEEC-E & \(1.52\) & \(8.82\) & \(0\) & \(-25\) & \(-33.33\) & \(-58.33\) & \(-66.67\) \\ EBCS & \(-2.9\) & \(-2.63\) & \(8.7\) & \(50\) & \(600\) & \(328.57\) & \(233.33\) \\ TEEN & \(-3.6\) & \(-5.13\) & \(8.7\) & \(50\) & \(75\) & \(200\) & \(100\) \\ \hline \hline \end{tabular}
\end{table}
Table 11: Percentage improvement of HFECS in terms of average residual energy.  
Figure 6: Average residual energy at round=2000 against variable network size.  
Figure 7: Residual energy against number of communication rounds.  
or 50% of the nodes present in the network have no residual energy left to continue their data delivery tasks can be treated as the network lifetime. Here, we considered two such time intervals, i.e., (i) when the first sensor node dies (FND) and (ii) when half the nodes in the network die, i.e., 50% of the sensor nodes have no residual energy left to continue their data sensing tasks (HND). The stacked grouped bar chart in Figure 8 demonstrates the network lifetime in terms of two different cases, i.e., First Node Dead (FND) and Half Nodes Dead (HND) for SEP-E, DEEC-E, EBCS, TEEN and HFECS against different network sizes. In every stack, we have five bars representing five different schemes, i.e., SEP-E, DEEC-E, EBCS, TEEN and HFECS. In each bar, we have two groups, i.e., FND and HND.  
It can be observed from Figure 8 that the performance behavior of all clustering schemes is analogous for network lifetime, i.e., a decreasing trend as we increase the network size. For smaller network sizes, the network lifetime is higher for all clustering schemes as the nodes located in close vicinity are easy to communicate with but, for larger network sizes, the network lifetime decreases rapidly due to the fact that sensor nodes are not located in the close vicinity and extra energy is being consumed for communication between sensor nodes, which results in decreased network lifetime. The performance of EBCS for network sizes of up to \(200\times 200\) m\({}^{2}\) is slightly better than HFECS. For smaller network sizes, we have a high density of sensor nodes in every cluster, so it is highly likely that a potential CH or a CM lose all of their residual energy in slightly less time than EBCS due to the extra computation of link connectivity calculations performed in every cluster. However, as we increase the network size, the uniformly random deployment of sensor nodes creates clusters with a lower number of sensor nodes as compared to the scenario of smaller network sizes, thus resulting in better network lifetime in comparison to EBCS. HFECS also adopts lossless data aggregation in multiple data packets at the CH level, which reduces the information flow from CHs to the BS, thus decreasing some of the extra energy spent on control packet overhead. The percentage improvement of HFECS in terms of network lifetime (FND and HND) is given in Tables 12 and 13.  
Figure 8: Network lifetime in terms of first node dead (FND) and half nodes dead (HND) against variable network size.