## 6 Simulation Results
### Performance Evaluation
In this paper, we define the lifetime of the network as the time duration before a fraction of nodes runs out of energy, and the results from Figure 6 show the efficiency of each algorithm when the sink is in the center. For instance, when the definition of the lifetime of the network is 30\(\%\) of nodes completely depleted of energy, the ratio of the lifetimes of the network (calculated in loops between zero until 30 events) under various algorithms is as follows. LEACH : CCBE(\(\alpha=1\)) : HEED : CCBE (\(\alpha=0.5\)) : CCBE(\(\alpha=0\)) = 0.58 : 0.62 : 0.88 : 0.94 : 1; this shows that the CCBE algorithm (when \(\alpha=0\), sink at center) has better performance in the network lifetime when analyzed with LEACH and HEED. Since  
Figure 7: Comparison of network lifetime (sink not in the center). LEACH and CCBE (\(\alpha=1\)) do not take into consideration the residual energy of nodes, the network lifetime decreases drastically compared to the other algorithms. In order to analyze the effect of packet loss due to the selection of CHs with lower energy, in this paper, we have compared the number of packets received at the sink for various protocols. From Figures 8 and 9, it is clear that when the sink node is in the center, it receives a higher number of packets compared to the sink that is not in the center. Figures 8 and 9 show that before the network disconnection, the sink node of the CCBE (\(\alpha=0.5\)) algorithm receives much more data packets than the other algorithms. In Figure 9, the received data with CCBE (\(\alpha=0.5,0\)) increase more quickly than the other protocols. Moreover, this is a result of using residual energy and the communication lost for CH selection. The number of packets received is shown in Tables 3 and 4 for both locations of the sink node. The sink node in the center for CCBE (\(\alpha  
In order to understand the performance of the MAC scheme proposed in this paper, the time delay with increasing number of nodes in the sensor network is shown in Figure 10. It is clear that the delay increases with the increasing number of sensor nodes in the network. In CCBE for all values of the \(\alpha\) MAC scheme is based on TDMA. Moreover, the number of slots required also increases. This results in increasing delay for end-to-end communication. In Figure 10, we have increased the number of CMs in each cluster from 10 to 20. Figure 10 compares the delay for both CCBE and CSMA/CA, which is used in LEACH and HEED. CSMA/CA has less delay due to the random access of the channel, and in CCBE, the nodes need to wait for their time slot for transmitting the data to other nodes. However, the energy consumed during the idle listening time for each sensor node in CCBE is decreased by letting those nodes sleep till it is time for the transmission or reception of packets. The number of clusters remained the same, even though the number of CMs is increased in each cluster. The number of time slots for CMs in the CHs is increased. This will result in a higher packet size, so more energy is consumed in the packet transmission. The packets size is maintained by aggregating \begin{table}
\begin{tabular}{c c c c c c} \hline  & \(\alpha=0\) & \(\alpha=0.5\) & HEED & LEACH & \(\alpha=1\) \\ \hline Lifetime (s) & 1892 & 1756 & 1682 & 1021 & 1121 \\ Packets & 1625 & 1794 & 1256 & 990 & 1054 \\ \hline \end{tabular}
\end{table} 
Table 4: Sink node not in the center. Figure 10: Comparison of the time delay. \begin{table}
\begin{tabular}{c c c c c} \hline  & \(\alpha=0\) & \(\alpha=0.5\) & HEED & LEACH & \(\alpha=1\) \\ \hline Lifetime (s) & 1956 & 1835 & 1723 & 1132 & 1207 \\ Packets & 1739 & 1843 & 1416 & 1081 & 1187 \\ \hline \end{tabular}
\end{table} 
Table 3: Sink node in the center. LEACH, low-energy adaptive clustering hierarchy. the data in the packets. Aggregating more data will result in more error or less precision at the sink node. Figure 11 shows the precision of data received at the sink node. The precision graph is obtained by comparing the values obtained at sink node with actual values sent by the CMs.