## 6 Simulation Results
### Performance Evaluation  
We compared the CCBE algorithm for different values of \(\alpha\) with the typical protocols LEACH and HEED by using various metrics: the energy consumption over simulation time, the fraction of alive nodes over time, the number of packets received at the sink, the maximum time delay with increasing number of nodes in the sensor network and the precision of the data received at the sink. The sink is placed at \begin{table}
\begin{tabular}{c c} \hline
**Propagation Factor** (\(\beta\)) & **2** \\ Network length & \(2000\) m \\ Simulation time (\(t\)) & 0.02 s \\ Number of nodes (\(N\)) & \(1500\) \\ Energy capacity of nodes (\(E_{cap}\)) & 2 J \\ Optimal cluster size (\(r\)) & \(25.06\) m \\ Min threshold power (\(p_{thr}\)) & \(8\times 10^{-15}\) W \\ Carrier frequency (\(f\)) & \(2.4\times 10^{4}\) Hz \\ Data Rate (\(d_{R}\)) & \(2.5\times 10^{5}\) bps \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters of the simulation. different locations of the sensor network to analyze the effect of location on energy consumption and network lifetime. The first performance metric, energy consumption over time, gives an idea of the rate of consumption of energy in the network. The initial energy given to each sensor node is two Joules. Figure 5 shows the variation of energy consumption with respect to the increasing number of sensor nodes in the network. As shown in Figure 5, the proposed CCBE (\(\alpha=0\)) protocol consumes less energy compared to other protocols, CCBE (\(\alpha=0.5\)), CCBE (\(\alpha=1\)), LEACH and HEED, respectively. CCBE (\(\alpha=0\)) consumes 64\(\%\) of the energy of the entire network before 30\(\%\) of the network nodes die. The energy consumption in CCBE is reduced by allowing the sensor nodes to sleep between the time for transmission and reception of packets. The energy consumption increases according to the increasing number of sensor nodes in the network for all algorithms. Less energy consumption means more network lifetime. This is analyzed using the network lifetime Figures 6 and 7. The network lifetime is defined as the fraction of nodes alive over time. This gives an idea of the time over which the network can send the data before all of the nodes in the network die. When \(\alpha\) is set to the optimal value, it will prolong the network lifetime; for instance, when the definition of the lifetime of the network is 30\(\%\) of nodes completely depleting their energy. Additionally, 30\(\%\) of nodes referred to above corresponds to a 70\(\%\) \"fraction of survived nodes\" in Figures 6 and 7. This 30\(\%\) of nodes does not have enough energy to receive or transmit a packet. In Figure 6, the network lifetime based on various values of \(\alpha\) from zero to one is shown, when the sink node is in the center. In both Figures 6 and 7, CCBE (\(\alpha=1\)) and LEACH, the network lifetime decreases drastically compared to the other algorithms. This is due to the fact that LEACH and CCBE (\(\alpha=1\)) do not take into consideration the residual energy of nodes during CH selection. This may result in selecting CHs with nodes having less energy. This may further affect the early depletion of energy for a particular node and the loss of packets. CCBE (\(\alpha=0\)) considers only residual energy during CH selection, which results in having the highest network lifetime compared to other protocols. In CCBE (\(\alpha=0\)), nodes with lower energy are never selected as CHs when the cluster contains nodes with higher residual energy. Moreover, this reduces the packet loss in end-to-end communications. Both the HEED and CCBE (\(\alpha=0.5\)) select CHs based on both residual energy and communication costs. This results in having a moderate network lifetime compared to other protocols. The network with the sink node in the center has more network lifetime due to the reduction of the number of packets that need to be aggregated and forwarded to the sink.