# An Energy Centric Cluster-Based Routing Protocol for Wireless Sensor Networks
## 5 Performance Evaluation
### Network Lifetime  
The network lifetime is defined as the number of rounds until a percentage of nodes die. The steady state is defined as the number of rounds until the first node dies. As the weight factor \(\alpha\) has an important role in the network lifetime of ECCR, we first analyze the steady state and network lifetime of ECCR for various values of the weight factor.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Location of the BS & (100,250) m \\ Number of nodes, \(N\) & 100 \\ Initial energy, \(E_{ini}\) & 0.5–1.5 J \\ Control packet size, \(l\) & 25 bytes \\ Data packet size, \(l\) & 500 bytes \\ Transmitter or receiver circuitry, \(E_{elc}\) & 50 mJ/bit \\ Data aggregation cost, \(E_{al}\) & 5 mJ/bit/signal \\ Computation cost of rank and energy, \(E_{com}\) & 5 mJ/bit/signal \\ Transmit amplifier cost, \(\epsilon_{up}\), if (\(d>d_{0}\)) & 0.0013 pJ/bit/m\({}^{4}\) \\ Transmit amplifier cost, \(\epsilon_{\mu}\), if (\(d\leq d_{0}\)) & 10 pJ/bit/m\({}^{2}\) \\ Diagonal length of a grid, \(R_{\text{d}}\) & \(\sqrt{2}\times(M/3)=94.28\) m \\ Maximum transmission range, \(R_{\text{max}}\) & \(2\times R_{\text{d}}=188.56\) m \\ Weight factor, \(\alpha\) & 0.8 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Simulation parameters setting.  
Figure 2: Example topology of the network.  
Figure 5: Number of alive nodes in each round in ECCR.  
Figure 6: Number of elected cluster heads in each round in ECCR.  
Figure 7: Total residual energy of the nodes in each round in ECCR.  
Based on the earlier analysis of weight factor and number of clusters, we set the value of \(\alpha=0.8\) and the initial number of clusters to 9 according to Equation (3). Then we evaluate the ECCR for the comparison of steady state and network lifetime with other protocols. The number of cluster heads in ECCR is predefined and static where it is varied in the protocols EADUC, HUCL and IEADUC. Figure 9 exhibits the distribution of the number of cluster heads in 30 randomly selected rounds of the protocols. The protocols control the competition radius and ensure that in each competition range, there is a cluster head. Therefore, the number of the cluster heads is well distributed across the network throughout their network lifetime. The trends of the energy consumption of the nodes in the protocols are distinctive. Trends vary according to their cluster head elections and data transmission to the BS.  
Figure 10 shows the ECCR outperforms the protocols in terms of steady state and network lifetime. The ECCR achieves on average of 3.16 times, 2.94 times and 1.47 times of steady state of the protocols EADUC, HUCL and IEADUC, respectively. The network lifetime considering 60% of the nodes are dead, ECCR enhances the network lifetime on average of 2.10, 1.05 and 1.04 times of the protocols, accordingly. The network lifetime of ECCR enhances significantly with increases of the percentage of dead nodes. ECCR achieves on average of 2.76, 1.42 and 1.51 times of the protocols considering 90% of the nodes are dead in the network.  
Figure 8: Number of alive nodes in each round in ECCR.  
Figure 9: Distribution of the number of cluster heads.