## 4 Performance Evaluation
### Influence of Number of Events  
Figure 7 shows the average and standard deviation of degree of backbone nodes as the number of nodes changes. In Figure 8(a), when the number of nodes increases, the network density also increases, thus the average degree of the backbone nodes increases. The range among degree of nodes is not high, so the average degree of each algorithm is similar. MMM always performs well, since it forms the backbone by taking into account the node degree. The average degree of backbone nodes of MCBT is similar to that of MMM because MCBT (\(\omega\) = 0.7) considers both degree and energy. If we set \(\omega\) to 0, MCBT has a similar value to MMM. As shown in Figure 8(b), the standard deviations of degree of backbone nodes in MCBT and MMM are very small values, such as 0.93 and 0.79. Nodes around the cluster head consume more energy than nodes located far from the cluster head, since they frequently transmit packets to the cluster head. However, if we select the nodes with high degree as cluster heads, \begin{table}
\begin{tabular}{|c|c|} \hline Network size & 500 m \(\times\) 500 m \\ \hline Transmission range & 28 m \\ \hline Initial energy & 2.5 J \\ \hline Data packet size & 500 bytes \\ \hline Control packet size & 15 bytes \\ \hline Energy consumption model \(E_{tx}\) & \(\alpha_{11}+\alpha_{2}\;r^{n}\) \\ \hline Energy consumption model \(E_{rx}\) & \(\alpha_{12}\) \\ \hline \(\alpha_{11},\;\alpha_{12}\) & 80 nJ/bit \\ \hline \(\alpha_{2}\) & 1 pJ/bit/m\({}^{2}\) \\ \hline \(n\) & 2 \\ \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. we could distribute the packet forwarding load among nodes around the cluster head, and thus extend the network lifetime. Figure 8 shows the average residual energy of backbone nodes after 30 sources initiate 20 events periodically. It appears to be a similar graph to that of the average residual energy in the early phase of backbone construction (Figure 7(a)). Therefore, we know that the stability of the backbone of MCBT is maintained after data transmission. Figure 9 shows the remaining energy of nodes when 30 sources initiate 40 events periodically. The lighter color of the node denotes a lower residual energy. HCDD has large differences in terms of residual energy between, before, and after event occurrence, compared with MCBT. This means the backbone of HCDD is composed of nodes with low energy. Thus, HCDD has many backbone nodes that exhaust energy when many events occur, which causes network disconnection. Figure 6: Residual energy of backbone nodes. Figure 7: Degree of backbone nodes. Figure 8: Average residual energy after event occurrence. Figure 9: Remaining energy of nodes after event occurrence. Figure 10 shows the maximum number of transmitted messages from source to sink before reconstruction of the backbone at different number of sources. The maximum number of transmitted messages is the performance metric to show the network lifetime indirectly. If the path differs for the same source and sink, the time can be affected by network conditions, such as collisions and delays. Therefore, the maximum number of transmitted messages, excluding those factors, is appropriate to measure the network lifetime. As the number of sources increases, the performances of MCBT and other schemes decrease. MMM performs 11% better when the number of sources is small. However, as shown in Figure 10, when the number of sources increases, the difference between MCBT and MMM becomes negligible. The good performance of MMM is due to the selection of cluster heads with a high degree. This provides load distribution among nodes around the cluster head, so the loss of energy due to packet forwarding is decreased. Moreover, the degree based algorithm such as MMM provides high connectivity. Even when the path used at the first time gets disconnected, it will be able to use another path. Therefore, the maximum number of transmitted messages is high.