## 4 Performance Evaluation  
### Simulation Environment  
Via the ns-2 simulator, we implement and compare the performance of MCBT with other backbone construction schemes, i.e., HCDD and MMM. Their information is listed in Table 1 (in Table 1, \(d\) is the maximum number of hops between the cluster head and ordinary node and \(n\) is the number of nodes in the network). The MAC layer follows the IEEE 802.11 MAC specification. Figure 4: Average and standard deviation of degree. Figure 5: The effect of weight factor (\(\omega\)) on the backbone. Figure 3: Average and standard deviation of residual energy. The main objective of our scheme is to create a stable backbone with the node's residual energy and degree taken into account, and each node transmits packets through this stable backbone. Thus, we evaluate the performance of the backbone construction scheme in terms of the average residual energy or degree of backbone nodes, the standard deviation of the residual energy or degree of backbone nodes, the average residual energy of backbone nodes after event occurrence, and the network lifetime. * **Average residual energy or degree of backbone nodes:** The residual energy or degree of the backbone nodes shows the stability of the backbone. The demands on the backbone nodes are larger than those of ordinary nodes and nodes around the cluster head consume more energy in order to forward packets. However, by selecting a node with higher energy or degree, the high energy consumption of specific nodes should be alleviated. * **The standard deviation of residual energy or degree of the backbone nodes:** Assume that the number of backbone nodes in the network is \(m\), the residual energy or degree of each backbone node is \(z\), and the average residual energy or degree of backbone nodes is \(\overline{z}\), then the standard deviation is represented by \(\sigma=\sqrt{\frac{\sum_{i=1}^{m}(z_{i}-\overline{z})^{2}}{m-1}}\). The standard deviation of the backbone nodes refers to the distribution rate of backbone nodes' residual energy or degree. A small standard deviation means that the residual energy or degree of each backbone node is similar to the average value and the residual energy or degree of each backbone node is almost uniform. If the average residual energy or degree of backbone nodes is high and their standard deviation is low, then the node with higher residual energy or degree is selected as a backbone node in advance. Moreover, the backbone is composed of nodes with even characteristics. This may decrease the rapid disconnection of the network caused by a load imbalance. * **The average residual energy of backbone nodes and the network lifetime after events occur:** We can evaluate the network lifetime by measuring the operational time until the backbone is disconnected or by counting the maximum number of transmitted messages from source to sink. This indirectly indicates how long a backbone is maintained before its reconstruction. Reconstruction overhead places a heavy load on the network, and it is important to ensure the backbone is stable and maintained for a long time. The time can be affected by variable factors, such as routing paths and data transfer collisions. Thus, in this paper, we compare the network lifetime with other algorithms by evaluating the maximum number of transmitted messages. The main parameters of our simulation are listed in Table 2. The sensor nodes are randomly selected as the source and a residual energy below 2.5 J is randomly assigned to each node. Our simulation environment uses the following energy model [24]: \(E_{tx}=\alpha_{11}+\alpha_{2}r^{n},\ E_{rx}=\alpha_{12}\), where \(E_{tx}\) and \begin{table}
\begin{tabular}{|c|c|c|} \hline Schemes & Cluster head selection criteria & Time complexity \\ \hline HCDD & ID & \(O(d)\) \\ \hline MMM & Degree & \(O(n)\) \\ \hline MCBT & Energy\&Degree & \(O(d)\) \\ \hline \end{tabular}
\end{table} 
Table 1: Three clustering schemes in simulation.