# A Cluster-Based Dual-Adaptive Topology Control Approach in Wireless Sensor Networks
## 4 Performance Evaluation
### Simulation Results and Analysis
Since the ICV-MIMO scheme has the slightly higher average bit error rate in intra-cluster links, it has the slightly higher average link delay in intra-cluster communications. However, as shown in Figure 3, due to the shortest average path hop-count in the four schemes, the ICV-MIMO scheme has the lowest average path delay among them. As shown in Figures 6 and 7, in the three CMIMO schemes, their average path delays have a more obvious difference than their average packet delivery ratios. This is because path delay is greatly affected by path hop-count, which is basically in line with the change of path hop-count. Due to the predefined value of low bit error rate, the difference of average bit error rate in intra-cluster links for the three CMIMO schemes is very small, and thus there is a small difference between their average packet delivery ratios in the paths from the cluster members to the sink. In the second group of simulations, we study the impact of the number of nodes on the average transmission power, the average path hop-count, the network lifetime, the network connectivity ratio, the average path delay, and the average packet delivery ratio for the ICV-MIMO scheme under the different typical values for \(\mu\), where \(w_{e}\) and \(w_{r}\) take 0.5 and 0.5 respectively. From Figure 8, one can observe that, the average transmission power increases with the value for \(\mu\). This is due to the fact that the average clustering range increases with the value for \(\mu\). From Figure 9, one can observe that, when the value for \(\mu\) gets smaller, the average path hop-count has smaller fluctuations with the variations in the number of nodes in the same simulation area. This may be because, on the one hand, the smaller \(\mu\) leads to the smaller clustering range which accommodates the smaller number of nodes, and the smaller variations in the number of nodes has less impact on the replacement of MCH; on the other hand, the smaller clustering range generates more neighboring MCHs for each elected MCH node. Therefore, these factors are conducive to the stability of the path. Figure 8: Average intra-cluster transmission power for the ICV-MIMO scheme under the different typical values for \(\mu\). Figure 9: Average path hop-count to sink for the ICV-MIMO scheme under the different typical values for \(\mu\). Figure 10 shows that the network lifetime decreases with the value for \(\mu\). The main reason is that, on the one hand, when the value for \(\mu\) is relatively small, the average number of neighboring MCH is relatively large and thus the connectivity between the clusters is not easy to be destroyed; on the other hand, since the smaller clustering range accommodates the smaller number of nodes, the load of single cluster is smaller, where total energy consumption is shared to more clusters and thus the network energy consumption is balanced further. Figure 11 reveals that the network connectivity ratio is less than 100% when the value for \(\mu\) takes 0.6. This is because the larger \(\mu\) leads to the larger clustering range. However, the network connectivity ratio is still more than 99%. The change trend of curves in Figure 12 is basically consistent with that in Figure 9, which further shows that path delay is mainly affected by path hop-count when the bit error rate of link is strictly controlled. From Figure 13, one can observe the fluctuation of curves though the absolute amount of change is very small, which may be caused by the randomness of the node distribution. Also, the curves are intertwined in Figure 13, where the main reason may be the fluctuation of path hop-count, since the bit error rate for each link is controlled to roughly the same value in inter-cluster communications. Figure 11: Network connectivity ratio for the ICV-MIMO scheme under the different typical values for \(\mu\). Figure 10: Network lifetime for the ICV-MIMO scheme under the different typical values for \(\mu\).