# A Cluster-Based Dual-Adaptive Topology Control Approach in Wireless Sensor Networks
## 4 Performance Evaluation
### Simulation Results and Analysis
In the third 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 when \(w_{e}\) and \(w_{r}\) take some typical values respectively, where \(\mu\) takes 0.33. The results from Figure 14 illustrates that the average intra-cluster transmission power slightly decreases with the value of \(w_{r}\). This is because the larger \(w_{r}\) tends to elect a MCH with the stronger communication coverage capability, where the average clustering range computed by this MCH according to the Equations (5) and (6) tends to be smaller in general due to the participation of more nodes. That is, for the average intra-cluster transmission power shown in Figure 14, its maximum value is limited by the clustering range. When \(w_{r}\) gets larger, the elected MCH's approximate maximum transmission range is larger, and thus more nodes are in this coverage. All these nodes' approximate maximum transmission ranges are used to compute an average value by using the Equation (5), which tends to lead to a smaller average value that is clustering range when the number of these nodes is larger. Therefore, one observes a decreasing trend with \(w_{r}\) in Figure 14. Also, the smaller clustering range generates the more clusters and thus there are the more neighboring MCHs for each MCH with the stronger communication coverage capability. This makes a source MCH has the higher possibility to find the shorter path to the sink, which is confirmed by the results shown in Figure 15.  
Figure 3:0 Path delay for the ICV-MIMO scheme under the different typical values for \(\mu\). Figure 3:1 Packet delivery ratio for the ICV-MIMO scheme under the different typical values for \(\mu\). In other words, for the average path hop-count to sink shown in Figure 15, this value is affected by the density of network graph consisting of MCHs. As mentioned above, when \(w_{r}\) gets larger, the average approximate maximum transmission range tends to reduce, and thus clustering range gets smaller and the number of clusters increases. Also, each MCH has the higher number of neighboring MCHs if it has a larger approximate maximum transmission range. Therefore, the network graph consisting of MCHs is denser, and it is more likely to find a shorter hop-count path to the sink. So, one observes a decreasing trend with \(w_{r}\) in Figure 3:2  
Figure 16 shows that the network lifetime slightly increases with the value of \(w_{e}\). The main reasons are that the larger value for \(w_{e}\) leads to the MCHs with the higher energy and thus the connectivity between the clusters is kept longer. Also, when the value for \(w_{e}\) is relatively smaller, the relatively larger value for \(w_{r}\) suppresses the deterioration of the network lifetime, so one can observe that the difference between the three curves in Figure 16 is not obvious. Figure 3:3 Average intra-cluster transmission power for the ICV-MIMO scheme under the different typical values for \(w_{e}\) and \(w_{r}\). Figure 3:4 Average path hop-count to sink for the ICV-MIMO scheme under the different typical values for \(w_{e}\) and \(w_{r}\). In a word, for the network lifetime shown in Figure 16, this value is mainly related to residual energy level of MCHs. When \(w_{e}\) gets larger, the elected MCHs have higher energy level and thus the network lifetime is longer. On the other hand, when \(w_{e}\) gets smaller, although the elected MCHs have relatively lower energy level, the network lifetime will not be significantly worse. This is because as \(w_{e}\) gets smaller, \(w_{r}\) gets larger accordingly, which leads to the lower average intra-cluster transmission power (as shown in Figure 14). Therefore, to a certain extent, it is able to compensate for the impact of the lower remaining energy on the network lifetime.