## 4 Simulation and Performance Evaluation
### Performance Analysis under Different Parameters  
#### 4.2.1 The Impact of Head Nodes' Threshold \(Th\)  
We first investigate the impact of head node re-election threshold on the performance of our algorithm by varying the value of \(Th\). The parameters we set are shown as follow: (1) the number of all nodes is 500; (2) \(r_{e}\) is 30 m; (3) the event area changes by period, and the period is 800 s; (4) one source node produces one data packet in one second; (5) the velocity of sink is 5 m/s; (6) \(Th\) can be 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80% and 90%. As we mentioned in Section 3.4, \(E^{\prime}\) as the current energy of the head node, while \(E\) is the original energy when it is elected as head node. If the ratio of \(E^{\prime}\) to \(E\) is below a threshold \(Th\), then head nodes will be re-elected.  
In Figure 14, (1) black line represents the impact of \(Th\) on the lifetime of network. The network can obtain a relatively long lifetime when \(Th\) increased from 20% to 70%. A lifetime achieves the biggest value when \(Th\) is 70%. When \(Th\) is too low or too high, network dies very soon. According to the definition of \(Th\), head nodes with a small \(Th\) consumes more energy when they retire. That means these retired head nodes have little energy while other nodes have much energy. These retired head nodes are easy to die. Network dies very soon with a small \(Th\). In the opposite condition, if \(Th\) has a big value, re-election will be carried out frequently. As the re-election process consumes energy, hence energy is consumed fast. Then network also dies soon. When \(Th\) is in the middle area, the network has a relative balanced condition, which leads to a longer network lifetime.  
(2) Red line represents the impact of \(Th\) on the average residual energy. When \(Th\) is 10%, the average residual energy is very high. As the analysis in (1), the end of network is just due to that some retired head nodes die soon. hence many nodes haven't consumed much energy. So the residual energy is high. When \(Th\) increases, residual energy decreases with longer lifetime. When \(Th\) reaches 80%, re-election is carried out frequently, and residual energy increases with a decreased lifetime. When \(Th\) is 90%, much energy is spent on re-election process. The residual energy decreases although this condition has a short lifetime. The lower residual energy is, the better network runs. When \(Th\) is 70%, the residual energy is lowest.  
(3) Blue line represents the impact of \(Th\) on variance of residual energy. The variance can reflect the balance of all nodes' energy consumption. The network is more balanced when the variance is lower. At first, the variance is very low, that is because retired head nodes die so fast. When the first node dies, most nodes consume little energy. However, with the increase of \(Th\), such as 20%, more nodes consume much energy while others consume little. The peak value is occurred in 20%.  
Figure 14: The impact of \(Th\) on the network performance.  
The variance is decreased from 20% to 90%. That is because the frequent re-election, and head nodes do not need to retire until much energy is consumed.  
According to (1), (2) and (3), network can get the longest lifetime, the lowest average residual energy and a very low variance of residual energy when 70% is adopted.