## 6 Simulation Results and Analysis
### Comparison of Network Lifetime
When the total number of nodes increases, the length of radius of each cluster decreases accordingly to maintain the number of nodes within the cluster unchanged essentially. Therefore, the energy consumption of the CHs in EBCAG  
Figure 13: Number of alive nodes in the three algorithms. does not change too much. For EBCH, when the first node dies, the number of data gathering cycles fluctuates to a certain extent with the increase of the number of nodes, and it appears to decrease slightly as a whole. The reason for this tendency is that the number of nodes in each cluster will increase when there are more and more nodes in the network, which enhances the workload of CH. Thus, as the energy consumption of CH increases, the moment when the first dead node appears is ahead of time. That is to say, EBCH is not suitable for the densely deployed network. In AEBDC, although the network load becomes heavier and heavier with the increase of the total number of nodes, the number of nodes in the RCCH increases accordingly. This ensures that more nodes can participate in competing for becoming the cluster header. This effectively balances the energy consumption of each RCCH. Therefore, in AEBDC, the time when the first dead node appears is postponed as the number of nodes increases. In other words, the data collection method proposed in this paper can be applied to various types of networks. It is worth mentioning that, in AEBDC, there are a few WCVs in the network to periodically recharge the nodes in each RCCH, and the actual available energy of nodes in AEBDC is greater than that in EBCAG and EBCH. Thus, the \"energy efficiency\" of the three methods are further analyzed, as shown in Figure 15.  
Figure 14: The time when the first dead node appears in the three algorithms. Figure 15: The energy efficiency of the three algorithms. Here, the \"energy efficiency\" is defined as the ratio between all nodes' energy consumption and the sum of their initial energy as well as the energy supplied for them. From the simulation result, it is known that the energy efficiency of AEBDC is much higher than that of EBCH and EBCAG when 5% or 30% of nodes die. Although the difference in energy consumption between the CNs and the CHs is reduced due to the cluster-header rotation strategy of EBCAG, it still consumes a lot of energy on calculating the optimal cluster radius as well as reclustering. On the other hand, the EBCH method adopts the local CH rotation scheme as well as the non-uniform deployment strategy to balance the energy consumption of CHs in each annulus. It reduces the expense on CH rotation, but there is still a large difference in energy consumption between cluster heads and non-cluster heads. Thus, the energy efficiency of EBCH is also lower than that of AEBDC. Moreover, the energy consumption of CCHs is approximately balanced in each round of data gathering time in our method, and the recharging scheme also ensures that the CCHs keep working before some common nodes die, which makes full use of energy. When 50% of nodes die, the energy efficiency of AEBDC is a little lower than the other two algorithms. This is because in AEBDC most of these dead nodes are common nodes and they are located in the outer annuluses. In this case, the energy consumption of CHs in the inner annuluses for forwarding data is great decreased. On the contrary, in EBCH and EBCAG, most of the CHs near the sink exhaust their energy in advance of the common nodes. Thus, the work load on the alive CHs becomes heavier, which increases its energy efficiency to a certain extent.