## 5 Results
### Network Lifetime  
The network lifetime is defined as the number of rounds in which the network starts to run until the last node dies.  
To better evaluate the network performance, we compare three parameters: FND, HND, and LND of algorithms in three scenarios. The notations used in Table 3 are as follows [39; 40; 41]:  
1. FND, the number of rounds in which the network starts running until the first node dies;
2. HND, the number of rounds in which the network starts running until half of the nodes die;
3. LND, the number of rounds in which all nodes die in the network.  
Table 3 shows the results of LEACH, K-LEACH, IEECHS, RCH-LEACH, and DCK-LEACH in terms of FND, HND, and LND in all scenarios. In addition, the simulation results in Figure 3(a)-c are consistent with that of Table 3. Figure 4(a)-c show the multiple simulation results of five algorithms in terms of LND (the number of rounds in which all nodes die in the network).  
In scenario 1 of Table 3, it is obvious that the FND, HND, and LND of the proposed algorithm are extended compared with that of LEACH (by 55 rounds, 221 rounds, and 534 rounds), K-LEACH (by 43 rounds, 365 rounds, and 680 rounds), IEECHS-WSN (by 62 rounds, 320 rounds, and 766 rounds), RCH-LEACH (by 57 rounds, 225 rounds, and 544 rounds), and DCH-LEACH (by 254 rounds, 485 rounds, and 904 rounds). Compared to LEACH, K-LEACH, IEECHS-WSN, and RCH-LEACH, the improvement of DCH-LEACH in FND is 362%, 490%, 309%, and 345%, in HND that is 119%, 32.8%, 51.5%, and 115%, and in LND that is 69.2%, 32.9%, 18%, and 66.1%. In scenarios 2 and 3, the FND, HND, and LND of our method are significantly longer than that of other protocols.  
In Figure 3(a)-c, the descending curve in DCK-LEACH is also gentler than that of LEACH, K-LEACH, IEECHS-WSN, and RCH-LEACH. It shows that the network time of DCK-LEACH is the longest compared with that of other protocols.  
Figure 4: _Cont._  
This is because the DCK-LEACH algorithm adopts the dual cluster-heads mechanism to shorten the communication distance between a single cluster-head and the base station and reduce the energy consumption imbalance caused by the single cluster-head communication mechanism. This reduces the energy consumption of both intra-cluster nodes' communication and the frequent re-electing of cluster-heads. FND is significantly extended.  
Due to reducing the number of re-clustering and communication requests for sending node information to the base station, the inter-cluster energy consumption is effectively reduced; therefore, HND and LND are continuously extended.  
Figure 5a-c show the network lifetime of LEACH, K-LEACH, IEECHS-WSN, RCH-LEACH, and DCK-LEACH in all scenarios, where sensor nodes are randomly deployed. In scenario 1, as shown in Figure 5a, in multiple repeated experiments, the network lifetime of DCK-LEACH is between [900 rounds, 1100 rounds], while the network lifetime of LEACH, K-LEACH, IEECHS-WSN, and RCH-LEACH are between [450 rounds, 600 rounds], [580 rounds, 700 rounds], [760 rounds, 850 rounds], and [500 rounds, 600 rounds]. Under the  
Figure 5: Comparison lifetime of the network in three scenarios: (**a**) 100 nodes, (**b**) 200 nodes, (**c**) 300 nodes. In x-axes of the figure, numbers 1, 2, 3, 4, 5, and 6 are the experiment IDs of multiple executions of the algorithm. Due to space limitations, we only listed the results of six experiments. Other multiple experiment results are similar and are not listed here.  
same simulation environment in various repeated experiments, the performance of the proposed algorithm is superior compared to that of other algorithms.  
In scenario 2 and scenario 3, as shown in Figure 5b,c, the same conclusion can be drawn. Other multiple experiment results are similar and are not listed here.  
During multiple experiments, the proposed algorithm can effectively prolong the network lifetime in the random deployment environment.