## 5 Simulations
### Performance of the ECHR Protocol
Figure 10 depicts the average energy consumption of each node _versus_ the simulation rounds when using three different protocols in the cases I and II. The average energy consumption of the ECHR protocol steadily increases during the simulation due to its energy-balancing capability. Moreover, the comparison between the results yielded by the LEACH and the LEACH-Coverage-U protocols clearly indicates that the 100 nodes deployed in the network are still alive and maintain a 100% sensing coverage at the 1,500 th simulation round in the case I when using the ECHR protocol. By contrast, the networks using the other two protocols have almost stopped working when the simulation reached the 1,500 th round. Moreover, in case II, the average energy dissipation of the ECHR protocol is almost the same as the other two protocols before the 3,000 th round, but after that, the average energy dissipation of sensor nodes using the LEACH and the LEACH-Coverage-U protocols are both less than that of the ECHR protocol. This is because some sensor nodes in the networks using the former two protocols have run out of energy before 3,000 th round. In other words, the cluster heads of the LEACH and the LEACH-Coverage-U network only need to transmit the data collected by a small number of sensor nodes. Nevertheless, the sensor networks using the LEACH and LEACH-Coverage-U protocols have lost a 100% coverage ratio when the simulation reaches the 3000 th round. In this regard, the proposed ECHR protocol more efficiently utilizes the energy of the redundant nodes, so the network lifetime is prolonged while a full sensing coverage is retained. Note that if the compression coefficient \(\mu\) of Equation (12) is set at 0 which is the same as the settings in [4,18], the ECHR protocol provides 572.9% and 440.1% increases in service time with a 100% sensing coverage ratio comparing with the LEACH and LEACH-Coverage-U protocols in the case I. In the case II, the ECHR also increases 136.7% and 163.6% service time with a 100% sensing coverage ratio comparing with the LEACH and LEACH-Coverage-U protocols. These increases are better than the experimental results when the compression coefficient \(\mu\) is set at 0.05. Figure 9: Comparison of the coverage ratio of the proposed ECHR protocol with those of other protocols. Figure 11 shows the distribution of active and dead nodes of the network in the case I. Figure 11(a) plots the distribution of the network topology of active and dead nodes when the number of dead nodes rises to 25, obtained by applying the LEACH protocol to the network. In this case, most of the dead nodes are located at the upper side of the network, _i.e._, distanced from the BS. This fact is because the energy consumption for transmitting data between the BS and these nodes are greater than the energy use when nodes are located at the bottom side. Figure 11(b) depicts  
Figure 10: Comparison of the average energy consumption of the proposed ECHR protocol with those of other protocols. Figure 11: Distribution of alive and dead nodes yielded by (**a**) LEACH protocol, (**b**) LEACH-Coverage-U protocol, and (**c**) the proposed ECHR protocol. (**d**) Distribution of active and dead nodes before the network fails to maintain 100% sensing coverage obtained by applying the proposed ECHR protocol. the distribution of active and dead nodes when the number of dead nodes is equal to 25 by applying the LEACH-Coverage-U protocol to the network. Comparing with Figure 11(a), the active nodes in Figure 11(b) are more dispersed because the locations of nodes are taken into account by the LEACH-Coverage-U protocol. However, the majority of dead nodes are still located at the upper side. Figure 11(c) shows the distribution of active and dead nodes when the number of dead node is equal to 25, obtained by applying the proposed ECHR protocol to the network.