## 5 Simulations
### Performance of the ECHR Protocol  
In this section, the performance of the ECHR protocol is compared with those of the LEACH [4] and the LEACH-Coverage-U [18] protocols via an extensive series of simulations. The simulations using different protocols are ceased once all nodes run out of energy, and the comparison results generated. In the case I, the same network model in both approaches [4, 18] mentioned above is used to examine the protocols. The LEACH and the LEACH-Coverage-U both set their _BS_ in a remote place, and each node can directly transmit data to the _BS_. Such a condition, however, is not suitable for a real-world environment, because each tiny low-cost sensor node does not have such strong communication capability. Consequently, in the simulation a gateway is located in the center of the monitoring area, _i.e._, located at (25, 25), equipped with a long distance wireless communication module (e.g., the global system for mobile communications module) capable of transmitting the sensed data to the _BS_. In each round, sensor nodes transmit sensing data to the gateway, and the gateway sends the sensing data of sensor nodes to the _BS_. Moreover, the path loss exponent \(\gamma\) of Equation (10) is set at 2.5 when transmitting data from the root node to the gateway [4, 18]. In the case II, the  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{2}{c}{**Parameters**} & \multicolumn{4}{c}{**Coverage-time (Rounds)**} \\ \(\lambda_{1}\) & \(\lambda_{2}\) & **100\%** & **95\%** & **90\%** & **80\%** \\ \hline
0 & 3.3 & 1,094 & 1,334 & 1,359 & 1,381 \\
0.3 & 3.3 & 1,583 & 1,675 & 1,692 & 1,709 \\
0.7 & 3.3 & 1,590 & 1,677 & 1,692 & 1,711 \\
10 & 3.3 & 1,578 & 1,657 & 1,671 & 1,687 \\
50 & 3.3 & 1,581 gateway is served as the _BS_ and located in the center of the monitoring area. Simulation results are presented as follows. Figure 8 shows the number of active sensor nodes _versus_ the simulation rounds. In the case I, the LEACH and the LEACH-Coverage-U protocols lose their first node around the 600\({}^{\text{th}}\) round. The proposed ECHR protocol is able to maintain all sensor nodes alive till the 1,500\({}^{\text{th}}\) round, which is approximately 2.5 times longer than those generated by the LEACH and the LEACH-Coverage-U protocols. Moreover, the lifetime of first node that runs out of its energy using the proposed ECHR protocol is longer than those using the LEACH and the LEACH-Coverage-U protocols in the case II. By contract, using the ECHR protocol, after the first node runs out of energy, the number of the active nodes sharply falls. This is because the proposed ECHR protocol is able to equalize the energy consumption over the entire network. Furthermore, by maintaining nodes surviving longer time when relaying data, the energy consumed in transmission can be significantly reduced. Hence, using the proposed ECHR protocol guarantees the WSN with high coverage precedence when applying the WSN to specific mission-critical areas, such as military surveillance and e-health care. Figure 9 depicts the coverage ratio _versus_ the simulation rounds. The proposed ECHR protocol performs relatively well when comparing to the LEACH and the LEACH-Coverage-U protocols. In the case I, for example the ECHR protocol maintains 100% coverage ratio until the 1,590\({}^{\text{th}}\) round, but the coverage ratios of LEACH protocol and the LEACH-Coverage-U protocol drop from 100% at the 802\({}^{\text{th}}\) and the 856\({}^{\text{th}}\) round, respectively. In other words, compared to the LEACH and the LEACH-Coverage-U protocols, the proposed ECHR protocol provides 98.3% and 85.7% increase in service time with a 100% sensing coverage ratio. The ECHR protocol also outperforms other protocols in the case II, and its network lifetime can be extended to nearly 1,250 rounds. Figure 8: Comparison of the active nodes of the proposed ECHR protocol with those of other protocols.