## 5 Simulations
### Performance Evaluation of the ECHR Protocol under Varying Weighting Coefficients  
The main goal of this simulation is to evaluate the performance of the ECHR protocol when applying it to a network with different weighting factors. The lifetime of the network with a full sensing coverage ratio achieved by using the ECHR protocol is also investigated. These factors are used to select a root node in each round and determine an energy-efficient route for each node. The framework of the divide and conquer method [26] is borrowed to dissect the proposed ECHR protocol. The first part of simulation is to find optimal weighting coefficients of Equation (4), \(\tau_{1}\) and \(\tau_{2}\), in the root node selection mechanism. In the second part of simulation, the effects of the parameters of Equation (7) are identified in the energy-aware hierarchical routing mechanism, \(\lambda_{1}\) and \(\lambda_{2}\). In the first part of simulation, a same network model is setup as mentioned above. The network with 100 nodes is deployed in an area of 50 \(\times\)50 m\({}^{2}\). In order to study the effect of weighting coefficients on the residual energy factor and the coverage factor in Equation (4), \(\lambda_{1}\) is set at 0.7 while \(\lambda_{2}\) is set at 3.3. Figure 4 shows three-dimensional plots of the lifetime of the network with a 100% sensing coverage ratio _versus_\(\tau_{1}\) and \(\tau_{2}\). After examining the simulation results, it is found that the optimum value of network lifetime with a 100% sensing coverage ratio can be obtained when \(\tau_{1}=1\) and \(\tau_{2}=3.1\). Figure 5 shows the coverage-lifetime comparison under varying \(\tau_{1}\) when set \(\tau_{2}\) is set at 3.1. The coverage-lifetime demonstrated in Figure 5 is the network lifetime when 100%, 95%, 90%, and 80% of network coverage is preserved, respectively. When \(\tau_{1}=1.0\), the network lifetime can provide a full sensing coverage over other \(\tau_{1}\) values. In this case, if the root node selection does not take the residue energy into account (_i.e._, \(\tau_{1}=0\)), the redundant nodes will always be chosen as the root node and their  
Figure 4: Plot of network lifetime with 100% sensing coverage _versus_\(\tau_{1}\) and \(\tau_{2}\) when \(\lambda_{1}=0.7\) and \(\lambda_{2}=3.3\). energy will run out fast. Under this circumstance, however, the data collected by active nodes needs to be transmitted for a long distance, because fewer intermediate nodes are used to transmit data. As a result, the active nodes run out of energy more quickly. On the contrary, the proposed root selection mechanism puts an emphasis more on energy-balancing than the coverage factor does when \(\tau_{1}\) is set at a large value, say 50. Such a situation leads to a scenario that the redundant node might not be chosen as the root node, network lifetime with a full sensing coverage may not last longer. Figure 6 shows the coverage-lifetime comparison results under different values of \(\tau_{2}\) when setting \(\tau_{1}\) at 1.0. When the sensing coverage is 100%, the network lifetime is the longest, if \(\tau_{2}=3.1\). In this case, the coverage factor in the root node selection is not taken into account (_i.e._, \(\tau_{2}=0\)). Such a situation is similar to the scenarios where \(\tau_{1}\) is set at a large value, as mentioned above. Moreover, the impact of the coverage factor on the root node selection mechanism is greater than that of the residual energy factor if \(\tau_{2}\) is set at a large value, e.g., 50. In this circumstance, the performance of the network is similar to the case where \(\tau_{1}=0\). In addition, we analyze the effects of varying weighting coefficients of the distance factor, \(\lambda_{1}\), and the residual energy factor, \(\lambda_{2}\), of Equation (7) on the energy-aware hierarchical routing algorithm. Figure 7 shows three-dimensional plots of the network lifetime with a 100% sensing coverage _versus_\(\lambda_{1}\) and \(\lambda_{2}\), when \(\tau_{1}=1\) and \(\tau_{2}=3.1\).