## 5 Performance Evaluation
The data report ratio \(\zeta\) can be formulated by the Expression (42):  
\[\zeta=p_{success}\ /\ P_{total} \tag{3}\]  
In the _Fixed_ approach, the neighboring sensors of the fixed sink will exhaust their energies prior to other sensors. Once these sensors fail, no sensor can directly communicate with the fixed sink, resulting in network partition. As a result, as shown in Figure 8, the _Fixed_ curve sharply drops when the neighboring sensors of the fixed sink fail. The _Angle-based_, _RMDC_, and _EBDC_ approaches employ mobile sink to collect data. By applying these three approaches, the readings generated by sensors can always be forwarded to mobile sink since these three schemes maintain the network connectivity using mobile sink. Consequently, the data report ratios of _Angle-based_, _RMDC_, and _EBDC_ keep constant values. However, the proposed _EBDC_ mechanism guarantees no coverage holes appeared in the monitoring region while the _Angle-based_ and _RMDC_ approaches result in coverage holes, as shown in Figure 7.  
**Figure 8.** Comparison of _Fixed_, _Angle-based_, _RMDC_, and _EBDC_ in terms of data report ratio \(\zeta\). Figure 9(a,b) investigate the total energy consumptions required for sensors located in the boundary track (track \(k_{n}\)) and center track (track \(k_{1}\)), respectively. We randomly select a _boundary sensor_ and a _central sensor_ that are located in the boundary and center tracks, respectively, and then observe their energy consumptions. The _Fixed_ approach deploys a fixed sink located at the central point of the monitoring region. This implies that the selected boundary sensor only needs to deliver its reading to its neighbor without any packet forwarding workloads. Hence, as shown in Figure 9(a), the _Fixed_ scheme has better performance than the other three compared approaches. However, as shown in Figure 9(b), the _Fixed_ scheme has the worst performance since sensors closer to the fixed sink would have much higher data-relaying workloads. By applying the _RMDC_ approach, the mobile sink always moves along the boundary track to collect data. Consequently, the boundary sensor has much higher data-relaying workloads while the central sensor only needs to deliver its reading without any packet forwarding workload. As a result, the _RMDC_ has the best performance in Figure 9(b) and the worst performance in Figure 9(a). In the proposed _EBDC_ and _Angle-based_ approaches, both selected boundary and central sensors will be visited by mobile sink. Therefore, the performances of the proposed _EBDC_ and _Angle-based_ approaches in Figure 9(a,b) are between the _Fixed_ and _RMDC_ approaches. In particular, since the proposed _EBDC_ mechanism takes into consideration the factor of energy balancing, the performance of _EBDC_ is better than that of _Angle-based_ scheme, as shown in Figure 9(a,b). Figure 10 compares the proposed _EBDC_, _Fixed_, and _RMDC_ approaches in terms of the degree of energy balancing. Without loss of generality, we investigate the average energy difference between the central and boundary sensors. The average energy differences of the _Fixed_ and _RMDC_ approaches are increased with the elapsed days. This is because the two sinks applying the _Fixed_ and _RMDC_ approaches execute the data collection task in the center and boundary tracks, respectively. The data-relaying workloads of _Fixed_ and _RMDC_ approaches are hence concentrated on the central and boundary sensors, respectively, leading to an energy-unbalance problem. In the proposed _EBDC_ mechanism, the data-relaying workloads of all sensors can be totally balanced in each round. Therefore, as shown in Figure 10, the average energy difference of the proposed _EBDC_ mechanism periodically drops to 0 Joule when the mobile sink completes the data collection task in each round. Figure 9: Comparison of _Fixed_, _Angle-based_, _RMDC_, and _EBDC_ in terms of energy consumption. (**a**) The energy consumption of a randomly selected boundary sensor; (**b**) The energy consumption of a randomly selected central sensor.