## 5 Performance Evaluation
As a result, the network lifetime of _Fixed_ approach is much shorter than those of the _Angle-based_, _RMDC_, and _EBDC_ approaches. In the _RMDC_ approach, since the mobile sink always moves along the outmost (boundary) track, the number of sensors which can be visited by the mobile sink is smaller than those of _Angle-based_ and _EBDC_ approaches. Hence, the network lifetime of the _RMDC_ approach is shorter than those of _Angle-based_ and _EBDC_ approaches. By applying the _Angle-based_ approach, the mobile sink traverses the edges of each fan belonging to odd or even sets one by one, as shown in Figure 5(a,b), respectively. Therefore, the number of sensors which can be visited by the mobile sink is obviously larger than that of _RMDC_ approach. Applying the proposed _EBDC_ approach, the mobile sink moves with a well established schedule and hence the data-relaying workloads are shared by all sensors. Consequently, the performance of _Angle-based_ is worse than _EBDC_. In general, as shown in Figure 6(a), the average network lifetime of the proposed _EBDC_ mechanism is approximately five times longer than that of the _Fixed_ approach, 1.6 times longer than that of the _RMDC_ scheme, and 1.2 times longer than that of the _Angle-based_ approach. On the other hand, as shown in Figure 6(b), the average network lifetime of the proposed _EBDC_ mechanism is approximately three times longer than that of the _Fixed_ approach, 2.2 times longer than that of the _RMDC_ scheme, and 1.2 times longer than that of the _Angle-based_ approach. Figure 7 further measures the monitoring quality when the coverage hole appears. It compares the proposed _EBDC_, _Angle-based_, _Fixed_, and _RMDC_ approaches in terms of the coverage ratio \(\sigma\). Let \(A_{\textit{cover}}\) denote the area size which is covered by sensors in the monitoring region. Let \(A_{\textit{M}}\) denote the area size of the monitoring region. The coverage ratio \(\sigma\) can be formulated by the Expression (41):  
\[\sigma=A_{\textit{cover}}\ /\ A_{\textit{M}} \tag{41}\]  
**Figure 7.** Comparison of _Fixed_, _Angle-based_, _RMDC_, and _EBDC_ in terms of coverage ratio \(\sigma\). The four approaches have 100% coverage ratio for 20 days starting from the day that the four approaches are applied. Since the data-relaying workload of the _Fixed_ approach is totally shared by a small number of sensors, the curve of the _Fixed_ approach drops earlier than the curves of the other compared schemes. The coverage ratio of _RMDC_ approach is decreased with the elapsed days. In particular, it is interesting that the _RMDC_ curve has a stair shape. This is because the mobile sink always moves along the boundary track (track \(k_{n}\)) of the monitoring region. Hence, the sensors located in the boundary track simultaneously exhaust their energies. As a result, the _RMDC_ curve drops significantly. After that, the mobile sink will treat track \(k_{n-1}\) as the new boundary track. The coverage ratio of the _Angle-based_ approach is also decreased with the elapsed days. However, in the _Angle-based_ approach, since the number of sensors which share the data-relaying workloads is larger than that of _RMDC_, the _Angle-based_ curve drops slower than _RMDC_ curve. In the proposed _EBDC_ mechanism, the mobile sink moves along trajectory \(J_{m}^{m,s}\) to collect data. As a result, the energy consumptions of all sensors can be balanced and thus the _EBDC_ curve keeps a constant shape. In general, the proposed _EBDC_ mechanism has either 0% or 100% coverage ratios. Figure 8 compares the proposed _EBDC_, _Angle-based_, _Fixed_, and _RMDC_ approaches in terms of the data report ratio \(\zeta\). Let \(p_{success}\) denote the number of packets which are successfully forwarded to the sink. Let \(P_{total}\) denote the total number of packets which are generated by all sensors.