# Cooperative Data Collection Mechanism Using Multiple Mobile Sinks in Wireless Sensor Networks
## 5 Performance Evaluations
By applying the proposed CDCA, the lifetime of WSN is increased with the number of mobile sinks. The BD-scenario has the longest network lifetime when the number of mobile sink is nine. This occurs because that more mobile sinks can visit more CPs and hence reduce average number of hops from each sensor to the corresponding CP. Since UD1-Scenario, UD2-Scenario and UD3-Scenario have holes which block data transmissions. As a result, the BD-scenario has the best performance in terms of network lifetime. Figure 6 compares the three algorithms in four scenarios in terms of fairness index. Let \(E_{i}\) denote energy consumption of sensor node \(s_{i}\) in each round. The _Fairness Index_ is defined by Expression (22). \[\tau_{fairness}=\frac{(\sum_{i=1}^{n}E_{i})^{2}}{n\sum_{i=1}^{n}E_{i}^{2}} \tag{22}\]  
Figure 4: Comparison of the four scenarios in terms of rendezvous time. Figure 5: Network lifetime for four scenarios in different number of mobile sink. (**a**) \(k=7\); (**b**) \(k=9\). As shown in Figure 6, the fairness indexes of three approaches, including CDCA, HiCoDG and BRPA, are compared. The BRPA approach partitions the monitoring region into several equal sub-regions and assigns each mobile sink to collect all sensors in each subregion. Since different sub-regions have different number of sensors, it has smaller fairness index value. In HiCoDG, the balance of the number of nodes in clusters is not considered. Furthermore, the distance from the current cluster-head to the next CP is not considered. Therefore, more overheads are needed for travelling from one CP to another one. As a result, fewer CPs can be joined, leading to a larger hop distance from each sensor to the corresponding CP. The proposed CDCA determines more CPs and distributes the workloads of data forwarding to them. Hence the fairness index of CDCA keeps to a constant value which is closed to 1 in all cases. In general, the proposed CDCA outperforms HiCoDG and BRPA schemes in terms of fairness index in all cases. The standard deviation (SD) of the energy consumption of each sensor node was measured using Equation (23). \[\mathrm{SD}=\sqrt{\frac{\sum_{1}^{n}\left(E_{x}\ -\ E_{avg}\right)^{2}}{n}} \tag{23}\]  
where \(E_{x}\) denotes energy consumption of sensor node \(s_{i}\) and \(E_{avg}\) denote average energy consumption of sensor node. A small SD value indicates that the network lifetime is long. Figure 7 further investigates the effects of the numbers of sensor nodes and mobile sinks on the SD value in four scenarios by applying three mechanisms. The number of sensor nodes was varied ranging from 300 to 800, and the number of mobile sinks was set ranging from 2 to 10. In general, the SD value is decreased with the number of sensor nodes. The BRPA yielded the largest SD value among the three compared mechanisms because the node balance in each subtree was not considered. For the HiCoDG scheme, multiple mobile sinks cooperate with each other to collect and relay data, resulting in a lower SD value, as compared with the existing BRPA. However, the SD value of the HiCoDG scheme was higher than that of the proposed CDCA mechanism. This occurs because it did not consider the node balance factor in each cluster. Moreover, the distance from the current cluster-head to the next cluster-head is not considered when constructing the path. The proposed CDCA mechanism partitions the sensor nodes into several disjoint subsets, and further selects as more as possible CPs in \(T_{i}\). Then CDCA constructs a path \(\tau_{i}\) passing through all CPs and collects data from higher burden CPs in each subset. After that, the CDCA further applies the speed control mechanism to maintain a stable  
Figure 6: Fairness index. (a) \(k=7\); (b) \(k=9\). rendezvous time point for global mobile sinks \(m_{0}\) and each mobile sink \(m_{i}\). As a result, the proposed CDCA mechanism yielded the lowest SD value, as shown in Figure 6.  
Let \(\zeta_{efficiency}\) represent the efficiency index equal to the average length cost multiplied by the resource unused rate.