## 6 Experimental Section  
In this section, we evaluate our algorithm using synthetic traces. In this trace, we repeat our experiments using a different number of UGVs which have four, six, and eight UGVs, respectively. The duty cycle of each UGV is randomly generated in Matlab. To eliminate excessive instances, we give a range as the reference of duty cycle generation. For example, in Figure 8, the range is from 5 to 30. It shows the case of six UGVs (represented by the circles) and cycles as indicated beside the circle. For simplicity, all the time are set to begin from 0. The number on the edge stands for the traveling time between surfacing locations of two UGVs. It is related to the distance and other geographical facts. In the experiments, the UGVs are randomly deployed in an \(x\times x\) square, where \(x\) is equal to half of the upper bound of the duty cycle range. In Figure 8, the square is \(15\times 15\). All the algorithms are implemented in Matlab. We run four algorithms on this trace that are three-hop, two-hop, one-hop and random, respectively. We compare the results with the optimal solution. The cycle of each UGV abides by the Gaussian distribution. Each UGV will generate a data packet per cycle. The optimal solution in Gaussian distribution is based on the graph after each cycle is determined. Figure 7: The demo shows how Algorithm 4 works. In the random algorithm, after visiting a UGV, the mobile sink will randomly choose the next destination. The one-hop algorithm will consider all neighbors of current visiting UGVs and choose the one with the test waiting time as the next destination. Note that it is not the shortest in distance but the nearest in time for the next surfacing. The two-hop algorithm will consider the two-hop situation that will have higher costs but will bring higher efficiency. The three-hop algorithm is too costly in the practice case so it is not included in the simulation. We run the simulation along the time scale, and Figure 9 shows the collected messages vs time. In general, the random algorithm shows the lowest performance, which is only about 65% that of the two-hop algorithm. Because the one-hop algorithm has a limited view of scheduling possibility, it may choose the wrong next hop so that its performance is only better than the random algorithm. The two-hop algorithm has much better performance than the previous two. It achieves around a 7% increment compared to the one-hop algorithm. The three-hop algorithm is only 5% better than the two-hop algorithm in the ideal case. From Figure 9a, there is limited space between the three-hop algorithm and the optimal algorithm so that any algorithms that consider more hops will get very limited performance improvement but with tremendous cost. In the ideal case, since each cycle is absolutely fixed, the increment of collected data is stable. Therefore, the lines are almost linear. In the practice case as shown in Figure 9b, there are a lot of variations during the collection process and the gap between curves are bigger than that in the ideal case. However, the trend of each line is similar in both cases, and the gap is getting bigger along the time scale. Since each UGV has a different surfacing schedule, the one with the longer cycle will appear less times. Figure 10 shows the distribution of a number of successful collected data for each UGV (eight UGVs in total). In the figure, we could find out how many times a UGV is visited during a time period. In both figures, the random algorithm shows an unpredictable distribution. It visits \(h\) a lot despite the fact that \(h\) has the longest cycles. The one-hop algorithm has a similar pattern with that of the optimal algorithm, but it spends too much time on \(h\). The two-hop has the same problem, but it gives more visits to the \(a\) and \(b\). In terms of the optimal algorithm, UGVs with shorter cycles are visited more frequently than those that have longer cycles. From the simulation, we draw a conclusion that the more hops we consider, the better performance we will get.