## 5 Simulation
### Comparison with Another Hybrid Scheduling Scheme  
This subsection presents simulations by comparing our proposed LDFM scheme with the hybrid scheduling scheme proposed in [25]. The hybrid scheduling scheme integrates vehicles and drones to allocate charging tasks by dividing the sensing region into three circular subregions (inner, middle and outer rings). Sensor nodes in the inner ring are directly charged by drones from the base station, those in the middle ring are charged by the vehicle and those in the outer ring are charged by drones carried by the vehicle. Notably, the number of drones and a single vehicle is consistent with our proposed scheme. (1) Impact of number of drones mounted on vehicle  
To evaluate the impact of the number of drones mounted on the vehicle, we conducted simulations with drone numbers ranging from 5 to 30 under three traffic loads. The drone speed was held constant at 35 m/s, and the threshold was set to 0.40. The results are presented in Figure 9. As Figure 9a shows, the number of charging request packets increases as the number of drones increases. Notably, under light traffic load, the LDFM scheme generated the same number of charging request packets as the hybrid scheme. However, under medium and heavy traffic loads, the LDFM scheme generated more charging request  
Figure 8: Comparison of the LDFM scheduling scheme under varying numbers of drones: (**a**) number of charging request packets and (**b**) number of nodes being charged in time. packets than the hybrid scheme; in particular, the LDFM obviously performed better under heavy traffic load. Figure 9b demonstrates that the number of nodes charged within a given time increases with the increasing number of drones, and the LDFM scheme obviously outperforms the hybrid scheme because it can charge more nodes within the same time under all three traffic loads. Moreover, from Figure 9c, we can see that the average distance traveled by the vehicle of the LDFM scheme is less than the hybrid scheme under all three traffic loads, which shows that the LDFM scheme wastes less energy on travelling, achieving better charging efficiency. We also note that the average distance under light traffic load is more than under medium and heavy traffic load because the charging requests occur less and dispersedly in one mission under light traffic load but more and densely under heavy traffic load. Specifically, when the number of drones reaches 20, the average distance is kept stable. The performance of the network obtained using the two schemes is improved with an increased number of nodes. The LDFM scheme obviously outperforms the hybrid scheme with respect to number of nodes being charged within the same time and the average distance under medium and heavy loads. Because the longest distance nodes are allocated to the drones, the time spent on one charging circle is less with LDFM. (2) Impact of Thresholds  
This subsection presents simulation results for varying node thresholds (ranging from 0.30 to 0.45) under three traffic loads. Figure 10 displays the performance metrics of both schemes under different thresholds across all three traffic loads. The higher the threshold is, the more frequent the charging requests occur. Similarly, the lower the threshold, although the charging requests generated are fewer, the shorter the residual lifetime of the nodes, making the nodes potentially unable to wait for the vehicles' or drones' charging service. As shown in Figure 10a, when the threshold is set at 0.38, the number of charging request packets and nodes being charged within a given time achieve the peak. In particular, the LDFM scheme generates more charging request packets than the hybrid scheme under heavy traffic load. This means that more nodes in the network with LDFM keep active. Furthermore, in Figure 10b,c, the LDFM scheme outperforms the hybrid scheme in terms of the number of nodes being charged within a given time and the average distance traveled by the vehicle under three different traffic loads.