## 5 Simulation and Results
### Performance of Our Proposed Algorithm  
As mentioned above, LEO communication systems face the challenge of uneven space-time distribution of terrestrial service requirements, and an effective beam hopping strategy should be able to overcome this obstacle. We first simulate in the scenarios of even and uneven traffic distribution in the cells. Specifically, in the scenario of even traffic distribution, the traffic intensity of each cell is similar, which is set as 400 packages. In the scenario of uneven traffic distribution, 20 hotspot cells among the 195 cells have a traffic intensity of 2100 packets, while the traffic intensity of the remaining non-hotspot cells is 210 packets. It is worth noting that, in the scenarios of even and uneven traffic distribution, the sum of the total traffic demand of all cells is roughly the same, but the traffic demand of hot spots in the uneven scenario are about 10 times that of non-hot spots. The comparison simulation results under the two scenarios are as follows. In the two scenarios of even and uneven distribution, the access success rates in the entire beam hopping period are 97.2% and 97.3%, respectively, and the average delays of all data packets are, respectively, 66.06 ms and 52.95 ms. As for the fairness between cells, the variance of the average delay of each cell is quite different in two scenarios, which comes to about 74 and 1188, respectively. The lighting times and demand response of each cell are shown in Figure 7.  
As we can see from the picture, when the demand distribution is relatively even, the number of times that each cell is illuminated in the entire beam hopping period is also very uniform. When the demand distribution is obviously uneven, the beam resources are inclined to the hotspot cells, and the number of times of being illuminated increases significantly, thus leading to an obviously shorter transmission delay in them. Although the demand distribution of the two cases is quite different, under our algorithm, the demand of each cell has been responded to in time. That is to say, the beam hopping scheme we designed can provide on-demand services. Next, we simulate under different traffic intensities to compare the performance of various algorithms. The traffic arrival intensity is set to 400, 500, 600 and 700 packages, respectively, and the system throughput, access success rate, average delay and fairness obtained by each algorithm are compared as shown in Figures 8-11. It is not difficult to observe from the figure that as the traffic intensity arriving at the cell continues to increase, the corresponding system throughput also increases gradually. Before the traffic intensity reaches 600, the growth is approximately linear. When the traffic demand further increases, the advantages of our proposed algorithm over the traditional genetic algorithm gradually emerge, and our algorithm can still maintain a stable throughput growth rate with a large traffic demand. Figure 8: Throughput performance with different algorithms. Figure 7: Comparison of even and uneven traffic distribution. (**a**) Illuminated times under even traffic distribution. (**b**) Demand response under even traffic distribution. (**c**) Illuminated times under uneven traffic distribution. (**d**) Demand response under uneven traffic distribution. In terms of the average access delay of all data packets in the beam hopping period, among the four algorithms, our proposed algorithm obtains the lowest delay, with an average delay of 99.03 ms when the traffic intensity reaches 700 packets. As the traffic demand increases, the average delay obtained by the polling-BH algorithm is steadily about 33% higher than our algorithm, while the growth rate of the delay obtained by the GAWIC-BH algorithm is gradually increasing. When the demand is small, the delay obtained by the GAWIC-BH algorithm is about 9% higher than that of our algorithm, and when the intensity reaches 700, the delay obtained by the GAWIC-BH algorithm reaches 167 ms, which is about 68% higher than our algorithm.