# Service-Driven Dynamic Beam Hopping with Resource Allocation for LEO Satellites
## 4 Simulation Results and Analysis
### Performance Comparison and Analysis  
To verify the long-term throughput performance of the algorithm in the multi-agent system applied in this paper, we tested scenarios with 100 time slots and different traffic demands. Figure 10 shows the relationship between the long-term throughput performance under different methods and different traffic demands. From the figure, we can observe that the performance of the algorithm in this paper outperforms other algorithms. Compared with the RBH, PBH, DF-BH and DQN, the long-term throughput of the algorithm in this paper increases by 30.3%, 22.7%, 13.9%, and 9.5%, respectively. The GA-BH also seeks the optimal solution in the entire action space, so its throughput performance is superior compared to other algorithms. However, due to its high computational complexity, the algorithm in this paper still has an advantage. When the system-provided capacity fails to meet traffic demands, specifically in scenarios where the normalized traffic volume exceeds 100%, the system throughput growth of other algorithms tends to stabilize. Under such conditions, the performance of the MARL-VDN algorithm in terms of system throughput is still significantly better than that of other algorithms. Figure 9: Episode total power consumption under optimization weight \(\alpha=0.5\). Similarly, we tested scenarios with 100 time slots and different traffic demands. Figure 11 shows the average packet queuing transmission delay of each method under different traffic demand scenarios. From the figure, we can observe that as the traffic demand increases, the average delay of all algorithms shows an upward trend. Compared with the RBH, PBH, GA-BH, DF-BH, and DQN, the average packet delay of the algorithm in this paper is reduced by 72.6%, 67.8%, 37.6%, 13.9%, and 23.2%, respectively. When the traffic demand exceeds the system capacity, the growth rate of the average delay of the algorithm in this paper is also relatively low. Compared with other algorithms, it can better adapt to different traffic demand scenarios and effectively control the average packet transmission delay. To verify the performance of the algorithm applied in this paper in the LEO beam hopping satellite communication system, we conducted tests based on historical service data. The throughput allocation for each ground beam position is shown in Figure 12. It can be seen that the throughput allocated to each beam position is highly compatible with the traffic demand, indicating that the algorithm in this paper can achieve on-board resource allocation on demand and avoid resource waste. The user satisfaction of the ground beam positions is shown in Figure 13. It can be seen from the figure that the user satisfaction level is high and stable, indicating that the algorithm in this paper can continuously guarantee users' experience in complex service scenarios. The packet delay performance of ground beam positions is shown in Figure 14. It can be observed that the average packet delay across beam positions is approximately 5.6 ms, which meets the real-time traffic requirements of LEO satellite communication. The above-mentioned  
Figure 11: Delay fairness versus normalized traffic demand with \(\alpha=0.5\). Figure 10: Long-term system throughput versus normalized traffic demand with \(\alpha=0.5\). of an overly large action space in traditional reinforcement learning but also ensure the convergence of the algorithm and the feasibility of the system. Under the MARL-VDN algorithm framework, we construct a multi-objective optimization model for beam hopping patterns and power allocation decision making, aiming to simultaneously maximize user satisfaction and minimize packet transmission delay. During training, agents continuously optimize strategies by interacting with the environment and learn cooperatively with each other to jointly improve the system's performance.