# A Beam Hopping Scheme Based on Adaptive Beam Radius for LEO Satellites
## 4 Presentation and Analysis of Simulation Results  
In this chapter, we will list all of our simulations that aim at examining the proposed algorithm in different aspects that can cause different system performance, and then visualize the results. At the end of every simulation, we will analyze and explain the results  
Comparison of Proposed and Traditional Algorithm in Constructed Scene That Defined in User Distribution Model  
In this simulation, we make a comparison between the traditional and proposed algorithms in the model constructed in Section 3.7. In addition, we change the delay sensitivity factor that is beneficial to reduce system delay to examine the proposed and traditional algorithm's performance. Figure 8 illustrates the performance of the two algorithms based on the constructed model. The pink dots represent the system performance metrics obtainedby the proposed algorithm, while the blue dots represent the system performance metrics obtained by the traditional algorithm. It can be observed that with the adoption of the proposed algorithm, there is a 3.44% improvement in system throughput, and the system delay is reduced by 35.5% compared to a delay factor of 2. Based on these results, further experiments were conducted to reduce system delay by increasing the delay sensitivity factor and examining the loss of system throughput.  
According to the experimental data, it is observed that when the delay sensitivity factor is 1, the system delay is reduced by 58.54%, and throughput is increased by 2.77%. When the delay sensitivity factor is 3, the system delay is reduced by 35.29%, and throughput is increased by 5.31%. When the delay sensitivity factor is 4, the system delay is reduced by 38.93%, and throughput is increased by 8.17%.  
Figure 9 depicts the delay distribution of all delay users under three delay factor scenarios. It can be observed that when the delay sensitivity factor is 2, the delay distribution range of delay users is very wide, ranging from 0 to 800. However, when the simulation adjusts the delay factor to 5, the delay distribution range of delay users is narrowed, with no users having a delay greater than 600. However, the number of low-delay users also  
Figure 8: Comparison of total delay and throughput between the proposed and traditional algorithms in the constructed Scenario.  
decreases. This indicates that the increase in the delay factor sacrifices the QoS of hot spot area users while improving the QoS of non-hot spot area users, especially those adjacent to hot spot areas. When the delay factor is increased to 4, the delay distribution range is further compressed. However, the performance improvement in delay at this point is not as significant as it was when the delay factor increased from 2 to 3. This is because the satellite cannot serve all users at all times. Under the current service conditions, there is inevitably a minimum total delay greater than 0, and it becomes increasingly difficult to improve the delay performance as it approaches this value.  
Furthermore, in the three subplots of Figure 9, the blue bars represent the distribution of user delays after applying the proposed algorithm, while the orange bars represent the distribution of user delays based on the traditional algorithm with different delay sensitivity factors. From the distribution of the blue bars compared to the orange bars, it can be inferred that the proposed algorithm, compared to the traditional algorithm, can reduce the number of high-delay users, thereby reducing the total system delay.