## 3 System Model and Problem Formulations
### Advanced Load Balancing Scheme Based on Optimized GA
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **CAGA** & **PAGA** & **GA** \\ \hline
**Crossover** & Two-point crossover & Two-point crossover & Two-point crossover \\ \hline
**Mutation** & Single-point mutation & Single-point mutation & Single-point mutation \\ \hline
**Select** & Tournament & Tournament & Tournament \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameter configuration for GA.

Figure 7: The simulation platform of load balancing for S-IoT-N.



### The Performance of Load Balancing for S-IoT-N and Analysis

In the above-mentioned simulation environment of satellite traffic load balancing, LB-CAGA is compared with the most widely studied integrated weighted access scheme (IWAS). The comparison of load balancing effects of the two schemes is shown in Figure 9.

Figure 8: The performance of improved GA.

Figure 9: The performance of improved load balancing schemes. As we can see from Figure 9, the system throughput of LB-CAGA and IWAS is consistent when the user density of the adjacent F-Sat-Beam is 0.5 and 0.6. When the user density of the adjacent F-Sat-Beam is 0.7, and the user density of the target F-Sat-Beam is less than 0.74, the system throughput of LB-CAGA and IWAS is consistent. When the user density of the adjacent F-Sat-Beam is 0.7, and the user density of the target F-Sat-Beam is more than 0.74, the system throughput of LB-CAGA is on average 0.4G higher than that of IWAS. When the user density of the adjacent F-Sat-Beam is 0.8, and the user density of the target F-Sat-Beam is less than 0.62, The system throughput of LB-CAGA and IWAS is consistent. When the user density of the adjacent F-Sat-Beam is 0.8, and the user density of the target F-Sat-Beam is greater than 0.62 and less than 0.82, the system throughput of LB-CAGA is on average 0.4G higher than that of IWAS. When the user density of the adjacent F-Sat-Beam is more than 0.82, the system throughput of LB-CAGA and IWAS is consistent. From the above analysis, we found that LB-CAGA does not achieve more system throughput than IWAS when the user density of F-Sat-Beam is too low or too high but achieves more system throughput when the user density of the F-Sat-Beam is high and still within the capacity of the serving satellite. The reasons are as follows:

When the user density of the F-Sat-Beam is low, the traffic load is still within the capacity of the serving satellite. Both schemes allow for the serving satellite to fully accommodate all user traffic. Consequently, the system throughput of both schemes is the same as the total traffic load. When the user density of the F-Sat-Beam is too high, the traffic load exceeds the capacity of the service satellite. Neither of the two schemes can make the serving satellite bear more traffic load. As a result, the system throughput of both schemes is the same as the capacity of the serving satellite. When the user density of F-Sat-Beam is high but still within the capacity of serving satellite, LB-CAGA can improve the total throughput of the system to a certain extent and maximize the efficiency of the satellite system. Under this condition, LB-CAGA has a better load-balancing effect than IWAS. ## 6 Conclusions

This paper proposes a novel load balancing scheme of adjacent beams for S-IoT-N based on the modeling of spatial-temporal distribution of users and advanced GAs. The main conclusions are as follows:

(1) We modeled the PDF of DoU in the direction of movement of SSP trajectory, which provided a multi-directional constraint for non-uniform distribution users in S-IoT-N. Compared with the existing model with permanent global distribution and pure random distributions, the proposed model can characterize the PDF variances of DoU more correctly in the scenario of a highly dynamic satellite.