## 4 Simulation
### Results and Analysis  
Two simulations were carried out, including the cases of uniform and nonuniform traffic distributions. Under a uniform traffic distribution, the traffic intensity of each cell was the same. Under a nonuniform traffic distribution, the traffic intensity of each cell was different. Figure 3 shows the comparison results of the four channel allocation algorithms under a uniform traffic distribution with different traffic intensities. It can be seen from Figure 3 that the performances of the different channel allocation algorithms decreased with an increase in the traffic intensity. In terms of the total performance, the RDCA was better than the FCA because the RDCA dynamically allocated eligible channels. The TSCA and SARSA were better than the RDCA. The reason was that RL can learn how to select and perform the actions from a continuous interaction with the environment; thus, the TSCA and SARSA could allocate more appropriate channels to the calls. The rejection probability of a new call with the TSCA was higher than SARSA. That was because the TSCA allocated more eligible channels to the handoff calls and the remaining eligible channels for the new calls were reduced. The rejection probability of a handoff call with the TSCA was much lower than that of the other algorithms. That was because the TSCA made full use of the temporal-spatial correlation of the handoff calls and allocated the eligible channels to the handoff calls. The rejection probabilities of a total call of the TSCA and SARSA were almost the same because they all performed optimal actions in real-time to allocate appropriate channels. Figure 4 shows a case of a nonuniform traffic distribution. The numbers in the hexagons were the traffic distribution proportions of each cell. Value 1 represented the standard traffic distribution proportion and its traffic intensity was equal to 5. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Description** & **Value** \\ \hline \(\alpha\) & Learning rate & 0.019389 \\ \(\delta\) & Decay factor of \(\alpha\) & 0.999999 \\ \(\gamma\) & Discount factor & 0.845 \\ \(\varepsilon\) & Exploration factor & 0.8 \\ \(N\) & The number of cells & 49 \\ \(K\) & The number of channels & 70 \\ \(r\) & The radius of cell & 450 km \\ \(v_{s}\) & The velocity of satellites & 7 k/s \\ \(1/\mu\) & Call duration & 3 min \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter settings of the simulation. Figure 3: Performance comparison under uniform traffic distributions. (**a**) The rejection probability of the new call; (**b**) the rejection probability of the handoff call; (**c**) the rejection probability of the total call. Figure 5 shows the comparison results of the four channel allocation algorithms under a nonuniform traffic distribution with different traffic intensities. It can be seen from Figure 5 that the performances of the different channel allocation algorithms decreased with an increase in the average traffic intensity. The performances of the four algorithms under a nonuniform traffic distribution were generally worse than that under a uniform traffic distribution. Figure 4: Nonuniform traffic distribution in cells. Figure 5: _Cont_. The performance of the same algorithm under different traffic distributions can be seen in Figures 3 and 5. It can be seen from Figures 3a and 5a that the advantage of a dynamic channel allocation was clearly reflected under a nonuniform traffic distribution. For instance, the rejection probability of a new call of the FCA was 2.4% higher than that of a uniform traffic distribution and the RDCA was 1.5% higher than that of a uniform traffic distribution at 10 Erlangs. In other words, the rejection probability of a new call of the FCA under a nonuniform traffic distribution was 19.98% higher than that under a uniform traffic distribution at 10 Erlangs and the rejection probability of a new call of the RDCA under a nonuniform traffic distribution was 12.74% higher.