## 5 Numerical Results
### Simulation Results  
Figure 8 shows the throughput rates of the five classes of algorithms (in Figures 8 and 9, VFL denotes variable frame length), and it can be clearly seen that the three classes of algorithms in this section have stable and high throughput rates when the arrival rate is greater than 100%, which is much greater than that of the IRSA algorithm and the Slotted ALOHA algorithm. The throughput of the algorithms with SIC is also better than that of the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of ACNs & 1 \\ Number of pieces of SUE & 220 \\ Frame duration & 44 ms \\ Slot duration & 4 ms \\ Minislot duration & 0.2 ms \\ Data packet duration & 4 ms \\ Access packet duration & 0.2 ms \\
2-copy probability & 0.5 \\
3-copy probability & 0.28 \\
8-copy probability & 0.22 \\ Initial estimated SUE arrival rate & 1/22 \\ Initial estimated access probability & 1 \\ Maximum iteration count & 200 \\ Simulation duration & 20,000 ms \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameter design. algorithms without SIC, and by introducing the serial interference technique, this section succeeds in increasing the original maximum throughput rate from about 37% to 70%. Meanwhile, it can be seen that the stability of STCA with variable frame length can be guaranteed, and different algorithms can be selected according to the different capabilities of equipment: if more attention is paid to fairness and the performance of the air access control equipment is better, then STCA with variable frame length can be selected; if it is only hoped to maximize the utilization of the channel, then STCA with SIC can be selected; if the performance of the air access control equipment is more general, then STCA without SIC can be selected. The three algorithms achieve the desired goal of maximizing the service channel utilization of the satellite, although they are implemented in different ways. Figure 9 presents a comparison of the TTC channel utilization for four different algorithms. The traffic load of 1000% refers to a scenario where the number of arriving packets is 10 times the maximum capacity of the TTS channel, used to verify the robustness of the proposed STCA protocol under extreme overload conditions. In Figure 9a, neither of the algorithms uses the SIC algorithm, while in Figure 9b, both algorithms implement SIC. In Figure 9c,d, two algorithms that implement SIC are compared with the commonly used algorithms. As shown, both algorithms achieve the theoretical results derived in the analysis. When the traffic load is less than 100%, TTC channel utilization grows almost linearly with the traffic load. This indicates that when the traffic load is below 100%, the ground terminals are able to promptly send their access requests to the satellite, and during the 20 s simulation, nearly all of the traffic data reach the receiving satellite. Under the same conditions, if a Slotted ALOHA algorithm is used, a large number of data packets remain in a retransmission state. Similarly, if IRSA is used, as shown in Figure 9b, a large number of data packets are still in a retransmission state when the traffic load is between 80% and 100%. Specifically, when the traffic load is 100%, about 40% of the data packets fail to reach the satellite terminal. When the traffic load exceeds 100%, it can be observed from both figures that TTC channel utilization approaches 100%, indicating that the system efficiently utilizes the limited satellite communication channel while minimizing the delay for the ground terminals. Under the same conditions, with IRSA, TTC channel utilization remains almost constant at 20%. In high-traffic-load scenarios, about 80% of the channel resources are wasted, which is unacceptable. This observation underscores the efficiency of the two algorithms designed in this study. Figure 8: Throughput rate comparison. To assess the system's stability, this section evaluates the TTC channel utilization over varying system operational times.