## 3 Problem Description  
The objective of this paper is to optimize the utilization of TTS. Since random access is not performed in TTS, no collision slots occur. Moreover, as the throughput \(S\) of CAS per unit time increases, the probability of idle slots in TTS decreases, leading to increased channel utilization. Therefore, the optimization goal is transformed into maximizing the throughput \(S\) of CAS per unit time. In a random competition scenario, the throughput \(S\) of the channel per unit time and the channel load \(G\) follow the following equation:  
\[S=Ge^{-G}. \tag{2}\]  
This paper considers two scenarios: one in which the ACN can only support random competition and another in which the ACN supports Serial Interference Cancellation (SIC) capability. The Successive Interference Cancellation (SIC) algorithm effectively enhances the capacity and spectral efficiency of multi-user systems by progressively eliminating interference in received signals. In SIC, each ground terminal generates multiple copies of each burst packet, which are transmitted in arbitrary slots of a frame. As shown in Figure 4, u1-u6 represent the burst copies of six users. Notably, only the third slot in the first frame contains a single burst (u3), referred to as a \"clean slot\" in this paper. All other slots contain two or more packets, which would be considered collisions in the Slotted ALOHA protocol--resulting in packet discarding and slot waste. With SIC, u3 can be decoded first. By identifying the other copy of u3 in slot two, Successive Interference Cancellation eliminates the u3 signal from slot two, converting it into a clean slot and recovering u2. Using the recovered u2 signal, the u1 signal in slot one can then be extracted. This process continues iteratively until all decodable signals are recovered. Users u4 and u5, however, remain mutually overlapped and deadlocked, requiring retransmission in the next frame. The retransmission here can refer to the distributed queueing method in [10] and the distributed queuing random access protocol in [11], which can further improve system performance. Similar to the approach in [12], where distributed queueing was introduced into the LoRa network, a similar method could be considered here. Considering that the increase in complexity would further increase the delay, this paper employs a random backoff mechanism for retransmissions instead. Compared with Slotted ALOHA, this approach reutilizes many burst packets that would otherwise be discarded, significantly improving the channel utilization of satellite communication networks and reducing latency. This process is termed SIC; however, its high computational complexity mandates that access control nodes possess robust processing capabilities. For systems that do not use the SIC algorithm, the optimization goal is  
\[P1:maxS=max\bigg{(}\frac{M_{i}P_{i}}{N_{C}}e^{-\frac{M_{i}P_{i}}{N_{C}}}\bigg{)}. \tag{3}\]  
In systems where the SIC algorithm can be used, each piece of SUE generates \(l\) copies during access and randomly transmits these \(l\) copies in \(N_{C}\) minislots. The probability distribution of \(l\) is expressed as follows:  
\[\Lambda(x)=\Lambda_{1}x+\Lambda_{2}x^{2}+...+\Lambda_{N_{C}}x^{N_{C}}, \tag{4}\]  
where \(\Lambda_{l}\) is the probability that the SUE generates \(l\) copies. Each copy contains a pointer to the locations of the other copies. When a minislot is in a successful state, the pointer of the copy finds the locations of the other copies selected by the SUE. Then, the SIC algorithm is used to recover the user's data packet. This method can convert a large number of collided minislots into successful minislots. Figure 4 is a schematic diagram of the SIC decoding process. The gray squares represent successful minislots, the white squares represent collided minislots, the gray circles indicate that the SUE has successfully gained access, and the white circles indicate that the SUE has not gained access. In [7], the SIC algorithm has an access load threshold \(G^{*}\).