## 2 Composition of LEO Satellite Network and APINT Model
### APINT Model
#### 2.3.4 Integrated Network Telemetry  
Based on passive telemetry, active telemetry, and the reporting process, along with the time constraints of inter-satellite transmission time and available SGLs intervals, an APINT model is proposed. The telemetry and reporting process of APINT is illustrated in Figure 2.  
When the service starts its transmission, the INT packet is placed in the header of the service packet for passive telemetry. At the same time, the target node sends active telemetry packets in the reverse direction along the service transmission path, towards the source node. During the transmission process, each node can perform metadata writing operations. Then, the INT packets and active telemetry packets converge at a certain node along the path, and the awareness information is integrated on the satellite and transmitted back to the ground along the SGL, while the service continues to transmit along the path to the target node. To avoid impacting the normal transmission of service, the arrival time of active telemetry packets sent in the reverse direction at the aggregation node should be earlier than the arrival time of the service, which means the selection of aggregation nodes on the awareness path is subject to the time constraints, as follows:  
\[\sum_{i=S_{a}}^{S_{r}-1}t_{\text{op}}^{i}>\sum_{j=S_{r}}^{S_{b}-1}t_{\text{ gap}}^{i}, \tag{6}\]  
where \(S_{r}\) is the aggregation node, with \(S_{r}\in P_{z}\). \(S_{a}\) is the source node and \(S_{b}\) is the target node. Multiple nodes may satisfy the above constraints, and these nodes are all potential selectable reporting nodes, denoted as \(S_{R}=\{S_{r1},S_{r2},\ldots,S_{rP}\}\). The time for the awareness data arrives at the potential reporting nodes is:  
\[T_{R}^{S_{rp}}\ =\sum_{i=S_{a}}^{S_{rp}-1}t_{\text{op}}^{i},i\in P_{z},S_{rp} \in S_{R}. \tag{7}\]  
However, due to the dynamic and unstable characteristics of the SGLs within satellite networks, only the potential reporting nodes capable of establishing stable SGLs are able to report awareness data. Furthermore, by combining the available SGL intervals of potential reporting nodes, it is possible to determine whether the awareness data can be reported. In this case, three situations exist:  
1. If the awareness data arrive at the potential reporting node before the establishment of the SGL, the awareness data must wait on the satellite until the SGL is successfully established, then the data can be transmitted back to the ground. 2. If the awareness data arrive at the potential reporting node within the visible link time range of the SGL, and there are no issues of link disconnection during the transmission period, the awareness data can be directly transmitted back to the ground. 3. If the awareness data arrives when the SGL is already disconnected, the awareness data must wait on the satellite until the next available SGL is established for transmission [21], which results in significant reporting delays. In summary, the time taken for the awareness data to ultimately reach the gateway station is:  
\[T_{\text{final}}^{S_{rp}}=\left\{ \begin{matrix}\begin{matrix}\text{f}_{r}^{S_{ rp}}+t_{\text{re}}^{S_{rp}},\text{ if }T_{R}^{S_{rp}}<\text{f}_{s}^{S_{rp}}\\ t_{\text{re}}^{S_{rp}}+T_{R}^{S_{rp}},\text{ if }\text{f}_{s}^{S_{rp}}<\text{f}_{s}^{S_{ rp}}<\text{f}_{e}^{S_{rp}},\text{ }\text{$\forall$}\text{S}_{rp}\in\text{S}_{R},\\ t_{e+1}^{S_{rp}}+t_{\text{re}}^{i},\text{if }T_{R}^{S_{rp}}>\text{f}_{e}^{S_{rp}} \end{matrix}\right.\end{matrix} \right. \tag{8}\]  
where \(\text{f}_{\text{re}}^{S_{rp}}\) is the potential satellite-ground transmission time for potential reporting nodes calculated based on Equation (5). \(\text{f}_{\text{e+1}}^{S_{rp}}\) represents the time for the next available SGL establishment for the potential reporting node. For each potential reporting node, the awareness time is calculated and the node with the minimum value is selected as the optimal reporting node.