## 2 Composition of LEO Satellite Network and APINT Model
### APINT Model
#### 2.3.1 Passive Telemetry  
The passive telemetry approach based on INT is employed within the network, where node resource status information is inscribed as metadata into telemetry packets as service flows through. The awareness data transmit with the service, and the service transmission path can be regarded as an awareness path [19]. The INT packet mainly consists of a telemetry packet header and telemetry data, where the telemetry packet header is a specified 12-byte content, and the telemetry data are primarily composed of the aggregated metadata from each node [20]. Due to the small length of INT packet, it can be directly placed in the header of the service packet without occupying payload space. After editing  
\begin{table}
\begin{tabular}{c c c c} \hline
**Symbol** & **Symbolic Meaning** & **Symbol** & **Symbolic Meaning** \\ \hline \(S_{i}\) & Satellite number & \(T_{\text{final}}^{S_{rp}}\) & Awareness data reach ground time \\ \(Z\) & Service identifiers & \(V_{Y}\) & Set of segments \\ \(P_{Z}\) & Transmission path & \(Y\) & Number of segments \\ \(T_{Z}\) & Time slots & \(N_{YY}\) & Number of satellites in segment \\ \(L_{ij}\) & Inter-satellite distance & Eva & Evaluation function value \\ \(C\) & Propagation rate & \(\overline{T_{V}^{Z}}\) & Average telemetry and reporting time \\ \(t_{\text{pro}}^{i}\) & Propagation delay & \(E_{Vi}\) & Average awareness overhead \\ \(t_{\text{trans}}^{i}\) & Transmission delay & \(B_{M}^{S_{Vi}}\) & Awareness overhead of metadata \\ \(t_{\text{meta}}^{i}\) & Metadata writing delay & \(\Delta\) & Floating range \\ \(t_{\text{op}}^{i}\) & Passive telemetry delay & \(W\) & State of Q-learning \\ \(t_{\text{ap}}^{i}\) & Active telemetry delay & \(A\) & Action of Q-learning \\ \(t_{\text{ge}}^{i}\) & SGL propagation time & \(R(w,a)\) & Reward function \\ \(T_{R}^{S_{rp}}\) & Awareness data arriving time & \(Q(w,a)\) & Q-values \\ \hline \end{tabular}
\end{table}
Table 1: List of variables.  
and integrating the resource status information of each node, the written metadata typically have a length of 4 to 8 bytes [11]. \(H_{\text{max}}\) represents the maximum cumulative number of hops that telemetry data can contain, which can be set and modified according to actual needs, with a common value of 8 hops. When the path length exceeds \(H_{\text{max}}\), subsequent nodes will no longer write metadata to the telemetry data or reset the telemetry data and cumulative number of hops after reporting the current telemetry data.  
In addition, the CPU processing time consumed by the node to read the telemetry packet header and write metadata into the telemetry data is denoted as \(t_{\text{meta}}^{i}\). Since the average length of the metadata is relatively short, the time taken to write the metadata is much smaller than the node's propagation delay and transmission delay, making \(t_{\text{meta}}^{i}\) a constant value. Therefore, the time consumed by each node for passive telemetry during the process of inserting awareness data, and transmitting them along with the service to the next node is as follows:  
\[t_{\text{op}}^{i}=t_{\text{pro}}^{i}+t_{\text{trans}}^{i}+t_{\text{meta}}^{i}, \forall i\in P_{z}, \tag{3}\]