## 3 System Model and Problem Formulation  
### LEO-MSN Model  
The LEO-MSN communication network, including satellites, ground stations, user terminals, and remote servers, is considered in this paper. The communication starts with a user terminal and ends with a remote server, and the data packets can be forwarded through ISLs of LEO satellite in space. The LEO-MSN at each moment can be defined as an undirected graph \(G(t)=(V,E(t))\), where \(V\) and \(E\) represent the set of vertices and edges in the graph, respectively. Node \(v_{i}\in V\) represents a satellite, ground station, user terminal, or remote server. Edge \(e_{i,j}\in E\) represents a link between two network nodes \(i\) and \(j\) in the network. The position of each satellite is calculated based on the simplified general perturbations 4 (\(SGP4\)) [40] orbital propagation model with the input parameter TLE (Two-Line Element set). The satellite coordinates are updated with the following formula:  
\[r_{i}(t)=SGP4(TLE_{i},t),\Delta t=60\;\text{s} \tag{1}\]  
where \(TLE_{i}\) contains the parameters of the orbital half-length axis, the eccentricity, the orbital inclination, and the ascending node declination.  
Each LEO satellite can establish an Inter-Satellite Link (ISL) with two satellites in the same orbital plane and two satellites in adjacent orbital planes. Since the spatial distance between the front and rear satellites in the same orbital plane is fixed, the ISL within the orbit is assumed to be stable over the system period. For satellites that are uniformly distributed in the same orbital plane, the distance between two neighboring satellites can be calculated using the following equation:  
\[L_{inter}=2(R_{earth}+h)\cdot sin(\frac{\pi}{2N_{L}}) \tag{2}\]  
Satellites in adjacent orbital planes can be calculated using the following formula:  
\[L_{adj}=2(R_{earth}+h)\cdot sin(\frac{\Delta\Omega\cdot\sin\theta}{2}) \tag{3}\]  
where \(R_{earth}\) is the radius of the Earth (in km), and \(h\) is the height of the satellite orbit. \(N_{L}\) is the number of satellites in the same orbital plane, \(\theta\) is the orbital inclination, and \(\Delta\Omega\) is the difference in longitude of the orbital plane. The relevant terms introduced in this section are listed in Table 2.  
According to the NTN networking architecture proposed by 3 GPP [25], user terminals need to pass through nodes with different functional protocols when accessing the network for service transmission, specifically including the service functions of the access network, transmission network, and core network. In this paper, we assume that the satellites and ground stations in LEO-SN can deploy different network functions, and each satellite or ground station can provide at most one function. Based on this, the network nodes in LEO-SN can be classified into nodes with processing functions and nodes with transparent forwarding functions [41,42], where the processing function nodes can provide certain functions during service transmission, including two kinds of functions, gNB and NGC (core network functions, including AMF, UPF, etc.), which can provide on-board access and on-board data processing functions, while the satellite with transparent forwarding function nodes only provides transparent forwarding service (TM). We can denote the set of nodes with the processing function and the set of nodes with the transparent forwarding function as \(VF=\{v_{i}\;|\;v_{i}\in\{gNB,NGC\}\}\), \(VNF=\{v_{i}\;|\;v_{i}\in\{TM\}\}\), respectively, so the set of nodes in LEO-SN can also be denoted as \(V=VF\cup VNF\cup V_{SFC},V_{Dst}\).