# DRL-Based Dynamic SFC Orchestration Algorithm for LEO Satellite Networks
## 3 System Model
### Physical Network Modeling  
In this paper, the physical network consists of satellites distributed on different orbits at the same orbital height and multiple ground nodes distributed across different regions. Due to the high-speed movement of LEO satellites relative to the ground and the relative motion between satellites in different orbits, the connection status and link propagation delays of satellite-ground links and inter-satellite links change dynamically with satellite movement, causing the entire satellite communication network topology to vary dynamically over time. For continuous-time dynamic resource management and allocation problems, modeling based on discrete time slots is typically used to simplify the problem. In the above scenario, satellite positions, link connectivity, and propagation delays can be accurately calculated and predicted for a certain period in the future using fixed given parameters [33]. Therefore, in this study, we model the dynamic characteristics of satellite networks through time-based snapshot sequences, representing different network states over time using a series of snapshots. Specifically, time is discretized into \(T\) time slots, denoted as \(t_{1},t_{2},\ldots,t_{T}\). During each time slot \(t\), the physical network topology remains unchanged, with topology changes occurring at time slot transitions. The physical network topology can be converted into an undirected graph \(G_{t}=(N,L(t))\), where \(N\) represents the node set, and \(L(t)\) represents the link set. Physical nodes can be categorized into ground nodes and satellite nodes based on their different network functions. \(N_{g}=\{n_{g,i}\}\) represents the set of all ground nodes. For any ground node \(n_{g,i}\in N_{g}\), it can only serve as a source or destination node for user services, and physical resource limitations are not considered; thus, VNFs cannot be deployed on ground nodes. \(N_{s}=\{n_{s,i}\}\) represents the set of all satellite nodes. Any satellite node \(n_{s,i}\in N_{s}\) has underlying physical resources capable of supporting VNF operation, such as CPU, memory, and storage. The resource capacities for each physical resource are \(C^{e}_{n_{s,i}}\), \(C^{m}_{n_{s,i}}\), and \(C^{s}_{n_{s,i}}\), respectively. Any type and number of VNFs can be deployed on a satellite node as long as they do not exceed the node's single resource capacity constraints. All ground nodes and satellite nodes together constitute the physical network's node set; thus, \(N=(N_{g}\cup N_{s})\), \(N_{g}\cap N_{s}=\emptyset\). \(L(t)=\{l_{i,j}(t)\}\) represents the set of all physical links at time \(t\). For any physical link \(\forall l_{i,j}(t)\in L(t)\), its attributes can be described by bandwidth capacity \(B_{i,j}\) and time-varying delay \(d_{i,j}(t)\). Link bandwidth \(B_{i,j}\) remains constant when the link is connected, while the link delay varies with time. When a link is disconnected, its bandwidth is considered zero, and the link delay is considered infinite. For any satellite node \(n_{s,i}\), it has two relatively stable intra-orbital links connecting satellites in the same orbit and two inter-orbital links connecting satellites in different orbits, whose states change over time. Additionally, when ground user nodes are within a LEO satellite's coverage area, the satellite can provide network access services to multiple ground users simultaneously, meaning a satellite can have multiple satellite-ground links connected at the same time. Due to the high-speed movement of LEO satellites and Earth's rotation, the states of inter-orbital links and satellite-ground links are unstable and change over time. The adjacency matrix \(M_{t}\) represents the network's link connection states at time \(t\), where element \(m_{i,j}(t)\) in the \(i\)-th row and \(j\)-th column represents the connection state between nodes i and j.