## 1 Introduction  
In recent years, countries around the world have been planning and building a Low-Earth-Orbit (LEO) satellite mobile communication system. The satellites in LEO have been moving at a high-speed relative to the ground, and seamless coverage requires a large number of satellites to be deployed in LEO, so the interconnection between satellites has become one of the key requirements of LEO satellite communication systems. On the other hand, since the control and measurement of the ground gateway station is required for the satellite communication system operation, and a large number of satellites are always moving at high speed, the interconnection between satellites is particularly important in order to ensure that the high-speed moving satellites can always maintain a link with the gateway station in the fixed area on the ground. As one of the key development directions in satellite communication systems, inter-satellite link technology can interconnect multiple satellites through inter-satellite links to realize information transmission and exchange between satellites and form a space communication with satellites as exchange nodes. The inter-satellite link refers to the link used for communication between satellites, which can reduce the number of inter-satellite hops and communication delay. In this kind of network, as the wireless coverage of nodes is limited, the data communication function is completed by single-hop communication or multi-hop forwarding. Within the maximum communication distance, network nodes communicate directly with neighbor nodes, and if the distance exceeds the maximum communication distance, routing technology is used to find the optimal path for forwarding communication. The mainstream routing technology is distributed, and each communication node is used as a communication terminal and has the function of routing forwarding. In order to reduce the network transmission traffic and improve the system efficiency, the path with the shortest number of hops between the two nodes will be selected as the optimal path. Literature [1] divides modern satellite routing algorithms into three strategies: centralized, distributed and hybrid. Early satellite networks used connection-based centralized routing algorithms. Ref. [2] proposed a finite state machine (Finite State Automata, FSA) routing algorithm which discretized and modeled the dynamic topology of the satellite network as a finite state machine, and allocated different routing tables for different network topologies in different states. However, it ignores the dynamic variability of inter-satellite links. The Flow Deviation (FD) proposed in [3] aims to find the path with the smallest end-to-end delay, and it is suitable for inter-satellite links with a small number of nodes. However, it is easy to cause packet loss and delay problems because static routing algorithms cannot perceive link state information. The proposed QoS routing algorithm MPQR in [4] uses a genetic algorithm and a simulated annealing algorithm at the source node to find the optimal path that satisfies the constraints of Quality of Service (QoS), which can simultaneously improve the end-to-end network delay, packet loss rate and link utilization. Different from centralized routing, each satellite node acts as an independent routing decision in distributed routing strategy. The Delay-oriented Adaptive Routing Algorithm (DOAR) proposed in [5] is used to solve the multipath load balancing and delay problems, while it is only for delay-sensitive services. Ref. [6] proposed Service-Oriented Routing with Markov Spacetime Graph (SOR-MSG) based on Markov Spacetime Graph. First, an MSG model is constructed through the connection duration and connection probability between satellite nodes. The satellites in the link autonomously select the next hop node based on the established MSG and QoS constraints, and finally determine the optimal path, but ignore the stability and reliability of the system.