# Load-Balancing Routing for LEO Satellite Network with Distributed Hops-Based Back-Pressure Strategy
## 1 Introduction  
The LEO satellite network (LSN) has the characteristics of wide coverage as well as a large communication capacity, which breaks through geographical restrictions by means of inter-satellite networking. Based on the above advantages, the LSN can provide global users with a high transmission rate, low delay, and seamless network access services. At present, the LEO satellite network plays an important role in the space-air-ground integrated network (SAGIN). The orbit altitude of the LEO satellite network ranges from 160 km to 2000 km. Compared with satellites deployed in geostationary orbit (GEO), the LSN obtains a better transmission rate and lower delay under less energy consumption [1; 2; 3]. For example, the polar-orbiting constellation, OneWeb, consists of 720 satellites with an orbital altitude of 1200 km. OneWeb is able to provide Internet connectivity around the world [4]. The Starlink constellation was proposed by SpaceX in 2015 [5]. Starlink plans to deploy about 42,000 satellites to create a giant LEO constellation to achieve near-global broadband Internet access. Due to the sudden time of network traffic and the uneven geographical distribution of terrestrial users, with the continuous expansion of user scale, the problem of load imbalance in LEO satellite networks is becoming more and more prominent. The LEO satellite network integrated with the terrestrial network is shown in Figure 1. The communication between two ground gateway stations is usually busy, which leads to congestion of the shortest path between them during the communication peak. In this case, the giant mesh topology of LSN provides multiple candidate paths. Through reasonable management and distribution of network load, a high transmission rate as well as low delay can be taken into account. Aiming at the load-imbalancing of the LSN, several load-balancing routing algorithms for the LSN have been proposed in recent years. [PERSON] et al. [6] proposed a load-balancing routing algorithm for 6G SAGIN based on Deep Q-Network. [PERSON] et al. [7] proposed a selective iterative Dijkstra algorithm (SIDA) to optimize the path finding process by reducing the reuse frequency of nodes. A selective split load-balancing strategy (SSLB) is proposed to solve the link congestion problem in LSNs. [PERSON] et al. [8] put forward a state-aware load-balancing (SALB) strategy, which estimates the link status and dynamically sets the queue delay weight. By adopting the shortest path tree to reduce the overhead, the throughput of LSN is optimized. [PERSON] et al. [9] put forward load-balancing routing based on congestion prediction (LBRA-CP), which converts the load-balancing problem to a multiple-target optimization problem. By predicting link congestion, intelligent optimization algorithms are utilized to solve the optimal path and improve the throughput of LSN. [PERSON] et al. [10] proposes the low-complexity routing (LCRA), which utilizes the congestion information of adjacent nodes to select the next hop with low congestion as the forwarding direction. When the path is unique, LCRA chooses to wait for a while before forwarding the packet, which improves the network transmission rate and reduces delay. The above research mostly depends on the global link-state information [11; 12], which leads to poor effect under heavy load. back-pressure (BP) routing processes the routed traffic through the congestion gradient of the packet queue between nodes, which performs excellent equalization effect in multi-hop networks, such as wireless sensor networks (WSNs) and mobile ad-hoc networks (MANETs) [13; 14]. Similar to multi-hop networks, data packets in the LSN follow the same characteristics. Therefore, BP routing is also suitable for the traffic burst and load imbalance of LSN. However, compared with WSNs or MANETs, nodal distance in the LSN is larger. The network topology is also consistent with the Manhattan network [9]. As a result of the above properties, there are many end-to-end alternative paths in the LSN.