# Load-Balancing Routing for LEO Satellite Network with Distributed Hops-Based Back-Pressure Strategy
## 1 Introduction
In this case, the original back-pressure routing will search for ample end-to-end paths, resulting in huge end-to-end delay and computation complexity. Based on the above analysis, the original BP routing is not applicable in LSN. In this paper, end-to-end hops count in the LSN, as a key transmission cost metric is introduced into BP routing. Different from traditional WSNs, inter-node distance in the LSN can reach hundreds or even thousands of kilometers. Take Starlink constellation Shell1 as an example [3]; when the orbit height is 550 km, the distance between adjacent satellites  
Figure 1: Load-imbalancing problem in LEO satellite network. in the same orbit is about 1972 km. For neighboring satellites in adjacent orbits, the distance varies from 880 km to 1400 km. Due to the huge distance between neighboring nodes, end-to-end transmission hops play an important role in network delay. During the optimization of the propagation path, the end-to-end residual hop count should also be considered on the basis of the BP strategy. This paper proposes a distributed hops-based BP routing (DHBP) and cache scheduling scheme, which combines the BP strategy with the end-to-end hops count to realize adaptive link load aware routing. At the same time, the streaming limit domain is introduced to reduce the propagation delay. Simulation results demonstrate that the proposed DHBP is able to optimize the network performance under the condition of lower transmission cost when compared with the centralized strategy [8; 9]. The main contributions of this work are summarized as follows:  
* Increased constellation scale leads to excessive complexity in interstellar hops count estimation. In response to this problem, based on analyzing the characteristics of inclined constellations, a theoretical model is proposed to explicitly estimate the minimum end-to-end hops count and the corresponding propagation direction, so as to reduce the computational complexity;
* Considering the heavy load in the LEO satellite network, we use the destination-hops-delay (DHD), i.e., calculate the transmission delay according to the estimated end-to-end hops count from the next hop to destination nodes. The DHBP for the LSN is proposed. DHBP measures the backlog of BP routes by DHD and dynamically selects the shortest path with low congestion to balance the traffic overhead;
* The network stability of the DHBP is analyzed by utilizing the time-delay measurement based on hops count, and the throughput optimization is proved in the LSN. Network simulation is conducted on OMNET++ to test the performance of the proposed scheme. Simulation results demonstrate that DHBP optimizes throughput and transmission cost, especially under bursty traffic environments. In Section 2, we summarize two ideas for load-balanced routing and analyze the current state of the research on BP routing. In Section 3, we establish the system model of the LEO satellite network. The estimation method of end-to-end hop count in the LSN is deduced. In Section 4, we introduce the DHBP routing. In Section 5, we analyze the network stability of DHBP, as well as throughput optimization. In Section 6, the simulation and the results are analyzed, and the conclusions are presented in Section 7.