Mega-constellation networks (MCNs) based on low earth orbit (LEO) satellites have become increasingly important with many projects in the design or implementation phase. For those MCN systems with inter-satellite links (ISLs), the large number of satellites increases the routing complexity and the required hop-count of ISL paths. This paper aims to provide insights into the topology and routing design in MCNs through the analysis of ISL paths. We propose a theoretical model to explicitly estimate the ISL hop-count between ground users in MCNs with inclined orbits. The spatial distribution properties of hop-count are derived based on the proposed method. Based on an exemplary constellation, that is Starlink, the global distribution patterns of hop-count and the path difference caused by different access satellites are illustrated for the first time. In Starlink, the difference of the paths from different starting satellites can be up to 45 hops. The numerical results show that optimizing the constellation phasing factor can effectively reduce the average hop-count, for both the whole network and specific regional users.

The Shortest Distance Path (SDP) problem is a critical routing issue in communication networks, particularly in satellite networks. Typically, SDP is solved by graph-based iterative algorithms, while an explicit or analytic approach is challenging. However, considering the orbit dynamics and topology regularity, this paper proposes, for the first time, an explicit analytic phase-based algorithm STEPCLIMB to directly solve the SDP in low-Earth orbit (LEO) satellite networks. Based on the relationship between satellite phase and inter-satellite link distance, the SDP is modeled with the satellite phase, and SDP problem is converted into a total phase offset problem through theoretical derivations. Then STEPCLIMB is derived in two cases, respectively. Monte-Carlo simulations verify STEPCLIMB’s accuracy, which has zero error in the mono-valley case and has less than 0.1% error in the bi-valley case. The algorithm performs better in larger-scale constellations and can save over 99.4% computational cost compared to Dijkstra algorithm. Further, the SDP pattern and features in Starlink constellation are analyzed. The model proves that most inter-plane hops in the SDP occur successively, and the simulations further indicate that these hops prefer satellites in the higher latitude regions.

Using satellite constellations to provide global Internet access services has recently drawn increasing attention. A low-Earth orbit (LEO) satellite network with multiple satellites provides global coverage, low latency, and operates independently, by which it effectively complements terrestrial IP networks. Satellite gateways are located on the ground and can serve as data exchange points between satellite networks and the Internet. As the placement scheme can affect network performance, finding appropriate sites for gateways constitutes a fundamental problem. This paper proposes a gateway placement optimization (GPO) method for LEO satellite networks in order to solve this problem by modeling it as a combination optimization problem. We aim to identify the best gateway locations that can balance traffic loads while using as few gateways as possible. The constraints to be satisfied concern the physical links between gateways and satellites: specifically, link interference, satellite bandwidth, and number of satellite antennas. We use a gravity model to estimate the traffic matrix from/to gateways and satellites, then we adopt and modify the discrete particle swarm optimization (PSO) algorithm to solve this problem. Finally, we apply the GPO method to numerical tests on real satellite constellations. The results indicate that our method performs well and effectively.