Minimum hop path model for LEO mega constellation networks with inter-layer satellite links: A theoretical analytic approach

Low Earth orbit (LEO) Mega-constellation networks (MCNs) with inter-satellite links (ISLs) are of great importance in terms of broadband communications . Compared to single-layer MCNs, multi-layer MCNs with inter-layer links (ILLs) bring better throughput and invulnerability at the cost of increased routing complexity. In this paper, for the first time, a theoretical analytic approach based on the non–homogeneous Poisson distribution is proposed to estimate the hop count between any two ground users for dual-layer MCNs with different ILL densities . Meanwhile, it is demonstrated that the establishment of ILLs reflects the dynamic features of ”small world” networks, which implies that introducing a small percentage of random connections to a regular network can significantly decrease the network diameter and the average shortest path length. Additionally, the uneven spatial distribution of hop count reduction is clarified. Results demonstrate that the implementation of ILLs effectively contributes to diminishing hop count. Remarkably, a mere 6% of ILLs leads to a substantial reduction of 22.3% in hop count for Starlink. These findings are helpful to the comprehension of constellation topological properties and provide valuable guidance for routing design and the deployment of ISLs.