3-ISL Topology: Routing Properties and Performance in LEO Mega-Constellation Networks

Mega-constellation networks widely employ inter-satellite links (ISLs) to enhance network connectivity. However, the ISLs, particularly the inter-plane ISLs that span different orbital planes, are dynamic and difficult to maintain. The inter-plane ISLs are less used and can be partly saved. Recently, a special ISL configuration with pruned inter-plane ISLs has been implemented in Starlink, yet less studied. This paper delves into the topological characteristics and routing issues of this pruned ISL pattern, specifically the 3-ISL topology. This topology is mathematically modeled and indexed, and key routing properties are derived, including the minimum hop-count, network diameter, network cost, and average path length of the 3-ISL topology. These fundamental properties are rigorously proven for both Mesh and Torus topologies. Additionally, the shortest path searching region and path diversity are deduced. Numerical simulations verify these propositions, and the results of mega-constellation scenarios suggest that pruning ISLs could lead to increased path distance, higher delay, and reduced network capacity. However, in certain constellation configurations, some metrics are comparable to those of the traditional 4-ISL topology, thereby potentially reducing system costs. Constellations with fewer orbital planes and more satellites in each plane are less affected by pruning ISLs and thus preferred. The findings can provide analytic insights for routing strategies and guide the integrated design of constellation configuration and ISL topology.