Tropical Geometric Route Decision-Making in Simulated Lunar Gateway Communications

Abstract

Communications networks involving space systems are complex and evolve over time. Orbital mechanics, light propagation, and asset availability are some characteristics that dictate the state of the space network over time, which means that traditional routing methods relying on e.g. Open Shortest Path First (OSPF) cannot be expected to work. This is mainly because traditional routing algorithms assume that the network parameters are not themselves dependent on time, and make assumptions regarding end-to-end connectivity. In order for a routing algorithm to work in a space network, the algorithm must, among other things, account for the fact that the links are constantly changing over time; rather than forwarding and dropping, routers must also be able to store data. In this paper, the authors propose a new method for computing optimal routes through a space network using tropical geometry. This method determines the times at which the single-source shortest-path (SSSP) tree changes using the Joswig algorithm [1]. The efficacy of this method is demonstrated through simulation using orbital analysis software.