Time division inter‐satellite link topology generation problem: Modeling and solution

Abstract

In this paper, we study the time-division inter-satellite link topology generation (TDILTG) problem for the well-known Chinese BeiDou Global Navigation Satellite System. The TDILTG problem consists in generating a time-division topology of the inter-satellite link network for the navigation satellite system to spread systematic data to all satellites via a few source satellites with the purpose of minimizing the time required to spread the data. We propose a mathematical model to formulate the TDILTG problem and study its 2 lower bounds through a thorough analysis of the problem characteristics. We also present a deterministic constructive (DC) algorithm to solve this problem approximately but very quickly, with a time complexity of O(n 3 ), where n is the number of satellites. Extensive experimental studies on a wide range of randomly generated instances show that the proposed DC algorithm is able to obtain the optimal solutions for most tested instances in less than 1 second. Meanwhile, we also validate that the DC algorithm performs well when the problem scale is large. Furthermore, we provide insights of the effects of different instance parameters on the final results. KEYWORDS combinatorial optimization, global navigation satellite system, heuristics algorithm, topology generation 1 | INTRODUCTION One of the most important issues for the inter-satellite link network management of the well-known Chinese Global Navigation Satellite System 1 is how to generate a topology of the inter-satellite link network in a time-division multiplexing transmission mode. This leads to an interesting optimization problem that we named the time-division inter-satellite link topology generation (TDILTG) problem. The purpose of this problem is to generate a topology that minimizes the period of time required for spreading data 1 while satisfying a set of transmission constraints.To make a low-power and large-scale inter-satellite link network, 2 the global Navigation Satellite System uses the time-division transmission mode to establish inter-satellites links, where the time horizon is divided into several slots. In each slot, each satellite connects to another satellite, and each satellite switches to another satellite in the next slot. It is thus appropriate to use an evolving graph to represent the topology of the intersatellite link network, where the edges of the graph evolve over time. In the meantime, ground stations need to transmit systematic data to all satellites via limited source satellites, and each satellite is expected to receive the data as soon as possible.Furthermore, each satellite in a pair of satellites having a connection must remain visible to the other within the effective time domain of the topology. Because the visibility relation of 2 satellites may change over time because of the relative motion of the satellites, the navigation system needs to generate the topology of the network every once in a while. It is thus necessary for the system to solve the problem automatically and effectively to meet the...

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