Spare Strategy Analysis and Design for Mega Satellite Constellations Using Markov Chain
This paper presents a Markov-chain-based method for the early-phase analysis and design of spare-management architectures for large-scale satellite constellations. To assess the long-run viability of such concepts of operations, satellite failure and replenishment processes are modeled as Markov chains and analyzed through their stationary solution. We reinvestigate an indirect spare strategy, modeled as a multi-echelon periodic-review reorder-point/order-quantity policy, in which spares are first delivered to parking orbits and then transferred to constellation planes. The stock levels in constellation and parking orbits are each modeled as independent Markov chains, and a fixed-point iteration yields a consistent joint stationary solution that describes the strategy's average behavior. This approach accurately captures the stochastic interplay within a multi-echelon model driven by orbital mechanics, avoiding the aggregation assumptions of prior works and remaining valid across a wider operating domain. Building on this fast, accurate analysis, we formulate an optimization problem and solve it via a genetic algorithm. Finally, we demonstrate the practical value of both the analysis method and the optimization framework in a real-world mega-constellation case study.