Spare Strategy for Large-Scale Satellite Constellations Under Dual Resupply Channels Using Markov Chain

Abstract

This paper presents a Markov-chain-based method for the early-phase analysis and design of hybrid spare-management architectures for large-scale satellite constellations.} The hybrid strategy combines two channels: an indirect path that stages spares in parking orbits via heavy launch for later transfer to constellation planes, and a direct path that delivers spares to in-plane orbits using small launch vehicles. {To assess the long-run viability of such concepts of operations, satellite failure and replenishment processes are modeled as a Markov chain:} the indirect channel follows a periodic-review reorder-point/order-quantity policy, while the direct channel uses a standard reorder-point/order-quantity policy. These coupled chains yield a periodic steady state over the right ascension of the ascending node cycle via fixed-point iteration, and the stationary distributions provide rigorous cost and resilience metrics. By directly modeling the stochastic, multi-echelon dynamics governed by orbital mechanics, our framework avoids the aggregation assumptions of prior works and remains valid across a wider operating domain. We also introduce an approximate analysis that preserves delay statistics while significantly reducing model size. Building on this fast, accurate analysis, we formulate a cost minimization problem with resilience constraints and solve it using a genetic algorithm. The framework is channel-neutral; the optimization autonomously selects the preferred path and roles. {A case study validates the analysis against Monte Carlo simulations and demonstrates the practical value of the framework in identifying the conditions under which the hybrid policy outperforms pure strategies.