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

TL;DR

This paper introduces a Markov-chain-based framework for analyzing and optimizing hybrid spare-management strategies in large-scale satellite constellations with dual resupply channels, balancing cost and resilience.

Contribution

It develops a novel, channel-neutral Markov model that accurately captures stochastic dynamics and guides optimal spare management policy design.

Findings

Hybrid strategy can outperform pure strategies under certain conditions.

The approximate analysis reduces computational complexity significantly.

Optimization identifies cost-effective, resilient resupply configurations.

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.