Analysis and Design of Satellite Constellation Spare Strategy Using Markov Chain

TL;DR

This work develops a Markov-chain based framework to optimize spare management for mega-constellations under two resupply strategies. It extends classical $(r,q)$ and $(r,q,T)$ inventory policies to orbital spares, modeling state transitions with a Markov chain and deriving stationary distributions as $\pi$ satisfying $\pi = P\pi$. It provides direct and indirect resupply analyses, including a fixed-point iterative coupling for the two orbit types, and validates results against Monte Carlo simulations, with optimization demonstrated via a simple cost model and a genetic-algorithm-based approach noted in the abstract. The framework enables fast, accurate design insights for spare strategy in orbital constellations, accounting for RAAN drift, parking orbits, lead-time randomness, and multi-echelon inventory dynamics, with practical impact on mission availability and cost efficiency.

Abstract

This paper introduces the analysis and design method of an optimal spare management policy using Markov chain for a large-scale satellite constellation. We propose an analysis methodology of spare strategy using a multi-echelon $(r,q)$ inventory control model with Markov chain, and review two different spare strategies: direct resupply, which inserts spares directly into the constellation orbit using launch vehicles; and indirect resupply, which places spares into parking orbits before transferring them to the constellation orbit. Furthermore, we propose an optimization formulation utilizing the results of the proposed analysis method, and an optimal solution is found using a genetic algorithm.

Figures (14)

• Figure 1: Two Different Replenishment Strategies (a) Direct Resupply (b) Indirect Resupply
• Figure 2: Stock level profile using $(r,q)$ policy
• Figure 3: Stock level profile using $(r, q, T)$ policy
• Figure 4: Propagation of state distribution during non-reordering period
• Figure 5: Propagation of state distribution during reorder waiting period