  Robotic on-orbit servicing (OOS) is expected to be a key technology and
concept for future sustainable space exploration. This paper develops a
semi-analytical model for OOS systems analysis, responding to the growing needs
and ongoing trend of robotic OOS. An OOS infrastructure system is considered
whose goal is to provide responsive services to the random failures of a set of
customer modular satellites distributed in space (e.g., at the geosynchronous
equatorial orbit). The considered OOS architecture is comprised of a servicer
that travels and provides module-replacement services to the customer
satellites, an on-orbit depot to store the spares, and a series of launch
vehicles to replenish the depot. The OOS system performance is analyzed by
evaluating the mean waiting time before service completion for a given failure
and its relationship with the depot capacity. Leveraging the queueing theory
and inventory management methods, the developed semi-analytical model is
capable of analyzing the OOS system performance without relying on
computationally costly simulations. The effectiveness of the proposed model is
demonstrated using a case study compared with simulation results. This paper is
expected to provide a critical step to push the research frontier of
analytical/semi-analytical models development for complex space systems design.
