A generic modeling framework for queueing-inventory systems with a single removable server

In this article, we use a quasi-birth-and-death (QBD) modeling approach to model queueing-inventory systems with a single removable server. We consider both finite and infinite queueing capacities. Breakdowns and start-up times are also taken into account. All stochastic times are allowed to be general distributions except for the breakdown intervals, which are assumed to be exponential. The general distributions are approximated by phase type representations, resulting in the matrix-algebraic approach to derive the probability vector of the queue length. Some performance measures of interest are obtained by using both hybrid and standard procedures to solve the proposed QBD models. An optimal control policy based on a two-critical number approach using some convexity properties is proposed and its validity is verified through extensive numeric studies.