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In this article, we consider a continuous review (s, S) inventory system withfailures of demand fulfillment (service) modeled as a Markov-modulated retrialqueueing system. The inventory system features a single product thatexperiences Markovian inter-demand and service intervals with random serviceinterruptions and instantaneous replenishments. A recently developed criterionfor the ergodicity of a class of discrete-timelevel-dependent-quasi-birth-and-death (LDQBD) processes with convergenttransition matrix rows is applied to the jump chain of the process in order toelicit a closed-form traffic-intensity formula. An analytic solution for thesteady-state average minimum cost is provided.

A Markov-Modulated (s, S) Inventory System with Repeated Calls and Blocked Demands