An (s, S) Inventory System with Unreliable Service and Repeated Calls in a Random Environment

Queueing systems are often used as the foundation for industrial models of all types, to include production lines and inventory systems. Here, we consider an inventory system with repeated calls and failures of service. The inventory system features a single product that experiences Markovian demand and service intervals with random service interruptions. Lead time for replenishment is instantaneous. The Markov-modulated duration of service and inter-demand times permit time-dependent variation of the exponential parameters of these processes, which thus imparts a greater degree of realism to the model. Due to the resulting complexity of the underlying Markov chain, a traffic intensity condition is difficult to obtain via conventional means. We thus employ a novel technique that utilizes a matrix-analytic drift approach to obtain a closed-form drift condition for the stability of the process. Estimates of the steady-state distribution of such models are then used to compute various system performance measures.