An inventory model with server interruptions and retrials

Abstract

In this paper we consider a single server queueing system to which customers arrive according to a Poisson process, each demanding exactly one unit of the inventoried item. Service time duration is exponentially distributed. Inventory is replenished according to (s, S) policy, with lead time following exponential distribution. The service may be interrupted according to a Poisson process in which case the service restarts after an exponentially distributed time. Upon arrival if a customer finds the server busy, it leaves the service area to join an orbit and retries for service from there. The interval between two successive repeated attempts is exponentially distributed. We assume that while the server is under interruption an arriving customer joins the system with some probability or leaves for ever with complementary probability. Further it is assumed that while the server is on interruption a retrying customer goes back to the orbit with a certain probability and with complementary probability leaves the system for ever. No arrival or retrial is entertained when the inventory level is zero. We model the above system as a level dependent quasi birth death process (LIQBD). The stability of the system has been studied using matrix analytic method and the steady state vector is obtained applying Neuts-Rao truncation procedure. Several system performance measures, including the waiting time of a customer in the orbit, has been derived and their dependence on different system parameters has been extensively investigated numerically.