An Inventory Model with Server Interruptions and Positive Lead Time

Abstract

Abtsrcat In this paper, we consider a single server queuing system with inventory where customers arrive according to a Poisson process. The time required to meet a demand follows an exponential distribution. Replenishment of inventory is according to the (s, S) policy with lead-time following exponential distribution. The service process may be interrupted in-between, with interruption time following exponential distribution. More than one in-terruption is possible during a particular service and at each time, the repair time of an interrupted server follows an exponential distribution. We assume that during interruption, the customer being served waits there until his service is completed and that no inventory is lost due to interruption. We also assume that, when the inventory level is zero no arrival is considered. Stability of the above system is analyzed and steady state vector is calculated using Matrix Analytic Methods. System performance measures such as expected number of customers in the system, expected inventory size, expected interruption rate, waiting time of a customer in the system etc are also obtained. A thorough numerical study of the dependence of the system performance measures on various system parameters has been carried out.