An infinite waiting hall at a multi-server inventory system

Abstract

This article considers a multi-server inventory system at a service facility. The customers arrive according to a Poisson process. The demanded items are delivered to the customers after performing some service on the item and this service time is distributed as negative exponential. The ordering policy is (s; S) policy, that is, once the inventory level drops to a prefixed level, say s(≥ 0); an order for Q(= S − s) items is placed. The joint probability distribution of the number of busy servers, number of customers in the queue and the inventory level is obtained in the steady state case. The Laplace-Stieltjes transforms of the first passage time and of the waiting time of a tagged customer are derived. Various system performance are derived and the total expected cost rate is computed under a suitable cost structure. The results are illustrated numerically.