Analysis of a Multi-server Queueing-inventory System with Non-homogeneous Poisson Arrivals

Abstract

In this paper, we consider a multi-server queueing-inventory system with non-homogeneous Poisson arrivals, where the service times and lead times are exponentially distributed. The arrival process of the customers depends on the inventory level. When the on-hand inventory level decreases to zero, one item is replenished immediately with zero lead time. We formulated the system as a quasi-birth-and-death (QBD) process and obtain a stability condition of the system. Then, we compute the stationary distribution of the system and some main performance measures which are used to derive the total cost function. Finally, the computation of optimal (s, S) policy are illustrated by numerical examples.