A Queueing Model with Two Types of MAPs Service During the Positive Inventory Using (s,S) Inventory Policy Management Method, Vacation, Setup, and Balking

Abstract

In this paper we consider a retrial inventory queueing model with two types of arrivals according to a Markovian arrival process (MAP), with a single-server retrial inventory, phase-type service during the positive inventory in all forms of services, balking, close down,  single vacation, and use of the (s, S) inventory policy management method, where the reorder point (s) is set below the desired stock level (S) to ensure that inventory is replenished as needed. An arriving item when the server is busy will join an infinite capacity orbit or balks. The server closes the serving process, and goes on a limited vacation time, if there is no item in orbit and it is being idle. Upon return from vacation, the server will proceed with a set up period before proceeding to serve if there is any item waiting. Accordingly, we will find the steady-state probability vector, the busy period, performance measures, cost analysis, and finally, some numerical examples.