A retrial queueing-inventory system with J-additional options for service and finite source

Abstract

A continuous review (s,S) inventory system at a service facility with finite homogeneous sources of demands and retrial is analysed. The lifetime of each item is assumed to be exponential. Before items are delivered to the customers, some basic service on the item must be performed. It is known as a regular or main service. The service may get interrupted according to a Poisson process and it restarts after an exponentially distributed time. If the server is idle at the time of arrival of a customer and the inventory level is positive, then the service begins immediately. After the completion of regular service, a customer may either abandon the system forever or demand for a second service from the same server, which is multi-optional. If any arriving customer finds that the server is busy or inventory level is zero, he/she either enters into the orbit with probability p or balks (does not enter) with probability 1-p. The stationary distribution of the number of customers in the system, server status and the inventory level is obtained by the matrix method. The Laplace-Stieltjes transform of the waiting time of the tagged customer is derived. Various system performance measures are derived and the total expected cost rate is computed under a suitable cost structure. A numerical illustration is given.