Stochastic decomposition in retrial queueing-inventory system

¹ Department of Mathematics Amrita School of Arts and Sciences Amrita Vishwa Vidyapeetham, Cochin 682024, India
² Department of Mathematics CMS College, Kottayam 686001 India

^* Corresponding author: achyuthacusat@gmail.com

Received: 6 September 2016
Accepted: 9 December 2018

Abstract

The purpose of this paper is to obtain product form solution for retrial – queueing – inventory system. We study an M/M/1 retrial queue with a storage system driven by an (s,S) policy. When server is idle, external arrivals enter directly to an orbit. Inventory replenishment lead time is exponentially distributed. The interval between two successive retrials is exponentially distributed and only the customer at the head of the orbit is permitted to access the server. No customer is allowed to join the orbit when the storage system is empty and also when the serer is busy. We first derive the stationary joint distribution of the queue length and the on-hand inventory in explicit product form. Using the joint distribution, we investigate long-run performance measures such as distribution of number of customers served, number of arrivals, number of customers lost during an interval of random duration and a cost function. The optimal pair (s,S) is numerically investigated.