Table of Contents
ISRN Operations Research
Volume 2014 (2014), Article ID 596031, 6 pages
http://dx.doi.org/10.1155/2014/596031
Research Article

Inventory with Positive Service Time and Retrial of Demands: An Approach through Multiserver Queues

Department of Mathematics, National Institute of Technology Calicut, Calicut, Kerala 673601, India

Received 30 December 2013; Accepted 22 January 2014; Published 17 March 2014

Academic Editors: P. Ekel, R. Varela, and X.-M. Yuan

Copyright © 2014 Anoop N. Nair and M. J. Jacob. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We analyze an inventory with positive service time and retrial of demands by considering the inventory as servers of a multiserver queuing system. Demands arrive according to a Poisson process and service time distribution is exponential. On each service completion, the number of demands in the system as well as the number of inventories (servers) is reduced by one. When all servers are busy, new arrivals join an orbit from which they try to access the service at an exponential rate. Using matrix geometric methods the steady state joint distribution of the demands and inventory has been analyzed and a numerical illustration is given.