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Journal of Probability and Statistics
Volume 2015, Article ID 505082, 8 pages
Research Article

An Production Inventory Controlled Self-Service Queuing System

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

Received 10 June 2015; Revised 17 September 2015; Accepted 27 September 2015

Academic Editor: Ramón M. Rodríguez-Dagnino

Copyright © 2015 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.


We consider a multiserver Markovian queuing system where each server provides service only to one customer. Arrival of customers is according to a Poisson process and whenever a customer leaves the system after getting service, that server is also removed from the system. Here the servers are considered as a standard production inventory. Behavior of this system is studied using a three-dimensional QBD process. The condition for checking ergodicity and the steady state solutions are obtained using matrix analytic method. Unlike classical queuing models, the number of servers varies in this model according to an inventory policy.