Table of Contents
ISRN Operations Research
Volume 2014 (2014), Article ID 356325, 12 pages
http://dx.doi.org/10.1155/2014/356325
Research Article

Discrete-Time State Dependent Bulk Service Queue with Multiple Vacations and Changeover Times

Department of Applied Mathematics, Andhra University, Visakhaptnam 530003, India

Received 1 February 2014; Accepted 24 February 2014; Published 24 March 2014

Academic Editors: R. Varela and X.-M. Yuan

Copyright © 2014 P. Vijaya Laxmi and D. Seleshi. 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

This paper presents the analysis of a discrete-time renewal input multiple vacations queue with state dependent service and changeover times under policy. The service times, vacation times, and changeover times are geometrically distributed. The server begins service if there are at least units in the queue and the services are performed in batches of minimum size and maximum size . At service completion instant, if the queue size is less than but not less than a secondary limit , the server continues to serve and takes vacation if the queue size is less than . The server is in changeover period whenever the queue size is at service completion instant and at vacation completion instant. Employing the supplementary variable and recursive techniques, we have derived the steady state queue length distributions at prearrival and arbitrary epochs. Based on the queue length distributions, some performance measures of the system have been discussed. A cost model has been formulated and optimum values of the service and vacation rates have been evaluated using genetic algorithm. Numerical results showing the effect of model parameters on the key performance measures are presented.