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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 834731, 11 pages
http://dx.doi.org/10.1155/2013/834731
Research Article

A Discrete-Time Retrial Queue with Vacations and Two Types of Breakdowns

College of Science, North University of China, Taiyuan 030051, China

Received 12 July 2013; Revised 21 September 2013; Accepted 21 September 2013

Academic Editor: Ram N. Mohapatra

Copyright © 2013 Feng Zhang and Zhifeng Zhu. 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 is concerned with a discrete-time retrial queueing model with vacations and two types of breakdowns. If the orbit is empty, the server takes at most vacations repeatedly until at least one customer appears in the orbit upon returning from a vacation. It is assumed that the server is subject to two types of different breakdowns and is sent immediately for repair. We analyze the Markov chain underlying the considered queueing system and derive the system state distribution as well as the orbit size and the system size distributions in terms of their generating functions. Then, we obtain some performance measures through the generating functions. Moreover, the stochastic decomposition property and the corresponding continuous-time queueing system are investigated. Finally, some numerical examples are provided to illustrate the effect of vacations and breakdowns on several performance measures of the system.