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Mathematical Problems in Engineering
Volume 2015, Article ID 835158, 12 pages
http://dx.doi.org/10.1155/2015/835158
Research Article

A Discrete-Time Geo/G/1 Retrial Queue with Two Different Types of Vacations

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

Received 9 January 2015; Revised 4 April 2015; Accepted 6 April 2015

Academic Editor: Alexander N. Dudin

Copyright © 2015 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

We analyze a discrete-time 1 retrial queue with two different types of vacations and general retrial times. Two different types of vacation policies are investigated in this model, one of which is nonexhaustive urgent vacation during serving and the other is normal exhaustive vacation. For this model, we give the steady-state analysis for the considered queueing system. Firstly, we obtain the generating functions of the number of customers in our model. Then, we obtain the closed-form expressions of some performance measures and also give a stochastic decomposition result for the system size. Moreover, the relationship between this discrete-time model and the corresponding continuous-time model is also investigated. Finally, some numerical results are provided to illustrate the effect of nonexhaustive urgent vacation on some performance characteristics of the system.