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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 738021, 9 pages
Research Article

Study on the Departure Process of Discrete-Time / / Queue with Randomized Vacations

1School of Economical Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China
2School of Business Administration, Southwestern University of Finance and Economics, Chengdu 611130, China

Received 9 March 2014; Revised 11 May 2014; Accepted 12 May 2014; Published 26 May 2014

Academic Editor: Luca Guerrini

Copyright © 2014 Chuanyi Luo et al. 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.


This paper presents an analysis of the departure process of a discrete-time queue with randomized vacations. By using probability decomposition techniques and renewal process, the expression of expected number of departures during time interval is derived. The relation among departure process, server state process, and service renewal process is obtained. The relation displays the decomposition characteristic of the departure process. Furthermore, the approximate expansion of the expected number of departures is gained. Since the departure process also often corresponds to an arrival process for a downstream queue in queueing network, it is hoped that the results obtained in this paper may provide useful information for queueing network.