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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 160697, 15 pages
http://dx.doi.org/10.1155/2015/160697
Research Article

Study on the Queue-Length Distribution in Queue with Working Vacations

1School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China
2Research Institute of Economics and Management, Southwestern University of Finance and Economics, Chengdu 611130, China
3School of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, China

Received 4 April 2015; Revised 8 June 2015; Accepted 14 June 2015

Academic Editor: Gabriella Bretti

Copyright © 2015 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.

Abstract

This paper analyzes a finite buffer size discrete-time queue with multiple working vacations and different input rate. Using supplementary variable technique and embedded Markov chain method, the queue-length distribution solution in the form of formula at arbitrary epoch is obtained. Some performance measures associated with operating cost are also discussed based on the obtained queue-length distribution. Then, several numerical experiments follow to demonstrate the effectiveness of the obtained formulae. Finally, a state-dependent operating cost function is constructed to model an express logistics service center. Regarding the service rate during working vacation as a control variable, the optimization analysis on the cost function is carried out by using parabolic method.