Journal of Applied Mathematics
Volume 2013 (2013), Article ID 587269, 10 pages
http://dx.doi.org/10.1155/2013/587269
Research Article

The Discrete-Time Bulk-Service Geo/Geo/1 Queue with Multiple Working Vacations

Jiang Cheng,1,2 Yinghui Tang,1 and Miaomiao Yu1,3

1School of Mathematics & Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, China
2College of Computer Science and Technology, Southwest University for Nationalities, Chengdu, Sichuan 610041, China
3School of Science, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China

Received 3 July 2012; Accepted 14 December 2012

Academic Editor: Alvaro Valencia

Copyright © 2013 Jiang Cheng 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 deals with a discrete-time bulk-service queueing system with infinite buffer space and multiple working vacations. Considering an early arrival system, as soon as the server empties the system in a regular busy period, he leaves the system and takes a working vacation for a random duration at time . The service times both in a working vacation and in a busy period and the vacation times are assumed to be geometrically distributed. By using embedded Markov chain approach and difference operator method, queue length of the whole system at random slots and the waiting time for an arriving customer are obtained. The queue length distributions of the outside observer’s observation epoch are investigated. Numerical experiment is performed to validate the analytical results.