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Journal of Applied Mathematics
Volume 2013, Article ID 587163, 6 pages
Research Article

On the Discrete-Time Queues under -Policy with Single and Multiple Vacations

1Department of Management Engineering, Sangmyung University, Cheonan 330-720, Republic of Korea
2Department of Industrial Engineering, Chonnam National University, Gwangju 500-757, Republic of Korea
3Department of Business Administration, Pai Chai University, Daejeon 302-735, Republic of Korea
4Department of Industrial and Systems Engineering, KAIST, Daejon 305-701, Republic of Korea
5Division of Business and Commerce, Baekseok University, Cheonan 330-704, Republic of Korea

Received 5 August 2013; Accepted 4 December 2013

Academic Editor: Alexander Timokha

Copyright © 2013 Sung J. Kim 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.


We consider the discrete-time queue under N-policy with single and multiple vacations. In this queueing system, the server takes multiple vacations and a single vacation whenever the system becomes empty and begins to serve customers only if the queue length is at least a predetermined threshold value N. Using the well-known property of stochastic decomposition, we derive the stationary queue-length distributions for both vacation models in a simple and unified manner. In addition, we derive their busy as well as idle-period distributions. Some classical vacation models are considered as special cases.