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On the Discrete‐Time GeoX/G/1 Queues under N‐Policy with Single and Multiple Vacations

Author

Listed:
  • Sung J. Kim
  • Nam K. Kim
  • Hyun-Min Park
  • Kyung Chul Chae
  • Dae-Eun Lim

Abstract

We consider the discrete‐time GeoX/G/1 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.

Suggested Citation

  • Sung J. Kim & Nam K. Kim & Hyun-Min Park & Kyung Chul Chae & Dae-Eun Lim, 2013. "On the Discrete‐Time GeoX/G/1 Queues under N‐Policy with Single and Multiple Vacations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:587163
    DOI: 10.1155/2013/587163
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    References listed on IDEAS

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    1. Tsung-Yin Wang, 2012. "Random N‐Policy Geo/G/1 Queue with Startup and Closedown Times," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Tsung-Yin Wang, 2012. "Random -Policy Geo/G/1 Queue with Startup and Closedown Times," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-19, November.
    3. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, December.
    4. Nam K. Kim & Kyung C. Chae & Mohan L. Chaudhry, 2004. "An Invariance Relation and a Unified Method to Derive Stationary Queue-Length Distributions," Operations Research, INFORMS, vol. 52(5), pages 756-764, October.
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    Cited by:

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