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

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  • 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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