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

Sung J. Kim, Nam K. Kim, Hyun-Min Park, Kyung Chul Chae and Dae-Eun Lim

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

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.

Date: 2013
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https://doi.org/10.1155/2013/587163

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:587163

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