Journal of Applied Mathematics

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

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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.

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J. Appl. Math., Volume 2013 (2013), Article ID 587163, 6 pages.

First available in Project Euclid: 14 March 2014

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Kim, Sung J.; Kim, Nam K.; Park, Hyun-Min; Chae, Kyung Chul; Lim, Dae-Eun. On the Discrete-Time ${\text{Geo}}^{X}/G/1$ Queues under $N$ -Policy with Single and Multiple Vacations. J. Appl. Math. 2013 (2013), Article ID 587163, 6 pages. doi:10.1155/2013/587163.

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