## Journal of Applied Mathematics

### On the Discrete-Time ${\text{Geo}}^{X}/G/1$ Queues under $N$-Policy with Single and Multiple Vacations

#### Abstract

We consider the discrete-time ${\text{Geo}}^{X}/G/1$ 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.

#### Article information

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

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394808327

Digital Object Identifier
doi:10.1155/2013/587163

Mathematical Reviews number (MathSciNet)
MR3147889

Zentralblatt MATH identifier
06950763

#### Citation

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. https://projecteuclid.org/euclid.jam/1394808327

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