Journal of Applied Mathematics (Jan 2013)

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,
  • Dae-Eun Lim

DOI
https://doi.org/10.1155/2013/587163
Journal volume & issue
Vol. 2013

Abstract

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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.