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On the Discrete-Time Queues under -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 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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  • Sung J. Kim & Nam K. Kim & Hyun-Min Park & Kyung Chul Chae & Dae-Eun Lim, 2013. "On the Discrete-Time Queues under -Policy with Single and Multiple Vacations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-6, December.
    • Handle: RePEc:hin:jnljam:587163
    DOI: 10.1155/2013/587163
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    Cited by:

    1. G. K. Tamrakar & A. Banerjee, 2020. "On steady-state joint distribution of an infinite buffer batch service Poisson queue with single and multiple vacation," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1337-1373, December.

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