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On the Discrete‐Time Geo/G/1 Queue with Vacations in Random Environment

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  • Jianjun Li
  • Liwei Liu

Abstract

A discrete‐time Geo/G/1 queue with vacations in random environment is analyzed. Using the method of supplementary variable, we give the probability generating function (PGF) of the stationary queue length distribution at arbitrary epoch. The PGF of the stationary sojourn time distribution is also derived. And we present the various performance measures such as mean number of customers in the system, mean length of the type‐i cycle, and mean time that the system resides in phase 0. In addition, we show that the M/G/1 queue with vacations in random environment can be approximated by its discrete‐time counterpart. Finally, we present some special cases of the model and numerical examples.

Suggested Citation

  • Jianjun Li & Liwei Liu, 2016. "On the Discrete‐Time Geo/G/1 Queue with Vacations in Random Environment," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:4029415
    DOI: 10.1155/2016/4029415
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    References listed on IDEAS

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    1. U. Yechiali & P. Naor, 1971. "Queuing Problems with Heterogeneous Arrivals and Service," Operations Research, INFORMS, vol. 19(3), pages 722-734, June.
    2. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, June.
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