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The Discrete-Time GI/Geo/1 Queue with Multiple Vacations

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Abstract

We study a discrete-time GI/Geo/1 queue with server vacations. In this queueing system, the server takes vacations when the system does not have any waiting customers at a service completion instant or a vacation completion instant. This type of discrete-time queueing model has potential applications in computer or telecommunication network systems. Using matrix-geometric method, we obtain the explicit expressions for the stationary distributions of queue length and waiting time and demonstrate the conditional stochastic decomposition property of the queue length and waiting time in this system.

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Authors and Affiliations

  1. Department of Mathematics, Yanshan University, Qinhuangdao, 066004

    Naishuo Tian

  2. Department of Finance, Marketing, and Decision Sciences, College of Business and Economics, Western Washington University, Bellingham, WA, 98225-9077, USA

    Zhe George Zhang

  3. Faculty of Business Administration, Simon Fraser University, Canada

    Zhe George Zhang

Authors
  1. Naishuo Tian
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  2. Zhe George Zhang
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Correspondence to Zhe George Zhang.

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Tian, N., Zhang, Z.G. The Discrete-Time GI/Geo/1 Queue with Multiple Vacations. Queueing Systems 40, 283–294 (2002). https://doi.org/10.1023/A:1014711529740

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