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A markov-modulated M/M/1 queue with group arrivals

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Abstract

We study anM/M/1 group arrival queue in which the arrival rate, service time distributions and the size of each group arrival depend on the state of an underlying finite-state Markov chain. Using Laplace transforms and matrix analysis, we derive the results for the queue length process, its limit distribution and the departure process. In some special cases, explicit results are obtained which are analogous to known classic results.

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Author notes

  1. Yixin Zhu

    Present address: Department of Industrial Engineering, SUNY, 14260, Buffalo, NY, USA

Authors and Affiliations

  1. Department of Operations Research, School of Engineering and Applied Science, The George Washington University, 20052, Washington, DC, USA

    Yixin Zhu

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  1. Yixin Zhu
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Zhu, Y. A markov-modulated M/M/1 queue with group arrivals. Queueing Syst 8, 255–263 (1991). https://doi.org/10.1007/BF02412254

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  • DOI: https://doi.org/10.1007/BF02412254

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