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A Discrete-Time Queueing Model in a Random Environment

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Queueing Theory and Network Applications (QTNA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11688))

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Abstract

To study the effect of burstiness in arrival streams on the congestion in queueing systems this paper presents a one-server queueing model in a random environment in discrete time. The environment can be in two states. The number of time slots between two consecutive transitions of the environment follows a geometric distribution with a transition-dependent parameter. In every slot customers arrive in batches, and the batch-size distribution depends on the environment. Each customer requires a generally distributed service time. Arriving customers are put in a queue which is served in FIFO order. Arrivals have precedence over departures and departures have precedence over a change of the environment. The generating functions of the number of customers in the queue and the individual waiting time will be derived. Numerical results will show the effect of the burstiness in the arrival stream on the waiting-time and the queue-size distribution by calculating in parallel the corresponding results for the standard discrete-time model with a mixed batch-size distribution, ceteris paribus.

This paper is based on the second author’s Master thesis [11].

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Authors and Affiliations

  1. Department of Econometrics and Operations Research, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands

    Rein Nobel & Annette Rondaij

Authors
  1. Rein Nobel
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  2. Annette Rondaij
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Corresponding author

Correspondence to Rein Nobel .

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Editors and Affiliations

  1. University of Tsukuba, Tsukuba, Japan

    Tuan Phung-Duc

  2. Nara Institute of Science and Technology, Nara, Japan

    Shoji Kasahara

  3. Ghent University, Ghent, Belgium

    Sabine Wittevrongel

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Nobel, R., Rondaij, A. (2019). A Discrete-Time Queueing Model in a Random Environment. In: Phung-Duc, T., Kasahara, S., Wittevrongel, S. (eds) Queueing Theory and Network Applications. QTNA 2019. Lecture Notes in Computer Science(), vol 11688. Springer, Cham. https://doi.org/10.1007/978-3-030-27181-7_20

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  • DOI: https://doi.org/10.1007/978-3-030-27181-7_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-27180-0

  • Online ISBN: 978-3-030-27181-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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