A Discrete-Time Queueing Model in a Random Environment

Rein Nobel*, Annette Rondaij

*Corresponding author for this work

    Research output: Chapter in Book / Report / Conference proceedingConference contributionAcademicpeer-review


    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.

    Original languageEnglish
    Title of host publicationQueueing Theory and Network Applications
    Subtitle of host publication14th International Conference, QTNA 2019, Ghent, Belgium, August 27–29, 2019, Proceedings
    EditorsTuan Phung-Duc, Shoji Kasahara, Sabine Wittevrongel
    Number of pages19
    ISBN (Electronic)9783030271817
    ISBN (Print)9783030271800
    Publication statusPublished - 2019
    Event14th International Conference on Queueing Theory and Network Applications, QTNA 2019 - Ghent, Belgium
    Duration: 27 Aug 201929 Aug 2019

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume11688 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349


    Conference14th International Conference on Queueing Theory and Network Applications, QTNA 2019


    • Discrete-time queue
    • Generating functions
    • Random environment


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