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Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue

Author

Listed:
  • Arnaud Devos

    (SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGENT), Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium)

  • Joris Walraevens

    (SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGENT), Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium)

  • Dieter Fiems

    (SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGENT), Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium)

  • Herwig Bruneel

    (SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGENT), Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium)

Abstract

This paper compares two discrete-time single-server queueing models with two queues. In both models, the server is available to a queue with probability 1/2 at each service opportunity. Since obtaining easy-to-evaluate expressions for the joint moments is not feasible, we rely on a heavy-traffic limit approach. The correlation coefficient of the queue-contents is computed via the solution of a two-dimensional functional equation obtained by reducing it to a boundary value problem on a hyperbola. In most server-sharing models, it is assumed that the system is work-conserving in the sense that if one of the queues is empty, a customer of the other queue is served with probability 1. In our second model, we omit this work-conserving rule such that the server can be idle in case of a non-empty queue. Contrary to what we would expect, the resulting heavy-traffic approximations reveal that both models remain different for critically loaded queues.

Suggested Citation

  • Arnaud Devos & Joris Walraevens & Dieter Fiems & Herwig Bruneel, 2021. "Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue," Mathematics, MDPI, vol. 9(21), pages 1-25, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2723-:d:665901
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    References listed on IDEAS

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    1. Nimrod Dvir & Refael Hassin & Uri Yechiali, 2020. "Strategic behaviour in a tandem queue with alternating server," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 205-244, December.
    2. Arnaud Devos & Joris Walraevens & Dieter Fiems & Herwig Bruneel, 2020. "Analysis of a discrete-time two-class randomly alternating service model with Bernoulli arrivals," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 133-152, October.
    3. Jan-Kees Ommeren & Ahmad Al Hanbali & Richard J. Boucherie, 2020. "Analysis of polling models with a self-ruling server," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 77-107, February.
    4. Jasper Vanlerberghe & Tom Maertens & Joris Walraevens & Stijn Vuyst & Herwig Bruneel, 2016. "On the optimization of two-class work-conserving parameterized scheduling policies," 4OR, Springer, vol. 14(3), pages 281-308, September.
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    Cited by:

    1. Alexander Dudin & Sergei Dudin & Olga Dudina, 2023. "Analysis of a Queueing System with Mixed Service Discipline," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-19, June.

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