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Analysis of A Two-queue Discrete-time Model with Random Alternating Service Under High Occupancy in One Queue

Author

Listed:
  • Arnaud Devos

    (Ghent University)

  • Joris Walraevens

    (Ghent University)

  • Herwig Bruneel

    (Ghent University)

Abstract

We investigate a discrete-time two-queue system with a single server. At the beginning of every time slot, the single server randomly selects either queue 1 or queue 2 to serve. The decision of the server to select either queue 1 or queue 2 in each time slot is independent of the state of the system and is determined by a single parameter. The service times of the customers are deterministically equal to 1 time slot. The numbers of arrivals into both queues during consecutive slots are characterized by a joint probability generating function. By extending prior research, we analyze the behavior of the system as the number of customers in the first queue approaches infinity, thereby obtaining exact asymptotics for the stationary joint probability distribution of customer numbers in both queues.

Suggested Citation

  • Arnaud Devos & Joris Walraevens & Herwig Bruneel, 2024. "Analysis of A Two-queue Discrete-time Model with Random Alternating Service Under High Occupancy in One Queue," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-21, December.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:4:d:10.1007_s11009-024-10109-7
    DOI: 10.1007/s11009-024-10109-7
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    References listed on IDEAS

    as
    1. 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.
    2. Sem Borst & Onno Boxma, 2018. "Polling: past, present, and perspective," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 335-369, October.
    3. Toshihisa Ozawa, 2022. "Tail asymptotics in any direction of the stationary distribution in a two-dimensional discrete-time QBD process," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 227-267, October.
    4. Sem Borst & Onno Boxma, 2018. "Rejoinder on: Polling: past, present, and perspective," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 381-382, October.
    5. Masakiyo Miyazawa, 2011. "Rejoinder on: Light tail asymptotics in multidimensional reflecting processes for queueing networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 313-316, December.
    6. Yiqiang Q. Zhao, 2022. "The kernel method tail asymptotics analytic approach for stationary probabilities of two-dimensional queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 100(1), pages 95-131, February.
    7. Masakiyo Miyazawa, 2011. "Light tail asymptotics in multidimensional reflecting processes for queueing networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 233-299, December.
    8. Vladimir Vishnevsky & Olga Semenova, 2021. "Polling Systems and Their Application to Telecommunication Networks," Mathematics, MDPI, vol. 9(2), pages 1-30, January.
    9. Ahmad Hanbali & Roland Haan & Richard Boucherie & Jan-Kees Ommeren, 2012. "Time-limited polling systems with batch arrivals and phase-type service times," Annals of Operations Research, Springer, vol. 198(1), pages 57-82, September.
    10. 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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