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Analysis of Multi-Server Queueing System with Flexible Priorities

Author

Listed:
  • Konstantin Samouylov

    (Applied Mathematics and Communications Technology Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia)

  • Olga Dudina

    (Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus)

  • Alexander Dudin

    (Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus)

Abstract

In this paper, a multi-server queueing system providing service to two correlated flows of requests was considered. Non-preemptive priority was granted to one flow via the preliminary delay of requests in the intermediate buffers with different rates of extracting from the buffers. Customers’ impatience during waiting in the intermediate and main buffers was taken into account. The possibility of the use of the results of the mathematical analysis for managerial goals is numerically illustrated.

Suggested Citation

  • Konstantin Samouylov & Olga Dudina & Alexander Dudin, 2023. "Analysis of Multi-Server Queueing System with Flexible Priorities," Mathematics, MDPI, vol. 11(4), pages 1-22, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:1040-:d:1072765
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    References listed on IDEAS

    as
    1. Baccara, Mariagiovanna & Lee, SangMok & Yariv, Leeat, 2023. "Task allocation and on-the-job training," Journal of Economic Theory, Elsevier, vol. 207(C).
    2. Laurentiu Rece & Sorin Vlase & Daniel Ciuiu & Giorgian Neculoiu & Stefan Mocanu & Arina Modrea, 2022. "Queueing Theory-Based Mathematical Models Applied to Enterprise Organization and Industrial Production Optimization," Mathematics, MDPI, vol. 10(14), pages 1-32, July.
    3. Peter W. Glynn, 2022. "Queueing theory: past, present, and future," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 169-171, April.
    4. Joris Walraevens & Thomas Giel & Stijn Vuyst & Sabine Wittevrongel, 2022. "Asymptotics of waiting time distributions in the accumulating priority queue," Queueing Systems: Theory and Applications, Springer, vol. 101(3), pages 221-244, August.
    5. Valentina Klimenok & Alexander Dudin & Olga Dudina & Irina Kochetkova, 2020. "Queuing System with Two Types of Customers and Dynamic Change of a Priority," Mathematics, MDPI, vol. 8(5), pages 1-25, May.
    6. O Jouini & A Roubos, 2014. "On multiple priority multi-server queues with impatience," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(5), pages 616-632, May.
    7. Amir Elalouf & Guy Wachtel, 2022. "Queueing Problems in Emergency Departments: A Review of Practical Approaches and Research Methodologies," SN Operations Research Forum, Springer, vol. 3(1), pages 1-46, March.
    8. Seokjun Lee & Sergei Dudin & Olga Dudina & Chesoong Kim & Valentina Klimenok, 2020. "A Priority Queue with Many Customer Types, Correlated Arrivals and Changing Priorities," Mathematics, MDPI, vol. 8(8), pages 1-20, August.
    9. Joris Walraevens, 2022. "Asymptotics in priority queues: from finite to infinite capacities," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 361-363, April.
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    Cited by:

    1. Mario Lefebvre, 2024. "A Controlled Discrete-Time Queueing System as a Model for the Orders of Two Competing Companies," Games, MDPI, vol. 15(3), pages 1-8, May.
    2. A. N. Dudin & S. A. Dudin & O. S. Dudina, 2023. "Randomized Threshold Strategy for Providing Flexible Priority in Multi-Server Queueing System with a Marked Markov Arrival Process and Phase-Type Distribution of Service Time," Mathematics, MDPI, vol. 11(12), pages 1-23, June.
    3. Sindhu S & Achyutha Krishnamoorthy & Dmitry Kozyrev, 2023. "A Two-Server Queue with Interdependence between Arrival and Service Processes," Mathematics, MDPI, vol. 11(22), pages 1-25, November.

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