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Proof of the conjecture on the stability of a multi-class retrial queue with constant retrial rates

Author

Listed:
  • Bara Kim

    (Korea University)

  • Jeongsim Kim

    (Chungbuk National University)

Abstract

This study considers a multi-class single-server retrial queue with constant retrial rates in which service times are generally distributed with different service rates for each class. Avrachenkov (Queueing Systems 100:177–179, 2022) formulated the conjecture on the stability of this queueing system. We completely resolve the conjecture by using the fluid limit approach.

Suggested Citation

  • Bara Kim & Jeongsim Kim, 2023. "Proof of the conjecture on the stability of a multi-class retrial queue with constant retrial rates," Queueing Systems: Theory and Applications, Springer, vol. 104(3), pages 175-185, August.
    • Handle: RePEc:spr:queues:v:104:y:2023:i:3:d:10.1007_s11134-023-09881-z
    DOI: 10.1007/s11134-023-09881-z
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    References listed on IDEAS

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    1. Konstantin Avrachenkov, 2022. "Stability and partial instability of multi-class retrial queues," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 177-179, April.
    2. K. Avrachenkov & E. Morozov & R. Nekrasova & B. Steyaert, 2014. "Stability Analysis And Simulation Of N-Class Retrial System With Constant Retrial Rates And Poisson Inputs," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-18.
    3. Bara Kim & Jeongsim Kim, 2020. "Stability of a multi-class multi-server retrial queueing system with service times depending on classes and servers," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 129-146, February.
    Full references (including those not matched with items on IDEAS)

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