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Stability of a cascade system with multiple stations

Author

Listed:
  • Bara Kim

    (Korea University)

  • Jeongsim Kim

    (Chungbuk National University)

Abstract

This paper considers an m-station cascade system with renewal arrival processes and general service time distributions. Miyazawa and Morozov (Queueing Syst 100:225–227, 2022a; Stability of a cascade system with two stations and its extension for multiple stations, 2022b. arXiv:2203.14294v1 ) formulated a conjecture on the stability of this cascade system. In this paper, we show that this conjecture is not true for $$m\ge 3$$ m ≥ 3 . We also show that when $$m\ge 3$$ m ≥ 3 , the stability condition is not determined solely by the moments of the interarrival and service times, but also depends on their distributions. In addition, we provide the necessary and sufficient condition for the stability of this cascade system by modifying a result of Miyazawa and Morozov (2022).

Suggested Citation

  • Bara Kim & Jeongsim Kim, 2023. "Stability of a cascade system with multiple stations," Queueing Systems: Theory and Applications, Springer, vol. 104(1), pages 53-64, June.
    • Handle: RePEc:spr:queues:v:104:y:2023:i:1:d:10.1007_s11134-023-09871-1
    DOI: 10.1007/s11134-023-09871-1
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    References listed on IDEAS

    as
    1. Masakiyo Miyazawa & Evsey Morozov, 2022. "Stability condition of a cascade system with a general number of stations," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 225-227, April.
    2. E. Morozov & B. Steyaert, 2013. "Stability analysis of a two-station cascade queueing network," Annals of Operations Research, Springer, vol. 202(1), pages 135-160, January.
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    Cited by:

    1. Masakiyo Miyazawa & Evsey Morozov, 2023. "Stability of a cascade system with two stations and its extension for multiple stations," Queueing Systems: Theory and Applications, Springer, vol. 104(3), pages 155-174, August.

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