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Scaling Limits of a Tandem Queue with Two Infinite Orbits

Author

Listed:
  • Anatoly Nazarov

    (Institute of Applied Mathematics and Computer Science, National Research Tomsk State University, 36 Lenina Ave., Tomsk 634050, Russia)

  • Tuan Phung-Duc

    (Institute of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8573, Japan)

  • Svetlana Paul

    (Institute of Applied Mathematics and Computer Science, National Research Tomsk State University, 36 Lenina Ave., Tomsk 634050, Russia)

  • Mariya Morozova

    (Institute of Applied Mathematics and Computer Science, National Research Tomsk State University, 36 Lenina Ave., Tomsk 634050, Russia)

Abstract

This paper considers a tandem queueing network with a Poisson arrival process of incoming calls, two servers, and two infinite orbits by the method of asymptotic analysis. The servers provide services for incoming calls for exponentially distributed random times. Blocked customers at each server join the orbit of that server and retry to enter the server again after an exponentially distributed time. Under the condition of low retrial rates, we prove that the joint stationary distribution of scaled numbers of calls in the orbits weakly converges to a two-variable Normal distribution.

Suggested Citation

  • Anatoly Nazarov & Tuan Phung-Duc & Svetlana Paul & Mariya Morozova, 2023. "Scaling Limits of a Tandem Queue with Two Infinite Orbits," Mathematics, MDPI, vol. 11(11), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2454-:d:1156239
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    References listed on IDEAS

    as
    1. Pourbabai, Behnam, 1993. "Tandem behavior of a telecommunication system with repeated calls: II, A general case without buffers," European Journal of Operational Research, Elsevier, vol. 65(2), pages 247-258, March.
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    Cited by:

    1. Jia Xu & Liwei Liu, 2024. "Analysis of a Two-Stage Tandem Queuing System with Priority and Clearing Service in the Second Stage," Mathematics, MDPI, vol. 12(10), pages 1-23, May.

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