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Scaling Limits of a Tandem Retrial Queue with Common Orbit and Poisson Arrival Process

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Distributed Computer and Communication Networks: Control, Computation, Communications (DCCN 2021)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 13144))

Abstract

In this paper, we consider an asymptotic analysis for the stationary queue length of a tandem queueing system with one orbit, Poisson arrival process of incoming calls and two sequentially connected servers. Under the condition that the average delay time of calls in the orbit is extremely large, we obtain the asymptotic probability distribution of the number of calls there. It turns out that the scaled version of the number of calls in the orbit follow the Gaussian distribution. Then we evaluate the applicability of the asymptotic results by simulation.

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Author information

Authors and Affiliations

  1. National Research Tomsk State University, 36 Lenina Avenue, 634050, Tomsk, Russia

    Anatoly Nazarov, Svetlana Paul & Mariya Morozova

  2. University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

    Tuan Phung-Duc

Authors
  1. Anatoly Nazarov
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  2. Svetlana Paul
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  3. Tuan Phung-Duc
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  4. Mariya Morozova
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Editor information

Editors and Affiliations

  1. V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

    Vladimir M. Vishnevskiy

  2. Applied Probability and Informatics Department, RUDN University, Moscow, Russia

    Konstantin E. Samouylov

  3. V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

    Dmitry V. Kozyrev

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Nazarov, A., Paul, S., Phung-Duc, T., Morozova, M. (2021). Scaling Limits of a Tandem Retrial Queue with Common Orbit and Poisson Arrival Process. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2021. Lecture Notes in Computer Science(), vol 13144. Springer, Cham. https://doi.org/10.1007/978-3-030-92507-9_20

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  • DOI: https://doi.org/10.1007/978-3-030-92507-9_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92506-2

  • Online ISBN: 978-3-030-92507-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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