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Mathematical Model of the Tandem Retrial Queue M | GI | 1 | M | 1 with a Common Orbit

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Information Technologies and Mathematical Modelling. Queueing Theory and Applications (ITMM 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1605))

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Abstract

This paper considers a retrial tandem queue with single orbit, Poisson arrivals of incoming calls and without intermediate buffer. The first server provides services for incoming calls for an arbitrary random time, while the second server does for an exponentially distributed random time. Blocked customers at either the first server or the second server join the orbit and stay there for an exponentially distributed time before retrying to enter the first server again. Under an asymptotic condition when the mean of retrial intervals is extremely large, we derive a diffusion limit, which is further utilized to obtain an approximation to the number of customers in the orbit in stationary regime.

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Authors and Affiliations

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

    Svetlana Paul, Anatoly Nazarov & Mariya Morozova

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

    Tuan Phung-Duc

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

Correspondence to Svetlana Paul .

Editor information

Editors and Affiliations

  1. Belarusian State University, Minsk, Belarus

    Alexander Dudin

  2. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Tomsk State University, Tomsk, Russia

    Alexander Moiseev

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Paul, S., Nazarov, A., Phung-Duc, T., Morozova, M. (2022). Mathematical Model of the Tandem Retrial Queue M | GI | 1 | M | 1 with a Common Orbit. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2021. Communications in Computer and Information Science, vol 1605. Springer, Cham. https://doi.org/10.1007/978-3-031-09331-9_11

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  • DOI: https://doi.org/10.1007/978-3-031-09331-9_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-09330-2

  • Online ISBN: 978-3-031-09331-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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