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Diffusion Approximation for Multiserver Retrial Queue with Two-Way Communication

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Distributed Computer and Communication Networks (DCCN 2020)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 12563))

Abstract

In this paper, we consider a multiserver retrial queue with two-way communication. Incoming calls arrive according to the stationary Poisson process and occupy the servers. Durations of incoming calls have an exponential distribution. If all the servers are busy upon arrival, the incoming call joins the orbit. The time spent by the call in the orbit is an exponential random variable. Idle servers also make outgoing calls whose durations follow an exponential distribution. We derive the diffusion limits of the number of calls in the orbit and the approximation of its stationary probability distribution.

The publication has been prepared with the support of RFBR according to the research project No.18-01-00277.

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Author information

Authors and Affiliations

  1. Institute of Applied Mathematics and Computer Science, National Research Tomsk State University, 36 Lenina ave., Tomsk, 634050, Russia

    Anatoly Nazarov, Svetlana Paul & Olga Lizyura

  2. Faculty of Engineering Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

    Tuan Phung-Duc

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

Correspondence to Svetlana Paul .

Editor information

Editors and Affiliations

  1. Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia

    Vladimir M. Vishnevskiy

  2. RUDN University, Moscow, Russia

    Konstantin E. Samouylov

  3. Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia

    Dmitry V. Kozyrev

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Nazarov, A., Phung-Duc, T., Paul, S., Lizyura, O. (2020). Diffusion Approximation for Multiserver Retrial Queue with Two-Way Communication. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks. DCCN 2020. Lecture Notes in Computer Science(), vol 12563. Springer, Cham. https://doi.org/10.1007/978-3-030-66471-8_43

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  • DOI: https://doi.org/10.1007/978-3-030-66471-8_43

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-66470-1

  • Online ISBN: 978-3-030-66471-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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