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Multidimensional Central Limit Theorem of the Multiclass M/M/1/1 Retrial Queue

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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 the multiclass M/M/1/1 retrial queueing system. Customers of each class arrive from outside the system according to a Poisson process. The service times of customers are assumed to be exponentially distributed with the parameter corresponding to the type of the customer. If the server is busy incoming customers join the orbit according to their type and make a delay for an exponentially distributed time. Equations for the characteristic function of the multi-dimensional probability distribution of the numbers of customers in the orbits are obtained. These equations are investigated by method of asymptotic analysis under the long delay condition of customers in the orbits. It is shown that the probability distribution can be approximated by a multi-dimensional Gaussian distribution. Equations are obtained for finding the parameters of this probability distribution.

The reported study was funded by 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., 634050, Tomsk, Russian Federation

    Anatoly Nazarov & Yana Izmailova

  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. Yana Izmailova
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Corresponding author

Correspondence to Yana Izmailova .

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., Izmailova, Y. (2020). Multidimensional Central Limit Theorem of the Multiclass M/M/1/1 Retrial Queue. 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_23

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  • DOI: https://doi.org/10.1007/978-3-030-66471-8_23

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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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