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Two-Phase Resource Queueing System with Requests Duplication and Renewal Arrival Process

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Distributed Computer and Communication Networks (DCCN 2020)

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

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Abstract

In this paper, we analyze a two-phase resource queueing system with duplication at the second phase under the assumption that customers enter the system according to a renewal process and take up random resource amounts that do not affect the time of their service (for video-conference or streaming traffic). We apply the dynamic screening method and the asymptotic analysis method to obtain an approximation for the stationary probability distribution of the total amount of occupied resources in the system under increasing arrival rate. In more detail, we show that the three-dimensional probability distribution of the total resource amounts on the system blocks is three-dimensional Gaussian, obtain its parameters (means vector and covariance matrix) and verify the correctness of the asymptotic using discrete-event simulation.

The publication has been prepared with the support of the “RUDN University Program 5-100” (recipient E. Lisovskaya, Conceptualization and Methodology), of the University of Pisa under the PRA 2018–2019 Research Project “CONCEPT – COmmunication and Networking for vehicular CybEr-Physical sysTems” (recipient M. Pagano, Software), and the reported study was funded by RFBR and Tomsk region according to the research project 19-41-703002 (recipient A. Galileyskaya, Investigation).

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Author information

Authors and Affiliations

  1. National Research Tomsk State University, 36 Lenina Ave., Tomsk, Russian Federation

    Anastasia Galileyskaya & Svetlana Moiseeva

  2. Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., Moscow, 117198, Russian Federation

    Ekaterina Lisovskaya

  3. Department of Information Engineering, University of Pisa, Via Caruso 16, 56122, Pisa, Italy

    Michele Pagano

Authors
  1. Anastasia Galileyskaya
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  2. Ekaterina Lisovskaya
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  3. Michele Pagano
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  4. Svetlana Moiseeva
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Corresponding author

Correspondence to Ekaterina Lisovskaya .

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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Galileyskaya, A., Lisovskaya, E., Pagano, M., Moiseeva, S. (2020). Two-Phase Resource Queueing System with Requests Duplication and Renewal Arrival Process. 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_27

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  • DOI: https://doi.org/10.1007/978-3-030-66471-8_27

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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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