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The Analytical Method of Transient Behavior of the M|M|1|n Queuing System for Piece-Wise Constant Information Flows

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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

The analytical method for studying the behavior of queuing system with abruptly changing information flows is presented in this paper for the first time. The proposed method is based on the conception of fundamental matrix of the Kolmogorov system and allows studying the transient and stationary modes of functioning different types of queuing system. The transient behavior of the M|M|1|n system with constant flows and piecewise constant arrival and service rates of flows are considered. It is obtained the analytical expressions for the state probabilities of the queuing system as in transient and in stationary mode. The conception of transient time for the queuing system has been introduced and the formulas for calculation of such transient performance metrics as throughput, a number of received and processed packets have been obtained for the first time.

The reported study was funded by RFBR, project number 19-29-06043.

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Authors and Affiliations

  1. V.A. Trapeznikov Institute of Control Sciences RAS, Profsoyuznaya 65 Street, Moscow, Russia

    Konstantin Vytovtov, Elizaveta Barabanova & Vladimir Vishnevsky

Authors
  1. Konstantin Vytovtov
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  2. Elizaveta Barabanova
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  3. Vladimir Vishnevsky
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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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Vytovtov, K., Barabanova, E., Vishnevsky, V. (2021). The Analytical Method of Transient Behavior of the M|M|1|n Queuing System for Piece-Wise Constant Information Flows. 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_15

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  • DOI: https://doi.org/10.1007/978-3-030-92507-9_15

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-92507-9

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