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Low-Priority Queue Fluctuations in Tandem of Queuing Systems Under Cyclic Control with Prolongations

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Distributed Computer and Communication Networks (DCCN 2015)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 601))

Abstract

A tandem of queuing systems is considered. Each system has a high-priority input flow and a low-priority input flow which are conflicting. In the first system, the customers are serviced in the class of cyclic algorithms. The serviced high-priority customers are transferred from the first system to the second one with random delays and become the high-priority input flow of the second system. In the second system, customers are serviced in the class of cyclic algorithms with prolongations. Low-priority customers are serviced when their number exceeds a threshold. A mathematical model is constructed in form of a multidimensional denumerable discrete-time Markov chain. The recurrent relations for partial probability generating functions for the low-priority queue in the second system are found.

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Acknowledgments

This work was fulfilled as a part of State Budget Research and Development program No. 01201456585 “Mathematical modeling and analysis of stochastic evolutionary systems and decision processes” of N.I. Lobachevsky State University of Nizhny Novgorod and was supported by State Program “Promoting the competitiveness among world’s leading research and educational centers”

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Authors and Affiliations

  1. N. I. Lobachevsky State University of Nizhny Novgorod, Gagarina Avenue 23, 603950, Nizhny Novgorod, Russia

    Victor Kocheganov & Andrei V. Zorine

Authors
  1. Victor Kocheganov
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  2. Andrei V. Zorine
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Correspondence to Victor Kocheganov .

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Editors and Affiliations

  1. V.A. Trapeznikov Institute of Control Sc, Russian Academy of Sciences V.A. Trapeznikov Institute of Control Sc, Moscow, Russia

    Vladimir Vishnevsky

  2. V.A. Trapeznikov Inst. of Control Scienc, Russian Academy of Sciences V.A. Trapeznikov Inst. of Control Scienc, Moscow, Russia

    Dmitry Kozyrev

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Kocheganov, V., Zorine, A.V. (2016). Low-Priority Queue Fluctuations in Tandem of Queuing Systems Under Cyclic Control with Prolongations. In: Vishnevsky, V., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2015. Communications in Computer and Information Science, vol 601. Springer, Cham. https://doi.org/10.1007/978-3-319-30843-2_28

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  • DOI: https://doi.org/10.1007/978-3-319-30843-2_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30842-5

  • Online ISBN: 978-3-319-30843-2

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