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Tandem of Infinite-Server Queues with Markovian Arrival Process

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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

We consider a tandem queueing system with infinite number of servers and Markovian arrival process. Service times at the system stages are i.i.d. and given by distribution functions individually for each stage. The study is performed under the asymptotic condition of the arrivals rate growth. It is shown that multi-dimensional probability distribution of customers number at the system stages can be approximated by multi-dimensional Gaussian distribution which parameters are obtained in the paper.

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Acknowledgments

The work is performed under the state order of the Ministry of Education and Science of the Russian Federation (No. 1.511.2014/K).

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Authors and Affiliations

  1. Tomsk State University, Lenin ave. 36, 634050, Tomsk, Russia

    Alexander Moiseev & Anatoly Nazarov

Authors
  1. Alexander Moiseev
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  2. Anatoly Nazarov
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Corresponding author

Correspondence to Alexander Moiseev .

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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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Moiseev, A., Nazarov, A. (2016). Tandem of Infinite-Server Queues with Markovian Arrival Process. 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_34

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  • DOI: https://doi.org/10.1007/978-3-319-30843-2_34

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30842-5

  • Online ISBN: 978-3-319-30843-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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