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International Conference on Information Technologies and Mathematical Modelling

ITMM 2015: Information Technologies and Mathematical Modelling - Queueing Theory and Applications pp 114–127Cite as

On a Flow of Repeated Customers in Stable Tandem Cyclic Queueing Systems

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 564))

Abstract

We investigate tandem queueing systems with control of conflicting input flows using cyclic algorithms with readjustments. Input flows are modulated by a finite-state synchronous Markov chain. Customers arrive in Poisson flows of batches with intensities and batch size distributions determined by the environment. All serviced customers from the first input flow and randomly selected serviced customers from the second conflicting input flow in the first system are transferred with random speeds to the second queueing system. We develop a numerical algorithm to evaluate the stationary probability distribution for the number of customers joining the transfer queue at each stage of servers’ operation.

A.V. Zorine—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 Nizhni 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 Nizhni Novgorod, 23 Prospekt Gagarina, 603950, Nizhni Novgorod, Russia

    Andrei V. Zorine & Vladimir A. Zorin

Authors
  1. Andrei V. Zorine
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  2. Vladimir A. Zorin
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Corresponding author

Correspondence to Andrei V. Zorine .

Editor information

Editors and Affiliations

  1. Applied Mathematics and Computer Science, Belarusian State University, Minsk, Russia

    Alexander Dudin

  2. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Kemerovo State University, Anzhero-Sudzhensk, Russia

    Rafael Yakupov

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© 2015 Springer International Publishing Switzerland

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Zorine, A.V., Zorin, V.A. (2015). On a Flow of Repeated Customers in Stable Tandem Cyclic Queueing Systems. In: Dudin, A., Nazarov, A., Yakupov, R. (eds) Information Technologies and Mathematical Modelling - Queueing Theory and Applications. ITMM 2015. Communications in Computer and Information Science, vol 564. Springer, Cham. https://doi.org/10.1007/978-3-319-25861-4_10

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  • DOI: https://doi.org/10.1007/978-3-319-25861-4_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25860-7

  • Online ISBN: 978-3-319-25861-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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