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On Gaussian Approximation of Queueing Networks with Different Starting Load

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Information Technologies and Mathematical Modelling. Queueing Theory and Applications (ITMM 2018, WRQ 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 912))

Abstract

In this work Markov multi-channel queueing networks with rate of the external load varying with time are considered. It is assumed that the starting load in the network can be not only a fixed constant value, but also can be asymptotically increasing in a series scheme. A many-dimensional service process of the network is introduced as the number of calls in the network nodes at the corresponding instant of time. For the service process, approximating Gaussian processes are constructed for both cases of starting load, when the network operates in heavy traffic regime. Correlation characteristics of the limit processes are written via the network parameters. It is proved that a many-dimensional Ornstein-Uhlenbeck process approximates the service process if the number of calls in the network nodes is asymptotically large at the initial instant of time.

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Authors and Affiliations

  1. Applied Statistics Department, Taras Shevchenko National University of Kyiv, Volodymyrska str., 64, Kyiv, 01601, Ukraine

    Eugene Lebedev & Hanna Livinska

Authors
  1. Eugene Lebedev
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  2. Hanna Livinska
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Corresponding author

Correspondence to Hanna Livinska .

Editor information

Editors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Belarusian State University, Minsk, Belarus

    Alexander Dudin

  2. Institute of Applied Mathematics and Computer Science, Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Institute of Applied Mathematics and Computer Science, Tomsk State University, Tomsk, Russia

    Alexander Moiseev

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Lebedev, E., Livinska, H. (2018). On Gaussian Approximation of Queueing Networks with Different Starting Load. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM WRQ 2018 2018. Communications in Computer and Information Science, vol 912. Springer, Cham. https://doi.org/10.1007/978-3-319-97595-5_3

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  • DOI: https://doi.org/10.1007/978-3-319-97595-5_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-97594-8

  • Online ISBN: 978-3-319-97595-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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