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On Comparison of Waiting Time Extremal Indexes in Queueing Systems with Weibull Service Times

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Information Technologies and Mathematical Modelling. Queueing Theory and Applications (ITMM 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1605))

Abstract

The paper is devoted to the tail asymptotics analysis of the steady-state waiting times in the queuing systems in which service times have Weibull distributions. We deduce conditions under which the service times in two different queueing systems are stochastically ordered. Then we show that, under the same conditions, the normalizing sequences of the stationary waiting times and their extremal indexes are ordered. These results are then illustrated numerically for GI/G/1 queues with different shape parameters of the Weibull service times.

The research has been prepared with the support of Russian Science Foundation according to the research project No. 21-71-10135.

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Authors and Affiliations

  1. Petrozavodsk State University, Lenin Str. 33, Petrozavodsk, 185910, Russia

    Irina Peshkova & Evsey Morozov

  2. Institute of Applied Mathematical Research of the Karelian Research Centre of RAS, Pushkinskaya Str. 11, Petrozavodsk, 185910, Russia

    Irina Peshkova, Evsey Morozov & Maria Maltseva

  3. Moscow Center for Fundamental and Applied Mathematics, Moscow State University, Moscow, 119991, Russia

    Evsey Morozov

Authors
  1. Irina Peshkova
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  2. Evsey Morozov
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  3. Maria Maltseva
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Corresponding authors

Correspondence to Irina Peshkova , Evsey Morozov or Maria Maltseva .

Editor information

Editors and Affiliations

  1. Belarusian State University, Minsk, Belarus

    Alexander Dudin

  2. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Tomsk State University, Tomsk, Russia

    Alexander Moiseev

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Peshkova, I., Morozov, E., Maltseva, M. (2022). On Comparison of Waiting Time Extremal Indexes in Queueing Systems with Weibull Service Times. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2021. Communications in Computer and Information Science, vol 1605. Springer, Cham. https://doi.org/10.1007/978-3-031-09331-9_7

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  • DOI: https://doi.org/10.1007/978-3-031-09331-9_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-09330-2

  • Online ISBN: 978-3-031-09331-9

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