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Retrial Queueing System MMPP/M/1 with Impatient Calls Under Heavy Load Condition

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Queueing Theory and Network Applications (QTNA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11688))

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Abstract

In this paper, a single server retrial queue MMPP/M/1 with impatient calls is analysed under the heavy load condition. The retrial queue has a dynamical rate of the calls patience depending on the number of calls in the orbit. It is proved that under the heavy load condition the asymptotic characteristic function of the number of calls in the orbit has the gamma distribution with obtained parameters. Also the formula for the system throughput is obtained. Some numerical examples are presented.

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Acknowledgments

The reported study was funded by RFBR according to the research project No. 19-41-703002.

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Authors and Affiliations

  1. National Research Tomsk State University, Lenina Avenue, 36, Tomsk, Russia

    Ekaterina Fedorova, Elena Danilyuk & Anatoly Nazarov

  2. Institute of Control Systems, Azerbaijan National Academy of Sciences, B. Vahabzadeh Street, 9, Baku, Azerbaijan

    Agassi Melikov

Authors
  1. Ekaterina Fedorova
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  2. Elena Danilyuk
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  3. Anatoly Nazarov
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  4. Agassi Melikov
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Corresponding author

Correspondence to Elena Danilyuk .

Editor information

Editors and Affiliations

  1. University of Tsukuba, Tsukuba, Japan

    Tuan Phung-Duc

  2. Nara Institute of Science and Technology, Nara, Japan

    Shoji Kasahara

  3. Ghent University, Ghent, Belgium

    Sabine Wittevrongel

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Fedorova, E., Danilyuk, E., Nazarov, A., Melikov, A. (2019). Retrial Queueing System MMPP/M/1 with Impatient Calls Under Heavy Load Condition. In: Phung-Duc, T., Kasahara, S., Wittevrongel, S. (eds) Queueing Theory and Network Applications. QTNA 2019. Lecture Notes in Computer Science(), vol 11688. Springer, Cham. https://doi.org/10.1007/978-3-030-27181-7_1

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  • DOI: https://doi.org/10.1007/978-3-030-27181-7_1

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  • Online ISBN: 978-3-030-27181-7

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