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Retrial Queue MMPP/M/1 with Server Switching

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Information Technologies and Mathematical Modelling. Queueing Theory and Applications (ITMM 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1803))

Abstract

In the paper, we study a retrial queueing system with one server with switching, where a service rate depends on the number of customers in the orbit (it has two values). The arrival process of customers is MMPP, the delay time in the orbit is distributed exponentially. To find the stationary distribution of the number of customers in the orbit, the method of the asymptotic analysis is proposed under the condition of a heavy load. It is proved that the asymptotic characteristic function has the gamma distribution form. The numerical analysis of obtained results is carried out.

This study was supported by the Tomsk State University Development Programme (Priority-2030).

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Authors and Affiliations

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

    Ksenya Khadzhi-Ogly, Radmir Salimzyanov & Ekaterina Fedorova

Authors
  1. Ksenya Khadzhi-Ogly
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  2. Radmir Salimzyanov
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  3. Ekaterina Fedorova
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Corresponding author

Correspondence to Ksenya Khadzhi-Ogly .

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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Khadzhi-Ogly, K., Salimzyanov, R., Fedorova, E. (2023). Retrial Queue MMPP/M/1 with Server Switching. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2022. Communications in Computer and Information Science, vol 1803. Springer, Cham. https://doi.org/10.1007/978-3-031-32990-6_7

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  • DOI: https://doi.org/10.1007/978-3-031-32990-6_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-32989-0

  • Online ISBN: 978-3-031-32990-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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