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International Conference on Queueing Theory and Network Applications

QTNA 2019: Queueing Theory and Network Applications pp 51–63Cite as

Stability Conditions of a Multiclass System with NBU Retrials

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

Abstract

We consider a multiclass multiserver retrial queuing system with classical retrial discipline: the customers, meeting server busy, are blocked on the corresponding (virtual) orbit and then retry to occupy server independently. The retrial times have general class-dependent distributions. The input process is renewal and a new arrival is class-i customer with a given probability \(p_i\). We exploit a regenerative structure of a basic process describing the dynamics of the system to establish stability conditions. More exactly, we show that, provided the retrial times belong to the New-Better-Than-Used class, the convenient requirement that the mean load (traffic intensity) is less than the number of servers, is the stability criterion of the model. A few numerical results are included which, in particular, show that this condition ensures stability of the system with the New-Worse-Than-Used Weibull retrial times as well.

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Acknowledgement

The study was carried out under state order to the Karelian Research Centre of the Russian Academy of Sciences (Institute of Applied Mathematical Research KRC RAS). The research is partly supported by Russian Foundation for Basic Research, projects 18-07-00147, 18-07-00156, 19-07-00303.

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Authors and Affiliations

  1. Institute of Applied Mathematical Research Karelian Research Centre RAS, Petrozavodsk, Russia

    Evsey Morozov & Ruslana Nekrasova

  2. Petrozavodsk State University, Petrozavodsk, Russia

    Evsey Morozov & Ruslana Nekrasova

Authors
  1. Evsey Morozov
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  2. Ruslana Nekrasova
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Corresponding author

Correspondence to Ruslana Nekrasova .

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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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Morozov, E., Nekrasova, R. (2019). Stability Conditions of a Multiclass System with NBU Retrials. 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_4

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  • DOI: https://doi.org/10.1007/978-3-030-27181-7_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-27180-0

  • Online ISBN: 978-3-030-27181-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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