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On Steady-State Analysis of \( \left[ M|M|m|m+n \right] \) -Type Retrial Queueing Systems

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Information Technologies and Mathematical Modelling. Queueing Theory and Applications (ITMM 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 800))

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Abstract

In this paper we introduce a bivariate Markov process \(Q(t)=\left( Q_1(t)),Q_2(t) \right) \in \left\{ 0,1,...,m+n \right\} \times Z_+.\) The process \(Q(t), t\ge 0,\) can be seen as the joint process of the number of servers and waiting positions occupied and the number of customers in the orbit of a \( \left[ M|M|m|m+n \right] \) -type retrial queueing system. For the truncated model of Q(t) stationary probabilities are written in explicit vector-matrix form. The result obtained is used for stationary distribution calculation in the model of Q(t) with the infinite orbit and for construction of explicit formulas for stationary probabilities of a \(\left[ M|M|1|1+1 \right] \) -model.

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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, Igor Makushenko, Hanna Livinska & Iryna Usar

Authors
  1. Eugene Lebedev
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  2. Igor Makushenko
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  3. Hanna Livinska
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  4. Iryna Usar
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Corresponding author

Correspondence to Hanna Livinska .

Editor information

Editors and Affiliations

  1. Belarusian State University, Minsk, Belarus

    Alexander Dudin

  2. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Kazan National Research Technological University, Kazan, Russia

    Alexander Kirpichnikov

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Lebedev, E., Makushenko, I., Livinska, H., Usar, I. (2017). On Steady-State Analysis of \( \left[ M|M|m|m+n \right] \) -Type Retrial Queueing Systems. In: Dudin, A., Nazarov, A., Kirpichnikov, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2017. Communications in Computer and Information Science, vol 800. Springer, Cham. https://doi.org/10.1007/978-3-319-68069-9_11

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  • DOI: https://doi.org/10.1007/978-3-319-68069-9_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68068-2

  • Online ISBN: 978-3-319-68069-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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