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The \(M/GI/\infty \) System Subject to Semi-Markovian Random Environment

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Information Technologies and Mathematical Modelling - Queueing Theory and Applications (ITMM 2015)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 564))

Abstract

In this paper we consider an \(M/GI/\infty \) queueing system operating in a semi-Markovian random environment. That is, the arrival rate and service-time distribution change according to the external semi-Markov process state transitions. The service policy subject to environment transitions is as follows: the service-time distribution of the present customers does not change until their service is finished. The purpose of our study is to obtain the probability distribution of the number of customers in the system under asymptotic condition of high arrival rate and frequent environment transitions. To do this, we first apply the method of supplementary variable and the original method of dynamic screening to our system. We then conduct the asymptotic analysis of the system to obtain the discrete probability distribution.

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Acknowledgments

The work is supported by Tomsk State University Competitiveness Improvement Program.

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Authors and Affiliations

  1. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov & Galina Baymeeva

Authors
  1. Anatoly Nazarov
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  2. Galina Baymeeva
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Corresponding author

Correspondence to Anatoly Nazarov .

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Editors and Affiliations

  1. Applied Mathematics and Computer Science, Belarusian State University, Minsk, Russia

    Alexander Dudin

  2. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Kemerovo State University, Anzhero-Sudzhensk, Russia

    Rafael Yakupov

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Nazarov, A., Baymeeva, G. (2015). The \(M/GI/\infty \) System Subject to Semi-Markovian Random Environment. In: Dudin, A., Nazarov, A., Yakupov, R. (eds) Information Technologies and Mathematical Modelling - Queueing Theory and Applications. ITMM 2015. Communications in Computer and Information Science, vol 564. Springer, Cham. https://doi.org/10.1007/978-3-319-25861-4_11

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  • DOI: https://doi.org/10.1007/978-3-319-25861-4_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25860-7

  • Online ISBN: 978-3-319-25861-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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