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Markov and Non-Markov Probabilistic Models of Interacting Flows of Annihilating Particles

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Information Technologies and Mathematical Modelling - Queueing Theory and Applications (ITMM 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 638))

Abstract

We propose Markov and non-Markov probabilistic models of how flows of annihilating particles interact, find the probability distribution of the number of positive applications in the model, and we present asymptotic results for the case of high intensity incoming flows. Then we study a system with non-exponential service where, using asymptotic analysis, we show that as the intensity of incoming flows grows, the probability distribution becomes Gaussian and find the parameters of the distribution. We also investigate flows of interacting particles as an infinitely linear queuing system with positive and negative applications of different systems and the probability distribution of the number of positive stationary applications in a system with exponential service is found. We also studied a case of arbitrary service by means of asymptotic analysis. We demonstrate that these systems are asymptotically equivalent.

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Acknowledgments

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

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Authors and Affiliations

  1. National Research Tomsk State University, TSU, 36 Lenin Prospekt, Tomsk, 634050, Russia

    Anatoly Nazarov

  2. V.A. Trapeznikov Institute of Control Sciences of RAS, Profsoyuznaya str. 65, Moscow, 117997, Russia

    Mais Farkhadov

  3. Intelligent Systems and Networks (ISN), Department of Electrical and Electronic Engineering, Imperial College London, EEE Bldg Rm 1009, South Kensington Campus, London, UK

    Erol Gelenbe

Authors
  1. Anatoly Nazarov
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  2. Mais Farkhadov
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  3. Erol Gelenbe
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Corresponding author

Correspondence to Mais Farkhadov .

Editor information

Editors and Affiliations

  1. Belarusian State University , Minsk, Belarus

    Alexander Dudin

  2. Tomsk State University , Tomsk, Russia

    Alexander Gortsev

  3. Tomsk State University , Tomsk, Russia

    Anatoly Nazarov

  4. Kemerovo State University , Anzhero-Sudzhensk, Russia

    Rafael Yakupov

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© 2016 Springer International Publishing Switzerland

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Nazarov, A., Farkhadov, M., Gelenbe, E. (2016). Markov and Non-Markov Probabilistic Models of Interacting Flows of Annihilating Particles. In: Dudin, A., Gortsev, A., Nazarov, A., Yakupov, R. (eds) Information Technologies and Mathematical Modelling - Queueing Theory and Applications. ITMM 2016. Communications in Computer and Information Science, vol 638. Springer, Cham. https://doi.org/10.1007/978-3-319-44615-8_25

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  • DOI: https://doi.org/10.1007/978-3-319-44615-8_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44614-1

  • Online ISBN: 978-3-319-44615-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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