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Sign CUSUM Algorithm for Change-Point Detection of the MMPP Controlling Chain State

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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

The authors consider the Markov modulated Poisson process with two states of the Markovian controlling chain. The flow intensity of the observed process depends on the unobserved controlling chain state. All the process parameters are supposed to be unknown. The paper develops a new sequential change-point detection method based on the cumulative sum control chart approach to determine the switching points of the flow intensity. Usage of special sign statistics allows the obtaining of theoretical characteristics of the proposed algorithm.

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Acknowledgements

Y. Burkatovskaya is supported by The National Research Tomsk State University Academic D.I. Mendeleev Fund Program (NU 8.1.55.2015 L) in 2014–2015 and by RFBR Grant 16-01-00121.

The authors are grateful to Prof. Sergey Vorobeychikov from Tomsk State University for useful comments.

Author information

Authors and Affiliations

  1. Institute of Cybernetics, Tomsk Polytechnic University, 30 Lenin Prospekt, 634050, Tomsk, Russia

    Yulia Burkatovskaya & Olga Tokareva

  2. Department of Applied Mathematics and Cybernetics, Tomsk State University, 36 Lenin Prospekt, 634050, Tomsk, Russia

    Yulia Burkatovskaya & Tatiana Kabanova

  3. International Laboratory of Statistics of Stochastic Processes and Quantitative Finance, Tomsk State University, 36 Lenin Prospekt, 634050, Tomsk, Russia

    Yulia Burkatovskaya

Authors
  1. Yulia Burkatovskaya
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  2. Tatiana Kabanova
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  3. Olga Tokareva
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Corresponding author

Correspondence to Tatiana Kabanova .

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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Burkatovskaya, Y., Kabanova, T., Tokareva, O. (2016). Sign CUSUM Algorithm for Change-Point Detection of the MMPP Controlling Chain State. 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_2

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  • DOI: https://doi.org/10.1007/978-3-319-44615-8_2

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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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