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Ergodicity and Polynomial Convergence Rate of Generalized Markov Modulated Poisson Processes

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Distributed Computer and Communication Networks: Control, Computation, Communications (DCCN 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1337))

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Abstract

Generalization of the Lorden’s inequality is an excellent tool for obtaining strong upper bounds for the convergence rate for various complicated stochastic models. This paper demonstrates a method for obtaining such bounds for some generalization of the Markov modulated Poisson process (MMPP). The proposed method can be applied in the reliability and queuing theory.

The work is supported by RFBR, project No 20-01-00575A.

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Acknowledgments

The author is grateful to E. Yu. Kalimulina for the great help in preparing this paper. The work is supported by RFBR, project No. 20-01-00575A.

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Authors and Affiliations

  1. V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya street, 117997, Moscow, Russia

    Galina Zverkina

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  1. Galina Zverkina
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Correspondence to Galina Zverkina .

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Editors and Affiliations

  1. V.A.Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

    Vladimir M. Vishnevskiy

  2. Peoples’ Friendship University of Russia (RUDN University), Moscow, Russia

    Konstantin E. Samouylov

  3. V.A.Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

    Dmitry V. Kozyrev

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Zverkina, G. (2020). Ergodicity and Polynomial Convergence Rate of Generalized Markov Modulated Poisson Processes. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2020. Communications in Computer and Information Science, vol 1337. Springer, Cham. https://doi.org/10.1007/978-3-030-66242-4_29

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  • DOI: https://doi.org/10.1007/978-3-030-66242-4_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-66241-7

  • Online ISBN: 978-3-030-66242-4

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