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Application of Method of Differential Inequalities to Bounding the Rate of Convergence for a Class of Markov Chains

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Differential and Difference Equations with Applications (ICDDEA 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 333))

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Abstract

We consider the linear system of differential equations \(\frac{d\mathbf{p}}{dt}=A(t)\mathbf{p}\), which is the forward Kolmogorov system, for a class of Markov chains with ‘batch’ births and single deaths. We apply the method of differential inequalities for obtaining bounds on the rate of convergence for the system. A specific queueing model is considered and the corresponding limiting characteristics are computing.

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Acknowledgements

This research was supported by Russian Science Foundation under grant 19-11-00020.

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Authors and Affiliations

  1. Vologda State University, Lenina, 15, Vologda, Russia

    Anastasia Kryukova, Victoria Oshushkova & Yacov Satin

  2. Institute of Informatics Problems FRC CSC RAS, Vologda Research Center RAS, Vologda State University, Lenina, 15, Vologda, Russia

    Alexander Zeifman

Authors
  1. Anastasia Kryukova
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  2. Victoria Oshushkova
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  3. Alexander Zeifman
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  4. Yacov Satin
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Corresponding author

Correspondence to Alexander Zeifman .

Editor information

Editors and Affiliations

  1. Department of Exact Sciences and Engineering, Military Academy, Lisbon, Portugal

    Sandra Pinelas

  2. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, USA

    John R. Graef

  3. Mathematik und Didaktik, Katholische Universität Eichstätt, Eichstätt, Bayern, Germany

    Stefan Hilger

  4. Huazhong University of Science and Technology, Wuhan, Hubei, China

    Peter Kloeden

  5. Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Xanthi, Greece

    Christos Schinas

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Kryukova, A., Oshushkova, V., Zeifman, A., Satin, Y. (2020). Application of Method of Differential Inequalities to Bounding the Rate of Convergence for a Class of Markov Chains. In: Pinelas, S., Graef, J.R., Hilger, S., Kloeden, P., Schinas, C. (eds) Differential and Difference Equations with Applications. ICDDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 333. Springer, Cham. https://doi.org/10.1007/978-3-030-56323-3_8

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