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Partial Diffusion Markov Model of Heterogeneous TCP Link: Optimization with Incomplete Information

Author

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  • Andrey Borisov

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44/2 Vavilova Str., 119333 Moscow, Russia
    Moscow Aviation Institute, 4, Volokolamskoe Shosse, 125993 Moscow, Russia
    Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, GSP-1, 1-52 Leninskiye Gory, 119991 Moscow, Russia
    Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, 119991 Moscow, Russia)

  • Alexey Bosov

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44/2 Vavilova Str., 119333 Moscow, Russia
    Moscow Aviation Institute, 4, Volokolamskoe Shosse, 125993 Moscow, Russia)

  • Gregory Miller

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44/2 Vavilova Str., 119333 Moscow, Russia)

  • Igor Sokolov

    (Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, GSP-1, 1-52 Leninskiye Gory, 119991 Moscow, Russia)

Abstract

The paper presents a new mathematical model of TCP (Transmission Control Protocol) link functioning in a heterogeneous (wired/wireless) channel. It represents a controllable, partially observable stochastic dynamic system. The system state describes the status of the modeled TCP link and expresses it via an unobservable controllable MJP (Markov jump process) with finite-state space. Observations are formed by low-frequency counting processes of packet losses and timeouts and a high-frequency compound Poisson process of packet acknowledgments. The information transmission through the TCP-equipped channel is considered a stochastic control problem with incomplete information. The main idea to solve it is to impose the separation principle on the problem. The paper proposes a mathematical framework and algorithmic support to implement the solution. It includes a solution to the stochastic control problem with complete information, a diffusion approximation of the high-frequency observations, a solution to the MJP state filtering problem given the observations with multiplicative noises, and a numerical scheme of the filtering algorithm. The paper also contains the results of a comparative study of the proposed state-based congestion control algorithm with the contemporary TCP versions: Illinois, CUBIC, Compound, and BBR (Bottleneck Bandwidth and RTT).

Suggested Citation

  • Andrey Borisov & Alexey Bosov & Gregory Miller & Igor Sokolov, 2021. "Partial Diffusion Markov Model of Heterogeneous TCP Link: Optimization with Incomplete Information," Mathematics, MDPI, vol. 9(14), pages 1-31, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1632-:d:592031
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    References listed on IDEAS

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    Cited by:

    1. Alexey Bosov & Andrey Borisov, 2022. "Comparative Study of Markov Chain Filtering Schemas for Stabilization of Stochastic Systems under Incomplete Information," Mathematics, MDPI, vol. 10(18), pages 1-20, September.

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