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Construction and Analysis of Queuing and Reliability Models Using Random Graphs

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  • Gurami Tsitsiashvili

    (Institute for Applied Mathematics, Far Eastern Branch of Russian Academy Sciences, 690041 Vladivostok, Russia)

Abstract

In this paper, the use of the construction of random processes on graphs allows us to expand the models of the theory of queuing and reliability by constructing. These problems are important because the emphasis on the legal component largely determines functioning of these models. The considered models are reliability and queuing. Reliability models arranged according to the modular principle and reliability networks in the form of planar graphs. The queuing models considered here are queuing networks with multi server nodes and failures, changing the parameters of the queuing system in a random environment with absorbing states, and the process of growth of a random network. This is determined by the possibility of using, as traditional probability methods, mathematical logic theorems, geometric images of a queuing network, dual graphs to planar graphs, and a solution to the Dirichlet problem.

Suggested Citation

  • Gurami Tsitsiashvili, 2021. "Construction and Analysis of Queuing and Reliability Models Using Random Graphs," Mathematics, MDPI, vol. 9(19), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2511-:d:651064
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    1. Benjamin Allen & Christine Sample & Robert Jencks & James Withers & Patricia Steinhagen & Lori Brizuela & Joshua Kolodny & Darren Parke & Gabor Lippner & Yulia A Dementieva, 2020. "Transient amplifiers of selection and reducers of fixation for death-Birth updating on graphs," PLOS Computational Biology, Public Library of Science, vol. 16(1), pages 1-20, January.
    2. Sergey V. Buldyrev & Roni Parshani & Gerald Paul & H. Eugene Stanley & Shlomo Havlin, 2010. "Catastrophic cascade of failures in interdependent networks," Nature, Nature, vol. 464(7291), pages 1025-1028, April.
    3. James R. Jackson, 1957. "Networks of Waiting Lines," Operations Research, INFORMS, vol. 5(4), pages 518-521, August.
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    Cited by:

    1. Viacheslav Morozov & Vladimir Shepelev & Viktor Kostyrchenko, 2022. "Modeling the Operation of Signal-Controlled Intersections with Different Lane Occupancy," Mathematics, MDPI, vol. 10(24), pages 1-24, December.

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