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Necessary Conditions for the Existence of Stationary Distribution in the Adaptive Control System of Conflict Flows

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Analytical and Computational Methods in Probability Theory (ACMPT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10684))

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Abstract

A control process for conflict flows of nonhomogeneous arrivals is considered. A mathematical model of a control system with variable structure is constructed and studied. Recurrence relations are found for the states of the server and the queues length. Recurrence relations are also obtained for one-dimensional probability distributions for the vector Markovian sequence of the system states in one step and in the number of steps equal to the number of the server’s basic states. We propose an iterative-majorant method that allows to find easily verifiable necessary conditions for the stationary probability distribution existence.

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References

  1. Haight, F.A.: Mathematical Theories of Traffic Flow. Academic Press, New York (1963)

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  2. Fedotkin, M.A., Fedotkin, A.M., Kudryavtsev, E.V.: Construction and analysis of a mathematical model of spatial and temporal characteristics of traffic flows. Autom. Control Comput. Sci. 48(6), 358–367 (2014)

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Authors and Affiliations

  1. National Research Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod, Russia

    Mikhail Fedotkin & Evgeniy Kudryavtsev

Authors
  1. Mikhail Fedotkin
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  2. Evgeniy Kudryavtsev
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Corresponding author

Correspondence to Mikhail Fedotkin .

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Editors and Affiliations

  1. Department of Applied Probability and Informatics, RUDN University, Moscow, Russia

    Vladimir V. Rykov

  2. City University of Hong Kong, Hong Kong, Hong Kong

    Nozer D. Singpurwalla

  3. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

    Andrey M. Zubkov

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Fedotkin, M., Kudryavtsev, E. (2017). Necessary Conditions for the Existence of Stationary Distribution in the Adaptive Control System of Conflict Flows. In: Rykov, V., Singpurwalla, N., Zubkov, A. (eds) Analytical and Computational Methods in Probability Theory. ACMPT 2017. Lecture Notes in Computer Science(), vol 10684. Springer, Cham. https://doi.org/10.1007/978-3-319-71504-9_9

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  • DOI: https://doi.org/10.1007/978-3-319-71504-9_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71503-2

  • Online ISBN: 978-3-319-71504-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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