Geodesic
A cybernetic model of cyclic control of conflicting flows with an after-effect
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 3, pp. 66-75 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Lyapunov–Yablonsky approach has been used to construct a mathematical model of the service process of conflicting input flows in the class of cyclic algorithms with re-adjustments. To define input flows with dependent inter-arrival intervals, a non-local description has been used. The flowcharts, information, coordinates, and function of the queueing system have been selected and described non-locally. A multi-dimensional Markov chain has been constructed with an uncountable measurable state space, which describes changes in the server state, fluctuations in the queue size, and states of the input flows. Some properties of the stochastic transition kernel have been established.
Keywords: controlling system, conflicting input flows, non-ordinary recurrent flow, non-local description, general Markov chain. 
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A. V. Zorine. A cybernetic model of cyclic control of conflicting flows with an after-effect. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 3, pp. 66-75. http://geodesic.mathdoc.fr/item/UZKU_2014_156_3_a6/

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