Analysis of flow dynamics on Buslaev contour networks

Marina Victorovna Yashina, Alexander Gennadievich Tatashev

Abstract


Traffic flow models on networks are relevant because of exponential growth of road transport in megalopolises worldwide. But there are not enough adequate approaches to describe such processes. Buslaev A.P. with co-authors had introduced networks of contours with common nodes, local particles movement on each contour in given direction and competition resolution rules in common nodes. The problem is to study limit system behavior in dependence on initial conditions. In mathematical models of communication systems and computer networks, particles correspond to messages or information blocks (message packages). Behavior of particles on a contour chain with two cells on each contour is similar to behavior of Ising model used in quantum mechanics. In particular, Ising model is used for modeling of behavior of experimental computers based on principles of quantum mechanics. Contour network models can be used for study of spectral quantization. We study a behavior contour networks of Buslaev type for regular cases depending on rules of competition resolutions in common nodes. Exact results were obtained for closed chain with opposite and odd-even resolution rules, and stochastic version of left-priority rule with non-zero probability of indecisive movement.

Keywords


Discrete dynamical systems Buslaev contour networks Traffic models Competition resolution rule Spectral cycles

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References


Buslaev A.P., Yashina M.V. Mathematical aspects on traffic of incompressible worms on simple circular structures. Proceedings of the 16th International Conference on Computational and Mathematical Methods on Science and Engineering, CMMSE 2016, 4-8 July, 2016, vol. 1, pp. 273 –279. ISBN 978-84-608-6082-2

V. V. Kozlov, A. P. Buslaev, A.G. Tatashev, M.V. Yashina. On dynamical systems modelling for transport and communication. CMMSE– 2014, CostaBallena, Rota, Cadiz (Spain) July 3rd-7th, 2014.

K. Nagel and M. Schreckenberg, Cellular automation model for freeway traffic, J. Phys. I. 9, 1992, pp. 296–305.

Blank M.L. Exact analysis of dynamical systems arising in models of traffic flow. Russian Mathematical Surveys (2000), vol. 55, no. 3, pp. 562- 563

Gray L, Grefeath D. The ergodic theory of traffic jams. Journal of Statistical Physics, 2001, vol 105,

no.3/4, pp. 413-452.

Biham O., Middleton A. A., Levine D. Self-organization and a dynamical transition in traffic-flow models //Physical Review A. – 1992. – Т. 46. – №. 10. – С. R6124.

D’Souza R. M. Coexisting phases and lattice dependence of a cellular automaton model for traffic flow //Physical Review E. – 2005. – Т. 71. – №. 6. – С. 066112.

Angel, O., Holroyd, A., & Martin, J. (2005). The jammed phase of the Biham-Middleton-Levine traffic model. Electronic Communications in Probability, 10, 167-178.

Austin, T. D., & Benjamini, I. (2006). For what number of cars must self organization occur in the Biham-Middleton-Levine traffic model from any possible starting configuration?

Bugaev A.S., Buslaev A.P., Kozlov V.V., Yashina M.V. Distributed Problems of Monitoring and Modern Approaches to Traffic Modeling, 14th International IEEE Conference on Intelligent Transportation Systems (ITSC 2011), (2011) 477 - 481.

Buslaev A.P., Tatashev A.G., Yashina M.V. Cluster flow models

and properties of appropriate dynamical systems / J. of Applied functional analysis, v. 8, n.1, 2013, p. 54-77

V. V. Kozlov, A. P. Buslaev, and A. G. Tatashev. On synergy of totally connected flows on chainmails. Proc. of the 13 International Conference on Computational and Mathematical Methods in Science and Engineering, Almeria, Spain. Vol. 3. 2013.

Buslaev A.P., Fomina M.Yu., Tatashev A.G., Yashina M.V. On discrete flow networks model spectra: statement, simulation, hypotheses. Journal of Physics: Conference Series, 1053 (2018) 012034, pp. 1–7

V.V. Kozlov, A. P. Buslaev, A. G. Tatashev Monotonic walks on a necklace and a coloured dynamic vector International Journal of Computer Mathematics, 92:9 (2015), 1910–1920. Taylor& Francis

S. Wolfram. Statistical mechanics of cellular automata, Rev. Mod. Phys., 55, 1983, pp. 601-644.

Buslaev A. P., Tatashev A. G., Yashina M. V. (2018) Flows spectrum on closed trio of contours. Eur. J. Pure Appl. Math., 11(1): 260-283.

V. V. Kozlov, A. P. Buslaev, and A. G. Tatashev (2015) A dynamical communication system on a network. J. Comput. Appl. Math., Vol. 275, p. 247–261

Kozlov V.V., Buslaev A. P., Tatashev A. G., Yashina M. V. (2015) Dynamical systems on honeycombs // Traffic and Granular Flow '13, Springer, 2015, Part II, 441–452.

Buslaev A.P., Тatashev A.G., Yashina M.V. (2013) Qualitative Properties of Dynamical System on Toroidal Chainmail // AIP Conference Proceedings, p. 1144-1147

Lukanin V.N., Buslaev A.P., Trofimenko Yu.W., Yashina M.V. (1998) Modelling and optimal control of transport flows in megapolis// International Journal of Vehicle Design, 19(3), 267-281.




DOI: http://dx.doi.org/10.21533/pen.v7i1.382

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Copyright (c) 2019 Marina Victorovna Yashina

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ISSN: 2303-4521

Digital Object Identifier DOI: 10.21533/pen

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License