On properties of closed/open two-dimensional network-chainmail with different rules of particle movement

Ivan Alekseevich Kuteynikov, Alexander Gennadievich Tatashev, Marina Victorovna Yashina


With the increase in the number of vehicles and the dimension of road networks, the problem of developing adequate and effective mathematical models to traffic simulation arises. The paper represents the traffic studies based on deterministic two-dimensional network of contours called chainmail introduced by A.P. Buslaev et al. Each contour consists of four cells and one particle moving around it. The open and closed versions of chainmail models with one-directional and co-directional particle movement are considered. The average velocity and other characteristics of chainmail are studied. Four theorems and hypotheses formulated in 2013, 2018 describing the dependence of average velocities of one-directional/co-directional particle movement on initial states of closed/open chainmail are tested and extended with the simulation modeling.


Two-dimensional chainmail, Dynamical systems, Self-organization, Simulation models

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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.

Buslaev, A. P., A. G. Tatashev, and M. V. Yashina. "Qualitative properties of dynamical system on toroidal chainmail." AIP Conference Proceedings. Vol. 1558. No. 1. AIP, 2013.

Fomina, Maria Ju, et al. "Cellular Automata as Traffic Models and Spectrum of Two-Dimensional Contour Networks—Open Chainmails." 2018 IEEE International Conference" Quality Management, Transport and Information Security, Information Technologies"(IT&QM&IS). IEEE, 2018.

Kozlov, V. V., 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.

Kozlov, Valery V., Alexander P. Buslaev, and Alexander G. Tatashev. "Behavior of pendulums on a regular polygon." Journal of Communication and Computer 11 (2014): 30-38.

DOI: http://dx.doi.org/10.21533/pen.v7i1.340


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Copyright (c) 2019 Ivan Kuteynikov

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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