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Comparison of Reproduction of Spatiotemporal Structures of Traffic Flows Using Various Ways of Averaging Data

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Mathematical Models and Computer Simulations Aims and scope

Abstract

This study is devoted to the approbation of a two-dimensional microscopic model of vehicle traffic created by the authors based on the theory of cellular automata (CA) on test problems presented in the literature. The obtained spatiotemporal structures of the traffic flow’s velocity distribution are compared with the experimental data. The choice of the optimal averaging method for a more adequate reflection of the results is theoretically substantiated and verified using a numerical experiment. The presented results confirm that the proposed CA model adequately reproduces the patterns observed in the velocity diagrams of real traffic flows and also provides greater similarity with the experimental data in comparison with the other presented models.

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REFERENCES

  1. S. Maerivoet and B. De Moor, “Cellular automata models of road traffic,” Phys. Rep. 419, 1–64 (2005).

    Article  MathSciNet  Google Scholar 

  2. A. P. Buslaev, A. G. Tatashev, and M. V. Yashina, “On cellular automata, traffic and dynamical systems in graphs,” Int. J. Eng. Technol. 7 (2), 351–356 (2018).

  3. B. S. Kerner, S. L. Klenov, and M. Schreckenberg, “Simple cellular automaton model for traffic breakdown, highway capacity, and synchronized flow,” Phys. Rev. E 84, 046110 (2011).

    Article  Google Scholar 

  4. B. S. Kerner, S. L. Klenov, G. Hermanns, and M. Schreckenberg, “Effect of driver over-acceleration on traffic breakdown in three-phase cellular automaton traffic flow models,” Phys. A: Stat. Mech. Its Appl. 392, 4083–4105 (2013).

    Article  MathSciNet  Google Scholar 

  5. T. P. E. Vranken and M. Schreckenberg, “Cellular automata intersection model,” Collect. Dyn. 5, A80 (2020). https://doi.org/10.17815/CD.2020.80

  6. H.-T. Zhao, X.-R. Liu, X.-X. Chen, and J.-C. Lu, “Cellular automata model for traffic flow at intersections in internet of vehicles,” Phys. A: Stat. Mech. Its Appl. 494, 40–51 (2018). https://doi.org/10.1016/j.physa.2017.11.152

    Article  MathSciNet  Google Scholar 

  7. H.-T. Zhao, S. Yang, and X.-X. Che, “Cellular automata model for urban road traffic flow considering pedestrian crossing street,” Phys. A: Stat. Mech. Its Appl. 462, 1301–1313 (2018). https://doi.org/10.1016/j.physa.2016.06.146

    Article  Google Scholar 

  8. X. Li and J.-Q. Sun, “Effects of turning and through lane sharing on traffic performance at intersections,” Phys. A: Stat. Mech. Its Appl. 444, 622–640 (2016).

    Article  MathSciNet  Google Scholar 

  9. J. Vasic and H. J. Ruskin, “Cellular automata simulation of traffic including cars and bicycles,” Phys. A: Stat. Mech. Its Appl. 391, 2720–2729 (2012).

    Article  Google Scholar 

  10. M. E. Lárraga and L. Alvarez-Icaza, “Cellular automaton model for traffic flow based on safe driving policies and human reactions,” Phys. A: Stat. Mech. Its Appl. 389, 5425–5438 (2010).

    Article  Google Scholar 

  11. J. S. L. Combinido and M. T. Lim, “Modeling U-turn traffic flow,” Phys. A: Stat. Mech. Its Appl. 389, 3640–3647 (2010).

    Article  Google Scholar 

  12. H. B. Zhu, “Numerical study of urban traffic flow with dedicated bus lane and intermittent bus lane,” Phys. A: Stat. Mech. Its Appl. 389, 3134–3139 (2010).

    Article  Google Scholar 

  13. K. Gao, R. Jiang, B.-H. Wang, and Q.-S. Wu, “Discontinuous transition from free flow to synchronized flow induced by short-range interaction between vehicles in a three-phase traffic flow model,” Phys. A: Stat. Mech. Its Appl. 388 , 3233–3243 (2009).

    Article  Google Scholar 

  14. J. von Neumann, Theory of Self-Reproducing Automata, ed. by A. W. Burks (University of Illinois Press, Urbana, IL, 1966; URSS, Moscow, 2010).

  15. S. Wolfram, A New Kind of Science (Wolfram Media, Champaign, IL, 2002). https://www.wolframscience.com/nks/.

    MATH  Google Scholar 

  16. K. Nagel and M. Schreckenberg, “A cellular automaton model for freeway traffic,” J. Phys. I France 2, 2221–2229 (1992).

  17. M. A. Trapeznikova, A. A. Chechina, and N. G. Churbanova, “Two-dimensional cellular automata model for simulation of traffic flow dynamics on the elements of city road network,” Mat. Model. 29 (9), 110–120 (2017).

    MathSciNet  MATH  Google Scholar 

  18. N. G. Churbanova, A. A. Chechina, M. A. Trapeznikova, and P. A. Sokolov, “Simulation of traffic flows on road segments using cellular automata theory and quasigasdynamic approach,” Math. Montisnigri 46, 72–90 (2019).

    Article  MathSciNet  Google Scholar 

  19. B. S. Kerner, The Physics of Traffic: Empirical Freeway Pattern Features, Engineering Applications, and Theory (Springer, Berlin, 2004).

    Book  Google Scholar 

  20. M. Treiber and A. Kesting, Traffic Flow Dynamics: Data, Models and Simulation (Springer, Berlin, 2013).

    Book  Google Scholar 

  21. M. O. Izmailova and I. Sh. Rakhmankulov, Category “Mean Value” and Its Methodological Significance in Scientific Research (Kazan. Univ., Kazan, 1982) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    A. A. Chechina, N. G. Churbanova & M. A. Trapeznikova

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  1. A. A. Chechina
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  2. N. G. Churbanova
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  3. M. A. Trapeznikova
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Correspondence to A. A. Chechina, N. G. Churbanova or M. A. Trapeznikova.

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Chechina, A.A., Churbanova, N.G. & Trapeznikova, M.A. Comparison of Reproduction of Spatiotemporal Structures of Traffic Flows Using Various Ways of Averaging Data. Math Models Comput Simul 13, 756–762 (2021). https://doi.org/10.1134/S2070048221050070

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