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Analytical Solution of the Mixed Traffic Flow Cellular Automaton FI Model with the Next-Nearest-Neighbor Interaction

Author

Listed:
  • Yanxin Zhang

    (Institute of Physical Science and Technology, Guangxi University, Nanning 530004, China)

  • Yu Xue

    (Institute of Physical Science and Technology, Guangxi University, Nanning 530004, China
    Guangxi Key Lab Relativist Astrophys, Nanning 530004, China)

  • Yanfeng Qiao

    (Institute of Physical Science and Technology, Guangxi University, Nanning 530004, China)

  • Bingling Cen

    (Institute of Physical Science and Technology, Guangxi University, Nanning 530004, China)

Abstract

Based on a one-dimensional (1D) traffic flow cellular automaton (CA) FI model, a deterministic next-nearest-neighbor interaction FI model (NIFI model) is proposed. Using the mean-field analysis, the analytical solution of the NIFI model in one-dimensional traffic flow is derived under periodic boundary conditions. For the mixed traffic flow, the occupancy and the mixing ratio are introduced to describe the mixing effect. Similarly, using the mean-field method, the exact solution of the mixed traffic flow is derived from the long-time evolution to reach the steady state. The numerical simulations are carried out for the mixed traffic flow with different vehicle lengths, maximum velocities, and mixing ratios to verify the analytical solutions. The results show that the numerical simulation results agree well with the analytical solution.

Suggested Citation

  • Yanxin Zhang & Yu Xue & Yanfeng Qiao & Bingling Cen, 2022. "Analytical Solution of the Mixed Traffic Flow Cellular Automaton FI Model with the Next-Nearest-Neighbor Interaction," Sustainability, MDPI, vol. 14(12), pages 1-12, June.
    • Handle: RePEc:gam:jsusta:v:14:y:2022:i:12:p:7127-:d:835737
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    References listed on IDEAS

    as
    1. Qiao, Yan-feng & Xue, Yu & Wang, Xue & Cen, Bing-ling & Wang, Yi & Pan, Wei & Zhang, Yan-xin, 2021. "Investigation of PM emissions in cellular automata model with slow-to-start effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    2. Wang, Xue & Xue, Yu & Cen, Bing-ling & Zhang, Peng & He, Hong-di, 2020. "Study on pollutant emissions of mixed traffic flow in cellular automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    3. Chowdhury, Debashish & Wolf, Dietrich E. & Schreckenberg, Michael, 1997. "Particle hopping models for two-lane traffic with two kinds of vehicles: Effects of lane-changing rules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 235(3), pages 417-439.
    4. Knospe, Wolfgang & Santen, Ludger & Schadschneider, Andreas & Schreckenberg, Michael, 1999. "Disorder effects in cellular automata for two-lane traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 265(3), pages 614-633.
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