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The theoretical analysis of the lattice hydrodynamic models for traffic flow theory

Author

Listed:
  • Ge, H.X.
  • Cheng, R.J.
  • Lei, L.

Abstract

The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but also connected with the microscopic car following model closely. The modified Korteweg–de Vries (mKdV) equation related to the density wave in a congested traffic region has been derived near the critical point since Nagatani first proposed it. But the Korteweg–de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail for the car following model. We devote ourselves to obtaining the KdV equation from the original lattice hydrodynamic models and the KdV soliton solution to describe the traffic jam. Especially, we obtain the general soliton solution of the KdV equation and the mKdV equation. We review several lattice hydrodynamic models, which were proposed recently. We compare the modified models and carry out some analysis. Numerical simulations are conducted to demonstrate the nonlinear analysis results.

Suggested Citation

  • Ge, H.X. & Cheng, R.J. & Lei, L., 2010. "The theoretical analysis of the lattice hydrodynamic models for traffic flow theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2825-2834.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:14:p:2825-2834
    DOI: 10.1016/j.physa.2010.03.007
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    Cited by:

    1. He, Jia & Yang, Hai & Huang, Hai-Jun & Tang, Tie-Qiao, 2018. "Impacts of wireless charging lanes on travel time and energy consumption in a two-lane road system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 1-10.
    2. Wang, Yunong & Cheng, Rongjun & Ge, Hongxia, 2017. "A lattice hydrodynamic model based on delayed feedback control considering the effect of flow rate difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 478-484.
    3. Liu, Yi & Cheng, Rong-jun & Lei, Li & Ge, Hong-xia, 2016. "The influence of the non-motor vehicles for the car-following model considering traffic jerk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 376-382.
    4. He, Jia & Huang, Hai-Jun & Yang, Hai & Tang, Tie-Qiao, 2017. "An electric vehicle driving behavior model in the traffic system with a wireless charging lane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 119-126.
    5. Li, Yongfu & Li, Kezhi & Zheng, Taixiong & Hu, Xiangdong & Feng, Huizong & Li, Yinguo, 2016. "Evaluating the performance of vehicular platoon control under different network topologies of initial states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 359-368.
    6. He, Jia & He, Zhengbing & Fan, Bo & Chen, Yanyan, 2020. "Optimal location of lane-changing warning point in a two-lane road considering different traffic flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    7. Liu, Hui & Sun, Dihua & Liu, Weining, 2016. "Lattice hydrodynamic model based traffic control: A transportation cyber–physical system approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 795-801.

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