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TDGL and MKdV equations for jamming transition in the lattice models of traffic

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  • Nagatani, Takashi

Abstract

The lattice models of traffic are proposed to describe the jamming transition in traffic flow on a highway in terms of thermodynamic terminology of phase transitions and critical phenomena. They are the lattice versions of the hydrodynamic model of traffic. Two lattice models are presented: one is described by the differential-difference equation where time is a continuous variable and space is a discrete variable, and the other is the difference equation in which both time and space variables are discrete. We apply the linear stability theory and the nonlinear analysis to the lattice models. It is shown that the time-dependent Ginzburg–Landau (TDGL) equation is derived to describe the traffic flow near the critical point. A thermodynamic theory is formulated for describing the phase transitions and critical phenomena. It is also shown that the perturbed modified Korteweg-de Vries (MKdV) equation is derived to describe the traffic jam.

Suggested Citation

  • Nagatani, Takashi, 1999. "TDGL and MKdV equations for jamming transition in the lattice models of traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 264(3), pages 581-592.
  • Handle: RePEc:eee:phsmap:v:264:y:1999:i:3:p:581-592
    DOI: 10.1016/S0378-4371(98)00466-X
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    Cited by:

    1. Liu, Fangxun & Cheng, Rongjun & Ge, Hongxia & Yu, Chenyan, 2016. "A new car-following model with consideration of the velocity difference between the current speed and the historical speed of the leading car," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 464(C), pages 267-277.
    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. 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.
    4. Redhu, Poonam & Gupta, Arvind Kumar, 2015. "Jamming transitions and the effect of interruption probability in a lattice traffic flow model with passing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 249-260.
    5. Sahoo, S. & Saha Ray, S., 2016. "Solitary wave solutions for time fractional third order modified KdV equation using two reliable techniques (G′/G)-expansion method and improved (G′/G)-expansion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 265-282.
    6. Kaur, Ramanpreet & Sharma, Sapna, 2017. "Analysis of driver’s characteristics on a curved road in a lattice model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 59-67.
    7. repec:eee:phsmap:v:490:y:2018:i:c:p:774-785 is not listed on IDEAS

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