The Study of The Dynamics of The One-dimentional Traffic Flow

• Main Authors: Chia-Ling Linda Huang, 黃佳伶
• Other Authors: Chi-Lun Lee
• Format: Others
• Language: en_US
• Online Access: http://ndltd.ncl.edu.tw/handle/42969868076127071217

碩士 === 國立中央大學 === 物理研究所 === 98 === We study the dynamics of the one-dimensional traffic flow through a car following model [1] which first proposed by Chandler et. al. We modify this model by introducing a distance factor and the repulsive Lennard-Jones potential to prevent car overtaking. The system that we are interested in is the one lane highway with the periodical boundary condition. The evolution of the jam which is caused by the unobvious perturbation was observed, and the fundamental diagram is shown. The traffic flow would become unstable and forming the jam when the density goes beyond a threshold. The jam forming process can be divided into three stages: (1) piling and overshooting, (2) releasing, and (3) steady. From the observation of the numerical results, we propose the conjecture of repeating motion which states that after reaching the steady state, the vehicle would repeat the motion of that in front by a time shift τ. Our study reveals that τ was about 1.1 seconds. Substituting τ into the equation of motion, the accelerating and the decelerating curves of a vehicle are reconstructed. We conclude that the highest density which was reachable without the traffic jam is 0.66 cars per meter, and the minimum density required for the jam forming is 0.03 cars per meter. Furthermore, the propagating speed of the cluster is -1.36 m/s.