The car following model considering traffic jerk

Based on optimal velocity car following model, a new model considering traffic jerk is proposed to describe the jamming transition in traffic flow on a highway. Traffic jerk means the sudden braking and acceleration of vehicles, which has a significant impact on traffic movement. The nature of the model is researched by using linear and nonlinear analysis method. A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow. The time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are derived to describe the traffic flow near the critical point and the traffic jam. In addition, the connection between the TDGL and the mKdV equations are also given.