TDGL and mKdV equations for car-following model considering traffic jerk and velocity difference

By introducing optimal velocity car-following model by Bando et al., we present an improved car-following model which is based on an optimal velocity model considering traffic jerk and full velocity difference. The nature of the model is researched by using linear and nonlinear analysis method. The analytical method and numerical simulation results show that the proposed model can describe the phase transition and critical phenomenon with the thermodynamic theory. In order to describe the traffic flow near the critical point, the time-dependent Ginzburg–Landau (TDGL) equation and the modified Korteweg–de Vries (mKdV) equation are derived. Additionally, the connection between the TDGL and the mKdV equation is also given. Theoretical analysis is demonstrated by numerical simulation.