TDGL equation in lattice hydrodynamic model considering driver's physical delay

Based on an extended lattice hydrodynamic model considering the delay of the driver's response in sensing headway, we get the time-dependent Ginzburg-Landau (for short, TDGL) equation to describe the transition and critical phenomenon in traffic flow by applying the reductive perturbation method. The corresponding solutions are obtained. Numerical simulation is carried out to examine the performance of the model and the results show coincidence with the analysis results. © 2013 Springer Science+Business Media Dordrecht.