Lattice hydrodynamic traffic flow model with explicit drivers' physical delay

An extended lattice hydrodynamic model is presented by considering the effect of drivers' delay in sensing relative flux. The linear stability criterion of the new model is obtained by employing the linear stability theory. By means of nonlinear analysis method, the modified Korteweg-deVries (mKdV) equation near the critical point is constructed and solved. The propagation behavior of traffic jam can thus be described by the kink-antikink soliton solution for the mKdV equation. The good agreement between the simulation results and the analytical results show that the drivers' delay in sensing relative flux effect plays an important role in traffic jamming transition.