Stability analysis of a new lattice hydrodynamic model by considering lattice's self-anticipative density effect

In this paper, a new lattice hydrodynamic model with consideration of the density difference of a lattice's current density and its anticipative density is proposed. The influence of lattice's self-anticipative density on traffic stability is revealed through linear stability theory and it shows that lattice's self-anticipative density can improve the stability of traffic flow. To describe the phase transition of traffic flow, the mKdV equation near the critical point is derived by using nonlinear analysis method. The propagating behavior of density wave in the unstable region can be described by the kink-antikink soliton of the mKdV equation. Numerical simulation validates the analytical results, which shows that traffic jam can be suppressed efficiently by considering lattice's self-anticipative density in the modified lattice hydrodynamic model.