A new lattice hydrodynamic model with the consideration of flux change rate effect

A new lattice hydrodynamic traffic flow model is proposed by considering the preceding lattice site's flux change rate effect. Using linear stability theory, stability condition of the presented model is obtained. It is shown that the stability region significantly enlarges as the flux change rate effect increases. To describe the propagation behavior of a density wave near the critical point, nonlinear analysis is conducted and mKdV equation representing kink-antikink soliton is derived. To verify the theoretical findings, numerical simulation is conducted which confirms that preceding lattice site's flux change rate can improve the stability of traffic flow effectively.