Lattice hydrodynamic modeling of traffic flow with consideration of historical current integration effect

A new traffic lattice hydrodynamic model with consideration of historical current integration effect is proposed in this paper and the influence of current integration effect on traffic flow is studied through linear and nonlinear analyses. The linear stability condition obtained by linear analysis reveals that the traffic stability can be enhanced by considering the impact of historical current integration effect. Also the nonlinear analysis shows that the traffic density wave in the unstable region near the critical point can be described by the kink-antikink solution of the mKdV equation. Finally, numerical simulation is carried out to verify the analytical results and it is proved that the historical current integration effect can improve the stability of traffic flow importantly.