Continuum traffic model with the consideration of two delay time scales

This paper presents a continuum traffic model. The derivation of this model is based upon the assumption that the stream velocity u reaches the equilibrium velocity u_e within the relaxation time T, while the equilibrium velocity u_e is adjusted to be attained through the driver’s reaction time t_r. It is also assumed that the former delay time scale is greater than the latter. A motion equation with nonconstant propagation velocity of a disturbance in traffic flow is derived that can reflect the anisotropy of disturbance propagation in real traffic, unlike some other higher-order continuum models. It indicates that in our model the undesirable “wrong-way travel” phenomenon and gaslike behavior have been eliminated. The formation and diffusion of traffic shock can be better simulated.