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.