Abstract: 

In this paper, we propose a new continuum model and study some qualitative properties. The new model contains an additional speed gradient term (anisotropic term) in comparison to Berg's model (Berg et al., 2000, Physical Review E, 61, 1056-1066). This anisotropic term guarantees the property that the characteristic speeds can be made less than or equal to the macroscopic flow speed. We extend this model for multi-class traffic flow with heterogeneous drivers. Each user class is characterized by their choice of speeds in a traffic stream. The choice of the speed of a particular user class at any location on the highway is affected by the presence of all user class on that location. Numerical simulations show that the model is able to explain some of the observed traffic phenomena such as platoon dispersion that challenge old homogeneous models presented in the literature.