A new anisotropic continuum model for traffic flow

This paper develops a new continuum model based upon an improved car-following model by using a series expansion of the headway in terms of the density. The new model contains an additional speed gradient term (Anisotropic term) in comparison to the Bergʹs model [Berg et al., Phys. Rev. E 61(2) (2000) 1056]. This anisotropic term guarantees the property that the characteristic speeds are always less than or equal to the macroscopic flow speed. This new model also overcomes the problem of negative flows and negative speeds (i.e. wrong way travel) that exists in almost every higher order continuum models. It is known that diffusive wave could lead to a “wrong way travel” under certain circumstances [C. F. Daganzo, Trans. Res. B 29 (1995) 277]. In our general model, a traffic dependent anisotropic factor controls the non-isotropic character and diffusive influence in these special circumstances. The stability of traffic flow is analyzed and found out that this new continuum model obeys the same stability criterion as Bergʹs model for zero anisotropic parameter.