Extended second-order multi-class traffic flow model with the relative drag function

In heterogenous traffic flow the interaction between different vehicle classes play an important role. This article deals with the extension of second order multiclass traffic flow models to accommodate some violation of lane discipline and heterogeneous choice of speeds in a traffic stream. It proposes a continuum model for the interaction of different classes of vehicles in the traffic based on the concept of a moving obstacle from fluid dynamics. Using the assumption that the slow vehicles can be considered as moving obstacles to the fastest ones a relative drag function is introduced in the dynamics of the velocity of each respective classes. The proposed model considers three different vehicle classes and it is shown to express a hyperbolic conservation system which preserves the anisotropic nature of vehicles. A stability criterion of the model is obtained using the linear stability analysis. The performance of the model is evaluated using the Roe numerical scheme. The results show that the heterogeneous traffic behaviour with this new model is more realistic.