Kinetic Theory in Vehicular Traffic Flow Modeling

Abstract. This paper discusses (gas) kinetic models in vehicular traffic flow theory. In analogy to gas dynamics, models in literature are based on Boltzmann like equations with different mean acceleration features and interaction profiles of the drivers. After a discussion of their underlying assumptions together with their applicability in traffic flow an advanced model is introduced. It avoids their drawbacks by adding the acceleration as an additional variable to single car state and can be used also in dense traffic. The interaction profile of this model is based on the microscopic action-point approach using two velocity dependent distance thresholds. The equation is solved with an adopted DSMC like method and results for homogeneous and stationary traffic flow are presented. They are compared with measured data and agree qualitatively