Kinetic Derivation of Macroscopic Anticipation Models for Vehicular Traffic

This paper has been motivated by the work of Aw and Rascle [SIAM J. Appl. Math., 60 (2000), pp. 916--938]. As noted by Daganzo [Transportation Res. B, 29 (1995), pp. 277--286] some macroscopic models for vehicular traffic encounter difficulties showing nonphysical effects in certain situations. In the paper by Aw and Rascle a new heuristic model has been presented that avoids these difficulties. We present here a kinetic derivation of a class of macroscopic traffic flow equations including the Aw--Rascle equations. The coefficients appearing in the equations are identified from the solutions of the underlying kinetic equations. Moreover, numerical experiments and comparisons between the different models are presented.