Traffic Flow on a Road Network Using the Aw–Rascle Model

The article deals with a fluid dynamic model for traffic flow on a road network. This consists of a hyperbolic system of two equations proposed in Aw and Rascle (2000 Aw , A. , Rascle , M. ( 2000 ). Resurrection of “second order” models of traffic flow . SIAM J. Appl. Math. 60 ( 3 ): 916 – 938 [CSA] [Crossref], [Web of Science ®] , [Google Scholar]). A method to solve Riemann problems at junctions is given assigning rules on traffic distributions and maximizations of fluxes and other quantities. Then we discuss stability in L ∞ norm of such solutions. Finally, we prove existence of entropic solutions to the Cauchy problem when the road network has only one junction.