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). 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(infinity) norm of such solutions. Finally, we prove existence of entropic solutions to the Cauchy problem when the road network has only one junction.
Garavello, M., Piccoli, B. (2006). Traffic flow on a road network using the Aw-Rascle model. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 31(2), 243-275 [10.1080/03605300500358053].
Traffic flow on a road network using the Aw-Rascle model
GARAVELLO, MAURO;
2006
Abstract
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). 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(infinity) norm of such solutions. Finally, we prove existence of entropic solutions to the Cauchy problem when the road network has only one junction.
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