The Aw-Rascle traffic model with locally constrained flow

Mauro Garavello (1) , Paola Goatin (2, 3)

1 DISTA - Dipartimento di Scienze e Tecnologie Avanzate
2 IMATH - Institut de Mathématiques de Toulon - EA 2134
3 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE

We consider solutions of the Aw-Rascle model for traffic flow fulfilling a constraint on the flux at $x=0$. Two different kinds of solutions are proposed: at $x=0$ the first one conserves both the number of vehicles and the generalized momentum, while the second one conserves only the number of cars. We study the invariant domains for these solutions and we compare the two Riemann solvers in terms of total variation of relevant quantities. Finally we construct ad hoc finite volume numerical schemes to compute these solutions.

Domaines: Equations aux dérivées partielles [math.AP]

Mauro Garavello, Paola Goatin. The Aw-Rascle traffic model with locally constrained flow. Journal of Mathematical Analysis and Applications, 2011, 378 (2), pp.634-648. ⟨10.1016/j.jmaa.2011.01.033⟩. ⟨hal-00638111⟩