  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.
