Optimization criteria for modelling intersections of vehicular traffic flow

We consider coupling conditions for the “Aw–Rascle” (AR) traffic flow model at an arbitrary road intersection. In contrast with coupling conditions previously introduced in [10] and [7], all the moments of the AR system are conserved and the total flux at the junction is maximized. This nonlinear optimization problem is solved completely. We show how the two simple cases of merging and diverging junctions can be extended to more complex junctions, like roundabouts. Finally, we present some numerical results.