We consider a multi-class (resp. source destination) model for traffic flow as introduced in M. Garavello and B. Piccoli, Source-Destination flow on a road network. We propose a reformulation and discuss the extension of this model to road networks by proposing criteria for solving Riemann problems at a road intersection. We present some numerical simulations for the derived conditions.
"Multi-class traffic models on road networks." Commun. Math. Sci. 4 (3) 591 - 608, September 2006.