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We extend the Phase Transition model for traffic proposed in [ 8 ], by Colombo, Marcellini, and Rascle to the network case. More precisely, we consider the Riemann problem for such a system at a general junction with \begin{document}$n$\end{document} incoming and \begin{document}$m$\end{document} outgoing roads. We propose a Riemann solver at the junction which conserves both the number of cars and the maximal speed of each vehicle, which is a key feature of the Phase Transition model. For special junctions, we prove that the Riemann solver is well defined.

The Riemann Problem at a Junction for a Phase Transition Traffic Model