  In this paper we study a phase transition model for vehicular traffic flows.
Two phases are taken into account, according to whether the traffic is light or
heavy. We assume that the two phases have a non-empty intersection, the so
called metastable phase. The model is given by the Lighthill-Whitham-Richards
model in the free-flow phase and by the Aw-Rascle-Zhang model in the congested
phase. In particular, we study the existence of solutions to Cauchy problems
satisfying a local point constraint on the density flux. We prove that if the
constraint F is higher than the minimal flux f -- c of the metastable phase,
then constrained Cauchy problems with initial data of bounded total variation
admit globally defined solutions. We also provide sufficient conditions on the
initial data that guarantee the global existence of solutions also in the case
F < f -- c. These results are obtained by applying the wave-front tracking
technique.
