A macroscopic traffic flow model with phase transitions and local point   constraints on the flow
  The two phase model for vehicular traffic flows recently appeared in \cite{goatin2006aw} and \cite{BenyahiaRosini01} is endowed with a point constraint on the flow to allow for the modelling of phenomena such as the effects of toll booths along a road. We describe in this paper two Riemann solvers for this model upon which an ulterior study of the cauchy problem should rely. 
Massimiliano D. Rosini and Benyahia Mohamed Ramiz
math.AP math.NA