A class of multi-phase traffic theories for microscopic, kinetic and   continuum traffic models
  In the present paper a review and numerical comparison of a special class of multi-phase traffic theories based on microscopic, kinetic and macroscopic traffic models is given. Macroscopic traffic equations with multi-valued fundamental diagrams are derived from different microscopic and kinetic models. Numerical experiments show similarities and differences of the models, in particular, for the appearance and structure of stop and go waves for highway traffic in dense situations. For all models, but one, phase transitions can appear near bottlenecks depending on the local density and velocity of the flow. 
Raul Borsche, Mark Kimathi, Axel Klar
math.NA