  Fundamental diagrams of vehicular traffic flow are generally multi-valued in
the congested flow regime. We show that such set-valued fundamental diagrams
can be constructed systematically from simple second order macroscopic traffic
models, such as the classical Payne-Whitham model or the inhomogeneous
Aw-Rascle-Zhang model. These second order models possess nonlinear traveling
wave solutions, called jamitons, and the multi-valued parts in the fundamental
diagram correspond precisely to jamiton-dominated solutions. This study shows
that transitions from function-valued to set-valued parts in a fundamental
diagram arise naturally in well-known second order models. As a particular
consequence, these models intrinsically reproduce traffic phases.
