%0 Journal Article
%T Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models
%A Benjamin Seibold
%A Morris R. Flynn
%A Aslan R. Kasimov
%A Rodolfo Ruben Rosales
%J Physics
%D 2012
%I arXiv
%X 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.
%U http://arxiv.org/abs/1204.5510v2