Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models

Details Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models

2012-04-24

arxiv.org/abs/1204.5510v1

Mathematics

Analysis of PDEs

26 pages, 21 figures

Scientific paper

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 as intrinsic properties of well-known second order models.

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