Constructing set-valued fundamental diagrams from Jamiton solutions in second order traffic models
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Seibold-2013-Constructing set-valued.pdf
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Author(s)
Rosales, Rodolfo R.
Kasimov, Aslan R.
Flynn, Morris R.
Seibold, Benjamin
Date Issued
October 2013
Journal
Networks and Heterogeneous Media
Publisher
American Institute of Mathematical Sciences (AIMS)
Citation
Rosales, Rodolfo R., Aslan R. Kasimov, Morris R. Flynn, and Benjamin Seibold. “Constructing set-valued fundamental diagrams from Jamiton solutions in second order traffic models.” Networks and Heterogeneous Media 8, no. 3 (September 2013): 745-772. © American Institute of Mathematical Sciences
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.3934/nhm.2013.8.745
