Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models
Genre
Journal ArticleDate
2013-09-01Author
Seibold, BFlynn, MR
Kasimov, AR
Rosales, RR
Subject
Second ordertraffic model
Payne-Whitham
Aw-Rascle-Zhang
jamiton
traveling wave
fundamental diagram
sensor data
effective flow rate
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http://hdl.handle.net/20.500.12613/5944
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10.3934/nhm.2013.8.745Abstract
Fundamental diagrams of vehicular traiic ow are generally multivalued in the congested ow regime. We show that such set-valued fundamental diagrams can be constructed systematically from simple second order macroscopic traiic 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 traiic phases. © American Institute of Mathematical Sciences.Citation to related work
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http://dx.doi.org/10.34944/dspace/5926