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

Seibold, B
; 
Flynn, MR
; 
Kasimov, AR
; 
Rosales, RR
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Journal Article
Date
2013-09-01
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Second order
 traffic 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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1204.5510v2.pdf
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DOI
10.3934/nhm.2013.8.745
Abstract
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.
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American Institute of Mathematical Sciences (AIMS)
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Networks and Heterogeneous Media
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