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

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    Genre
    Journal Article
    Date
    2013-09-01
    Author
    Seibold, B
    Flynn, MR
    Kasimov, AR
    Rosales, RR
    Subject
    Second order
    traffic model
    Payne-Whitham
    Aw-Rascle-Zhang
    jamiton
    traveling wave
    fundamental diagram
    sensor data
    effective flow rate
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/5944
    
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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.
    Citation to related work
    American Institute of Mathematical Sciences (AIMS)
    Has part
    Networks and Heterogeneous Media
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    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/5926
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