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

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    Type
    Article
    Authors
    Seibold, Benjamin
    Flynn, Morris R.
    Kasimov, Aslan R. cc
    Rosales, Rodolfo Rubén
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2013-10-04
    Preprint Posting Date
    2012-04-24
    Online Publication Date
    2013-10-04
    Print Publication Date
    2013-10
    Permanent link to this record
    http://hdl.handle.net/10754/562949
    
    Metadata
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    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
    Seibold, B., R. Flynn, M., R. Kasimov, A., … R. Rosales, R. (2013). Constructing set-valued fundamental diagrams from Jamiton solutions in second order traffic models. Networks & Heterogeneous Media, 8(3), 745–772. doi:10.3934/nhm.2013.8.745
    Sponsors
    The authors would like to thank J.-C. Nave for helpful discussions. The authors would like to acknowledge the support by the National Science Foundation. R. R. Rosales and B. Seibold were supported through grants DMS-1007899 and DMS-1007967, respectively. In addition, R. R. Rosales wishes to acknowledge partial support by the NSF through grants DMS-0813648, DMS-1115278, and DMS-0907955, B. Seibold through grants DMS-0813648 and DMS-1115269, and A. R. Kasimov through grant DMS-0907955. M. R. Flynn wishes to acknowledge support by the NSERC Discovery Grant Program.
    Publisher
    American Institute of Mathematical Sciences (AIMS)
    Journal
    Networks & Heterogeneous Media
    DOI
    10.3934/nhm.2013.8.745
    arXiv
    1204.5510
    Additional Links
    http://arxiv.org/abs/arXiv:1204.5510v2
    ae974a485f413a2113503eed53cd6c53
    10.3934/nhm.2013.8.745
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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