Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Preprint Posting Date2012-04-24
Online Publication Date2013-10-04
Print Publication Date2013-10
Permanent link to this recordhttp://hdl.handle.net/10754/562949
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AbstractFundamental 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.
CitationSeibold, 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
SponsorsThe 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.
JournalNetworks and Heterogeneous Media