TY - JOUR
T1 - Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models
AU - Seibold, Benjamin
AU - Flynn, Morris R.
AU - Kasimov, Aslan R.
AU - Rosales, Rodolfo Rubén
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.
PY - 2013/10/4
Y1 - 2013/10/4
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/562949
UR - http://arxiv.org/abs/arXiv:1204.5510v2
UR - http://www.scopus.com/inward/record.url?scp=84886024354&partnerID=8YFLogxK
U2 - 10.3934/nhm.2013.8.745
DO - 10.3934/nhm.2013.8.745
M3 - Article
SN - 1556-1801
VL - 8
SP - 745
EP - 772
JO - Networks and Heterogeneous Media
JF - Networks and Heterogeneous Media
IS - 3
ER -