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.
|Original language||English (US)|
|Number of pages||28|
|Journal||Networks and Heterogeneous Media|
|State||Published - Oct 4 2013|
Bibliographical noteKAUST 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.
ASJC Scopus subject areas
- Applied Mathematics
- Statistics and Probability
- Computer Science Applications