Conference paper · Book chapter
A General Microscopic Traffic Model Yielding Dissipative Shocks
Bogolyubov Institute for Theoretical Physics1
Institut national des sciences appliquées de Rouen Normandie2
Department of Applied Mathematics and Computer Science, Technical University of Denmark3
Department of Physics, Technical University of Denmark4
Plasma Physics and Fusion Energy, Department of Physics, Technical University of Denmark5
Dynamical Systems, Department of Applied Mathematics and Computer Science, Technical University of Denmark6
Center for Intelligent Drug Delivery and Sensing Using Microcontainers and Nanomechanics, Department of Health Technology, Technical University of Denmark7
We consider a general microscopic traffic model with a delay. An algebraic traffic function reduces the equation to the Aw-Rascle microscopic model while a sigmoid function gives the standard “follow the leader”. For zero delay we prove that the homogeneous solution is globally stable. For a positive delay, it becomes unstable and develops dispersive and dissipative shocks.
These are followed by a finite time singularity for the algebraic traffic function and by kinks for the sigmoid function.
| Language: | English |
|---|---|
| Publisher: | Springer |
| Year: | 2018 |
| Pages: | 375-382 |
| Proceedings: | 19th European Conference on Mathematics for Industry<br/> |
| Series: | Mathematics in Industry |
| ISBN: | 3319630814 , 3319630822 , 9783319630816 and 9783319630823 |
| Types: | Conference paper and Book chapter |
| DOI: | 10.1007/978-3-319-63082-3_59 |
| ORCIDs: | Christiansen, Peter Leth , Rasmussen, Jens Juul and Sørensen, Mads |
