Capacity drop and traffic control for a second order traffic model

Oliver Kolb (1) , Simone Göttlich (1) , Paola Goatin (2, 3, 4)

1 Department of mathematics [Mannheim]
2 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences
3 LJAD - Laboratoire Jean Alexandre Dieudonné
4 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)

In this paper, we illustrate how second order traffic flow models, in our case the Aw-Rascle equations, can be used to reproduce empirical observations such as the capacity drop at merges and solve related optimal control problems. To this aim, we propose a model for on-ramp junctions and derive suitable coupling conditions. These are associated to the first order Godunov scheme to numerically study the well-known capacity drop effect, where the outflow of the system is significantly below the expected maximum. Control issues such as speed and ramp meter control are also addressed in a first discretize-then optimize framework.

Mots clés: Traffic flow; second order model; on-ramp coupling; numerical simulations; optimal control

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Oliver Kolb, Simone Göttlich, Paola Goatin. Capacity drop and traffic control for a second order traffic model. Networks and Heterogeneous Media, 2017, 12 (4), pp.663-681. ⟨hal-01402608⟩