Optimization for a special class of traffic flow models: Combinatorial and continuous approaches
Simone Göttlich Oliver Kolb Sebastian Kühn
In this article, we discuss the optimization of a linearized traffic flow network model based on conservation laws. We present two solution approaches. One relies on the classical Lagrangian formalism (or adjoint calculus), whereas another one uses a discrete mixed-integer framework. We show how both approaches are related to each other. Numerical experiments are accompanied to show the quality of solutions.
keywords: Traffic networks conservation laws combinatorial optimization. control of discretized PDEs adjoint calculus
Capacity drop and traffic control for a second order traffic model
Oliver Kolb Simone Göttlich Paola Goatin

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.

keywords: Traffic flow second order model on-ramp coupling numerical simulations optimal control

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