Abstract
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.
Highlights
The description of vehicular traffic flow based on systems of conservation or balance laws has been proposed by many researchers during the last decades, see for example [9, 30] and the references therein
In contrast to first order traffic models consisting only of one scalar equation for the traffic density, second order models are characterized by a second equation for the evolution of traffic mean velocity
As we will see in the numerical experiments, our modeling approach covers the capacity drop effect and allows to solve optimal control problems such as speed limit and ramp metering, cf. subsection 4.3
Summary
The description of vehicular traffic flow based on systems of conservation or balance laws has been proposed by many researchers during the last decades, see for example [9, 30] and the references therein. The challenge here is to find appropriate conditions to ensure the conservation of mass and momentum flow. Once these coupling conditions are defined, they can be integrated in a finite-volume type numerical scheme. Typical control issues arising in the on-ramp context are speed limit and ramp metering These kind of traffic flow control problems have been mainly studied in the context of first-order models based on the Lighthill-Whitham-Richards (LWR) equations [22], see e.g. The outline is as follows: In Section 2 we present the Aw-Rascle model with relaxation term and the coupling conditions at on-ramps. Comparisons to the solution of the LWR model are given for all experiments
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