Macroscopic traffic models: Shifting from densities to “Celerities”

The advent of techniques to measure velocities of “GPS equipped vehicles” using satellite technology, replacing the density of the road traffic sensors, motivates and justifies the revision of conceptual, mathematical algorithms and software based models. This paper summarizes studies on the traffic...

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Bibliographic Details
Published in:Applied mathematics and computation 2010-10, Vol.217 (3), p.963-971
Main Author: Aubin, Jean-Pierre
Format: Article
Language:English
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Summary:The advent of techniques to measure velocities of “GPS equipped vehicles” using satellite technology, replacing the density of the road traffic sensors, motivates and justifies the revision of conceptual, mathematical algorithms and software based models. This paper summarizes studies on the traffic evolutions achieving the minimum of a congestion function controlled “macroscopic traffic velocities” called “celerities” instead of founding traffic regulation on the measures of traffic densities. The flux valued function is the Fenchel transform of the fundamental diagram and is a convex decreasing function. We use the properties of capture basins investigated in viability theory, specifically a Lax–Hopf formula characterizing them and the “Max-Plus” morphism of capture basins for deriving the statements proved in this paper. Traffic conditions involve as well boundary conditions or conditions on trajectories inside the domain.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2010.02.032