4 research outputs found
Kinetic derivation of a Hamilton-Jacobi traffic flow model
Kinetic models for vehicular traffic are reviewed and considered from the
point of view of deriving macroscopic equations. A derivation of the associated
macroscopic traffic flow equations leads to different types of equations: in
certain situations modified Aw-Rascle equations are obtained. On the other
hand, for several choices of kinetic parameters new Hamilton-Jacobi type
traffic equations are found. Associated microscopic models are discussed and
numerical experiments are presented discussing several situations for highway
traffic and comparing the different models
Fundamental diagrams in traffic flow: the case of heterogeneous kinetic models
Experimental studies on vehicular traffic provide data on quantities like
density, flux, and mean speed of the vehicles. However, the diagrams relating
these variables (the fundamental and speed diagrams) show some peculiarities
not yet fully reproduced nor explained by mathematical models. In this paper,
resting on the methods of kinetic theory, we introduce a new traffic model
which takes into account the heterogeneous nature of the flow of vehicles along
a road. In more detail, the model considers traffic as a mixture of two or more
populations of vehicles (e.g., cars and trucks) with different microscopic
characteristics, in particular different lengths and/or maximum speeds. With
this approach we gain some insights into the scattering of the data in the
regime of congested traffic clearly shown by actual measurements.Comment: 26 pages, 11 figure
Kinetic-controlled hydrodynamics for traffic models with driver-assist vehicles
We develop a hierarchical description of traffic flow control by means of
driver-assist vehicles aimed at the mitigation of speed-dependent road risk
factors. Microscopic feedback control strategies are designed at the level of
vehicle-to-vehicle interactions and then upscaled to the global flow via a
kinetic approach based on a Boltzmann-type equation. Then first and second
order hydrodynamic traffic models, which naturally embed the microscopic
control strategies, are consistently derived from the kinetic-controlled
framework via suitable closure methods. Several numerical examples illustrate
the effectiveness of such a hierarchical approach at the various scales.Comment: 30 pages, 12 figure