arXiv subjects

Michel Rascle

Publications and source records attributed to Michel Rascle.

3 recordsLinked to original sources

arXiv2009

A 2-phase traffic model based on a speed bound

We extend the classical LWR traffic model allowing different maximal speeds to different vehicles. Then, we add a uniform bound on the traffic speed. The result, presented in this paper, is a new macro- scopic model displaying 2 phases, based on a non-smooth 2x2 system of conservation laws. This model is compared with other models of the same type in the current literature, as well as with a kinetic one. Moreover, we establish a rigorous connection between a microscopic Follow-The-Leader model based on ordinary differential equations and this macroscopic continuum model.

math.AP↗

arXiv2007

On the existence and compactness of a two-dimensional resonant system of conservation laws

We prove the existence of a weak solution to a two-dimensional resonant 3x3 system of conservation laws with BV initial data. Due to possible resonance (coinciding eigenvalues), spatial BV estimates are in general not available. Instead, we use an entropy dissipation bound combined with the time translation invariance property of the system to prove existence based on a two-dimensional compensated compactness argument adapted from the paper of Tadmor, Rascle and Bagnerini, "Compensated compactness for 2D conservation laws", [JHDEs 2(3):697--712, 2005]. Existence is proved under the assumption that the flux functions in the two directions are linearly independent.

math.AP↗

arXiv2006

Balanced vehicular traffic at a bottleneck

The balanced vehicular traffic model is a macroscopic model for vehicular traffic flow. We use this model to study the traffic dynamics at highway bottlenecks either caused by the restriction of the number of lanes or by on-ramps or off-ramps. The coupling conditions for the Riemann problem of the system are applied in order to treat the interface between different road sections consistently. Our numerical simulations show the appearance of synchronized flow at highway bottlenecks.

physics.soc-ph↗