Michel Rascle

Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models

In this paper we establish a connection between a microscopic follow-the-leader model based on ordinary differential equations and a semidiscretization of a macroscopic continuum model based on a conservation law. Naturally, it also turns out that the natural discretization of the conservation law in Lagrangian coordinates is equivalent to a straightforward time discretization of the microscopic model. We also show rigorously that, at least in the homogeneous case, the macroscopic model can be viewed as the limit of the time discretization of the microscopic model as the number of vehicles increases, with a scaling in space and time (a zoom) for which the density and the velocity remain fixed. Moreover, a numerical investigation and comparison is presented for the different models.

Coupling Conditions for a Class of Second-Order Models for Traffic Flow

This paper deals with a model for traffic flow based on a system of conservation laws [A. Aw and M. Rascle, SIAM J. Appl. Math., 60 (2000), pp. 916-938]. We construct a solution of the Riemann problem at an arbitrary junction of a road network. Our construction provides a solution of the full system. In particular, all moments are conserved.

CONGESTION ON MULTILANE HIGHWAYS

We present a new model for traffic on a multilane freeway (with n lanes). Our basic descriptors are the car density

Optimization criteria for modelling intersections of vehicular traffic flow

\rho

An improved macroscopic model of traffic flow: Derivation and links with the Lighthill-Whitham model

(in cars/mile), taken across all lanes in the freeway, and the average car velocity u (in miles/hour). The flux of cars across all lanes is given by

A 2-Phase Traffic Model Based on a Speed Bound

\rho u = {\sum^n_{i=1}}\rho_i u_i

Convergence of the relaxation approximation to a scalar nonlinear hyperbolic equation arising in chromatography

, where

Balanced vehicular traffic at a bottleneck

\rho_i

COMPENSATED COMPACTNESS FOR 2D CONSERVATION LAWS

is the car density in the ith lane, and ui the velocity of cars in the ith lane. We shall track only

On the static and dynamic study of oscillations for some nonlinear hyperbolic systems of conservation laws

\rho