Differential and Integral Equations

Homogenization of second order discrete model and application to traffic flow

N. Forcadel and W. Salazar

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Abstract

The goal of this paper is to derive traffic flow macroscopic models from microscopic models. At the microscopic scales, we consider a Bando model, of the type following the leader, i.e., the acceleration of each vehicle depends on the distance to the vehicle in front of it. We take into account the possibility that each driver can have different characteristics such as sensibility to other drivers or optimal velocities. After rescaling, we prove that the solution of this system of ODEs converges to the solution of a macroscopic homogenized Hamilton-Jacobi equation which can be seen as a LWR (Lighthill-Whitham-Richards) model.

Article information

Source
Differential Integral Equations, Volume 28, Number 11/12 (2015), 1039-1068.

Dates
First available in Project Euclid: 18 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.die/1439901041

Mathematical Reviews number (MathSciNet)
MR3385134

Zentralblatt MATH identifier
1357.49113

Subjects
Primary: 49L25: Viscosity solutions 35B27: Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50] 90B20: Traffic problems

Citation

Forcadel, N.; Salazar, W. Homogenization of second order discrete model and application to traffic flow. Differential Integral Equations 28 (2015), no. 11/12, 1039--1068. https://projecteuclid.org/euclid.die/1439901041


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