On the micro-macro limit in traffic flow

DOI10.4171/RSMUP/131-13zbMath1295.35314MaRDI QIDQ396500

Rinaldo M. Colombo, Elena Rossi

Publication date: 13 August 2014

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

zbMATH Keywords

macroscopic traffic modelsfollow-the-leaderkinetic limitLighthill-Whitham and Richards modelmicroscopic traffic models

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Traffic problems in operations research (90B20)

Related Items (16)

On the micro-to-macro limit for first-order traffic flow models on networks ⋮ Traveling waves for a microscopic model of traffic flow ⋮ Constructing artificial traffic fluids by designing cruise controllers ⋮ Boundary coupling of microscopic and first order macroscopic traffic models ⋮ The continuum limit of follow-the-leader models -- a short proof ⋮ Follow-the-leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow ⋮ Traveling wave profiles for a follow-the-leader model for traffic flow with rough road condition ⋮ Particle approximation of a constrained model for traffic flow ⋮ Micro-Macro Limit of a Nonlocal Generalized Aw-Rascle Type Model ⋮ A justification of a LWR model based on a follow the leader description ⋮ A game-theoretic framework for autonomous vehicles velocity control: bridging microscopic differential games and macroscopic mean field games ⋮ Exact boundary controllability for free traffic flow with Lipschitz continuous state ⋮ Properties of the LWR model with time delay ⋮ Stationary wave profiles for nonlocal particle models of traffic flow on rough roads ⋮ Multiscale Control of Generic Second Order Traffic Models by Driver-Assist Vehicles ⋮ Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit

Uses Software

• LSODE

Cites Work

• A Rigorous Treatment of a Follow-the-Leader Traffic Model with Traffic Lights Present
• A Hölder continuous ODE related to traffic flow
• A 2-Phase Traffic Model Based on a Speed Bound
• On kinematic waves II. A theory of traffic flow on long crowded roads

This page was built for publication: On the micro-macro limit in traffic flow