From Heterogeneous Microscopic Traffic Flow Models to Macroscopic Models

DOI10.1137/20M1314410zbMath1461.35100arXiv1907.02310MaRDI QIDQ3387585

Nicolas Forcadel, Pierre Cardaliaguet

Publication date: 13 January 2021

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.02310

zbMATH Keywords

stochastic homogenizationtraffic flowmacroscopic modelsfollow-the-leader modelheterogeneous microscopic models

Mathematics Subject Classification ID

Nonlinear first-order PDEs (35F20) Traffic problems in operations research (90B20) PDEs with randomness, stochastic partial differential equations (35R60) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Viscosity solutions to PDEs (35D40) Hamilton-Jacobi equations (35F21)

Related Items (3)

Microscopic derivation of a traffic flow model with a bifurcation ⋮ Mean-field limit of a hybrid system for multi-lane car-truck traffic ⋮ Stochastic homogenization of Hamilton-Jacobi equations on a junction

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
• Homogenization of second order discrete model and application to traffic flow.
• A traffic flow model with non-smooth metric interaction: well-posedness and micro-macro limit
• Structure stability of congestion in traffic dynamics
• The continuum limit of follow-the-leader models -- a short proof
• A multispecies traffic model based on the Lighthill-Whitham and Richards model
• Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit
• Homogenization of fully overdamped Frenkel-Kontorova models
• Follow-the-leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow
• A Rigorous Treatment of a Follow-the-Leader Traffic Model with Traffic Lights Present
• Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models
• Scalar conservation laws and Hamilton-Jacobi equations in one-space variable
• Shock Waves on the Highway
• Stochastic Modeling and Simulation of Traffic Flow: Asymmetric Single Exclusion Process with Arrhenius look-ahead dynamics
• On kinematic waves II. A theory of traffic flow on long crowded roads

This page was built for publication: From Heterogeneous Microscopic Traffic Flow Models to Macroscopic Models