On the micro-to-macro limit for first-order traffic flow models on networks

DOI10.3934/nhm.2016002zbMath1346.35127arXiv1505.01372OpenAlexW3103513121MaRDI QIDQ316958

Emiliano Cristiani, Smita Sahu

Publication date: 30 September 2016

Published in: Networks and Heterogeneous Media (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.01372

zbMATH Keywords

networkstrafficLWR modelcar-following modelfollow-the-leader modelmany-particle limitmulti-path model

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Traffic problems in operations research (90B20) Boundary value problems on graphs and networks for ordinary differential equations (34B45) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Related Items (17)

Uncertainty quantification in hierarchical vehicular flow models ⋮ Transport of measures on networks ⋮ Specified homogenization of a discrete traffic model leading to an effective junction condition ⋮ Traveling waves for a microscopic model of traffic flow ⋮ 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 ⋮ Microscopic derivation of a traffic flow model with a bifurcation ⋮ Viscosity solutions of Hamilton-Jacobi equations in proper \(\text{CAT(0)}\) spaces ⋮ On the Microscopic Modeling of Vehicular Traffic on General Networks ⋮ The follow-the-leader model without a leader: an infinite-dimensional Cauchy problem ⋮ Microscopic and macroscopic models for coupled car traffic and pedestrian flow ⋮ Properties of the LWR model with time delay ⋮ Stationary wave profiles for nonlocal particle models of traffic flow on rough roads ⋮ Homogenization of a discrete model for a bifurcation and application to traffic flow ⋮ Multiscale Control of Generic Second Order Traffic Models by Driver-Assist Vehicles

Uses Software

• VISSIM

Cites Work

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