Numerical approximations of a traffic flow model on networks
type: Item
instance of: scholarly article
title: Numerical approximations of a traffic flow model on networks
zbMATH Open document ID: 1124.90005
author: Gabriella Bretti
author: B. Piccoli
author: Roberto Natalini
published in: Networks and Heterogeneous Media
publication date: 2007-04-13T00:00:00Z
review text: In the 1950s James Lighthill and Gerald Whitham and independently P. I. Richards proposed to apply fluid dynamic concepts to traffic. This leads to a hyperbolic conservation law that models the flow of cars in a single road. In this paper, traffic flow on a network of roads as in the urban context is considered. Junctions play a fundamental role, since the system is underdetermined even after prescribing the conservation of cars that can be written as the Rankine-Hugoniot condition. To determine a unique solution to Riemann problems at junctions, two criteria are assumed: (A) There are some fixed coefficients, the prescribed preferences of drivers, that express the distribution of traffic from incoming to outgoing roads; (B) Respecting (A), drivers' choices are made in order to maximize the flux. The numerical approximation is carried out by the Godunov scheme and discrete velocities kinetic schemes. The algorithms are presented and some small portions of urban networks are considered as test cases.
reviewed by: Martin Gugat
Mathematics Subject Classification ID: 90B20
Mathematics Subject Classification ID: 34B45
zbMATH DE Number: 5142459
zbMATH Keywords: Scalar conservation laws
zbMATH Keywords: traffic flow
zbMATH Keywords: fluid dynamic models
zbMATH Keywords: boundary conditions
MaRDI profile type: Publication
full work available at URL: nhm.2006.1.57
OpenAlex ID: W2022552551
DOI: 10.3934/NHM.2006.1.57
description: scientific article; zbMATH DE number 5142459