Fundamental diagrams for kinetic equations of traffic flow

Luisa Fermo; Andrea Tosin

doi:10.3934/dcdss.2014.7.449

Article Contents

2014, Volume 7, Issue 3: 449-462. Doi: 10.3934/dcdss.2014.7.449

This issue Previous Article A front tracking method for a strongly coupled PDE-ODE system with moving density constraints in traffic flow Next Article The LWR traffic model at a junction with multibuffers

Fundamental diagrams for kinetic equations of traffic flow

Luisa Fermo^1, and
Andrea Tosin^2,

1.
Department of Mathematics and Computer Science, University of Cagliari, Viale Merello 92, 09123 Cagliari
2.
Istituto per le Applicazioni del Calcolo "M. Picone", Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185 Roma

Received: May 2013

Revised: August 2013

Published: June 2014

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Abstract

In this paper we investigate the ability of some recently introduced discrete kinetic models of vehicular traffic to catch, in their large time behavior, typical features of theoretical fundamental diagrams. Specifically, we address the so-called ``spatially homogeneous problem'' and, in the representative case of an exploratory model, we study the qualitative properties of its solutions for a generic number of discrete microscopic states. This includes, in particular, asymptotic trends and equilibria, whence fundamental diagrams originate.

Keywords:

Mathematics Subject Classification: Primary: 90B20; Secondary: 34A34, 34D05.

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References

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