Issue Eur. Phys. J. B Volume 69, Number 4, June II 2009 Page(s) 539 - 548 Section Interdisciplinary Physics DOI 10.1140/epjb/e2009-00192-5 Published online 03 June 2009

Eur. Phys. J. B 69, 539-548 (2009)
DOI: 10.1140/epjb/e2009-00192-5

Derivation of non-local macroscopic traffic equations and consistent traffic pressures from microscopic car-following models

D. Helbing

ETH Zurich, UNO D11, Universitätstr. 41, 8092 Zurich, Switzerland

dhelbing@ethz.ch

Received 19 May 2008 / Received in final form 9 October 2008 / Published online 3 June 2009

Abstract
This contribution compares several different approaches allowing one to derive macroscopic traffic equation directly from microscopic car-following models. While it is shown that some conventional approaches lead to theoretical problems, it is proposed to use an approach reminding of smoothed particle hydrodynamics to avoid gradient expansions. The derivation circumvents approximations and, therefore, demonstrates the large range of validity of macroscopic traffic equations, without the need of averaging over many vehicles. It also gives an expression for the “traffic pressure”, which generalizes previously used formulas. Furthermore, the method avoids theoretical inconsistencies of macroscopic traffic models, which have been criticized in the past by Daganzo and others.

PACS
89.40.Bb - Land transportation.
45.70.Vn - Granular models of complex systems; traffic flow.
47.10.ab - Conservation laws and constitutive relations.

© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2009

What is OpenURL?