The European Physical Journal B

, Volume 70, Issue 2, pp 229–241

Derivation of a fundamental diagram for urban traffic flow

Interdisciplinary Physics

DOI: 10.1140/epjb/e2009-00093-7

Cite this article as:
Helbing, D. Eur. Phys. J. B (2009) 70: 229. doi:10.1140/epjb/e2009-00093-7


Despite the importance of urban traffic flows, there are only a few theoretical approaches to determine fundamental relationships between macroscopic traffic variables such as the traffic density, the utilization, the average velocity, and the travel time. In the past, empirical measurements have primarily been described by fit curves. Here, we derive expected fundamental relationships from a model of traffic flows at intersections, which suggest that the recently measured fundamental diagrams for urban flows can be systematically understood. In particular, this allows one to derive the average travel time and the average vehicle speed as a function of the utilization and/or the average number of delayed vehicles.


89.40.Bb Land transportation47.10.ab Conservation laws and constitutive relations51.10.+y Kinetic and transport theory of gases

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.ETH Zurich, UNO D11, Universitätstr. 41ZurichSwitzerland