Eur. Phys. J. B 70, 229-241 (2009)
https://doi.org/10.1140/epjb/e2009-00093-7

Derivation of a fundamental diagram for urban traffic flow

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

Corresponding author: ^a dhelbing@ethz.ch

Received: 11 July 2008
Revised: 22 December 2008
Published online: 14 March 2009

Abstract

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.