Eur. Phys. J. B 63, 255-264 (2008)
https://doi.org/10.1140/epjb/e2008-00234-6

Delay times in a cellular traffic flow model for road sections with periodic outflow

German Aerospace Center (DLR), Institute of Transportation Systems, Rutherfordstr. 2, 12489 Berlin, Germany

Corresponding authors: ^a thorsten.neumann@dlr.de - ^b peter.wagner@dlr.de

Received: 21 January 2008
Revised: 25 April 2008
Published online: 20 June 2008

Abstract

A simple cellular automaton to model traffic flow is used to analyze the impact of traffic lights on travel times. The model is investigated on a stretch of road with open boundaries, where the inflow is driven stochastically, but the outflow is controlled by a traffic light with periodically changing outflow rates. Especially in the transition regime from free flow to oversaturated flow, the detailed space-time structure can be used to derive analytical lower and upper boundaries for the travel time function. The analytical results have been verified by a simulation study. The function displays a strong non-trivial dependency on the length of the system, which is at odds with a well-known formula derived almost 50 years ago by Webster. Such a model is interesting both from a theoretical point of view and for applications.