Citation

Kuehne R. Transp. Traffic Theory 1984; 9: 21-42.

Copyright

(Copyright © 1984, Publisher varies)

DOI

unavailable

PMID

unavailable

Abstract

A continuum model for freeway traffic flow is described which includes relaxation of the equilibrium speed of the static speed-density relation ("fundamental diagram") and anticipation of traffic conditions downstream. Stability analysis shows that in light traffic the equilibrium solution given by the fundamental diagram is stable, while in dense traffic, jams with stop-start waves occur. The formation of stop-start waves is in full analogy to the creation of roll waves in inclined open channels with a suitable water height. The methods to derive such roll wave solutions from the basic hydrodynamic equations of shallow water theory are used to describe the stop-start waves in the freeway model. As in fluid dynamics, where the change from laminar flow to turbulent flow is announced by critical fluctuations, the change from steady traffic to traffic with jams and stop-start waves is indicated by large fluctuations. From theory and measurement of the broadening of the speed distribution due to the critical fluctuations an algorithm of traffic classification and incident detection is derived. On the basis of a simplified version of this algorithm using only local measurements of the speed distribution an automatic traffic jam warning system is developed.