Modelization of car traffic

On the left you see a space-time diagram of a real highway jam as measured from a helicopter. At left you see the time evolution of a pipe filled with granular material flowing under the influence of gravity. The formation of mobile clogs ressemble in many aspects real traffic jams.

With Kai Nagel we simulated a traffic model which reproduced highway jamming as described in our paper published in Physica A, Vol. 199, 254-269 (1993). Below you see a figure of the spatio-temporal evolution of a platoon, i.e. when many cars follow a slower car as obtained using this model. Clearly one observes fluctuations and jams of all sizes. In fact a power spectrum of the density as function of time shows a power law.

Some years later with Gerd Sauermann we analytically solved a continuous traffic model as presented in our paper in the proceedings of "Traffic and Granular Flow '97" edited by Schreckenberg and Wolf. Below you see a space-time diagram of jams as obtained with this model.