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.