Research Field: Traffic dynamics Under certain conditions, traffic of individual vehicles can become unstable, especially on motorways. Who was not yet amazed by traffic jams or stop-and-go waves, seemingly appearing ''out of nothing'', without any obvious cause? We investigate these instabilities and other aspects of nonlinear traffic dynamics by developing and simulating mathematical models: Microscopic traffic models describe the motion of each individual vehicle.
Macroscopic models describe the dynamics of locally averaged quantities like the density of vehicles, velocity, and velocity variance. The corresponding equations have some analogies to the Navier-Stokes equations of fluid dynamics. In our case, the analogy can be stressed even further: The equations of our models were derived from a kinetic equation
The results should help to prevent at least some of the traffic jams by providing effective algorithms for a dynamical, i.e., traffic-dependent control of

• speed limits
• overtaking restrictions
• green phases of street lights in cities
• others.

You can get information about the actual progress by looking at my recent publications. To get an impression, simulate two-lane traffic with a continuous "microscopic" model. You will see, how the interplay of perturbations and bottlenecks together with a high traffic flow will cause various types of trafic breakdowns.