See also the applets of Cay Horstmann and Kai Bolay.

How does the cellular automaton for traffic flow work?

The road is thought to be subdivided into cells, each 7.5 meters long. Every cell is either vacant or occupied by a vehicle with a discrete speed v that takes integer values from 0 to a maximum speed v_max. The gap g denotes the number of empty cells between two consecutive vehicles.

The speed is treated according to certain rules detailly explained in "Info & Details ...". A stochastic component, the deceleration probability P, is added in order to introduce fluctuations into the model.

With respect to real traffic data a simple calibration for, e.g., highway traffic can be done. The maximum speed v_max=5 corresponds to a "desired speed" of approx. 130 km/h, and the duration of one simulation step refers to approx. 1 second.

The explanation of the diagrams

The upper left one is a simple space-time plot. The red color indicates congested traffic. As the vehicles go to the right, the jam waves go backwards in space (see also records on real traffic). In the lower left one you can have a look at the road (this is the so-called Indianapolis scenario with periodic boundary conditions).

In this simulation the local flow of vehicles q [vehicles/time], the mean local speed v [sites/timestep] and the local density rho [vehicles/site] are measured. The relation among these three quantities are plotted the so-called fundamental diagrams on the right side. The two bar charts on the bottom show the global relative frequency f of the speeds and the gaps.

For further information and parameter tuning, please press the button "Info & Details ...".