Nagel–Schreckenberg model

The model was developed in the early 1990s by the German physicists Kai Nagel and Michael Schreckenberg.

One can think of a cell as being a few car lengths long and the maximum velocity as being the speed limit on the road.

These four actions are repeated many times, as long as is required to study any traffic jams that may form.

Above and to the right is a plot of the average velocity as a function of the density of cars, obtained from a simulation of the original Nagel–Schreckenberg model.

[2] To the right is the result of an example simulation run of the Nagel–Schreckenberg model, with maximum velocity 5, density of cars 0.35 and probability of deceleration p = 0.3.

Small traffic jams show up as dark bands, i.e., groups of cars that are nose-to-tail and moving slowly to the right.

This feature of one car braking at random and causing a jam is absent in a deterministic model.

A plot of the average velocity, <v>, as a function of the density of cars per cell, rho, in the Nagel–Schreckenberg model. The black curve is for p = 0, i.e., for the deterministic limit, while the red curve is for p = 0.3.
A road with jams of cars, in the Nagel–Schreckenberg model. Each line of pixels represents the road (of 100 cells) at one time. Black pixels are cells with cars in them, white pixels are empty cells. From the top to the bottom successive lines of pixels are the road at successive times, i.e., the top line is the road at t = 1, the line below it is the road at t = 2, etc. The road is circular ( periodic boundary conditions ), and cars move right exiting at the right edge and rejoining on the left edge. The car density is 0.35 and p = 0.3.