Nagel-Schreckenberg Traffic Model

A cellular automaton model of highway traffic: acceleration, braking, randomness, and jam formation.

Space-time diagram (time flows down)

Cars: 50

Max speed: 5

Brake prob p: 0.30

Speed (steps/s): 8

Density: - Avg speed: - Flow: -

Rules each step: (1) Accelerate: v → min(v+1, vmax). (2) Brake: v → min(v, gap−1). (3) Randomize: with prob p, v → max(v−1, 0). (4) Move: x → x+v. Phantom traffic jams emerge spontaneously even without bottlenecks.