Each cell on a circular road is either empty or contains a car with velocity v ∈ {0,…,v_max}. Each time step applies four rules simultaneously to all cars:
The random braking (p > 0) is the key: it spontaneously creates phantom traffic jams — backward-propagating waves with no accident. The space-time diagram (below road) shows car positions over time: diagonal streaks = free flow; vertical/backward-slanted bands = jams. The fundamental diagram (flow vs. density) shows a capacity drop at a critical density ρ_c ≈ 1/(v_max+1).