Traffic Jam Formation

Nagel & Schreckenberg (1992): cars on a ring road update simultaneously — accelerate if below v_max, brake if car ahead is close, randomly dawdle with probability p, then move. Even without any bottleneck, random braking creates density waves that propagate backward. At the critical density, flow peaks (fundamental diagram maximum). Jam waves travel backward at ~15 km/h in real traffic — a universal wave speed independent of road conditions. The space-time diagram (below ring) reveals these backward-moving structures.