TRAFFIC JAM FORMATION

Nagel-Schreckenberg CA: phantom jams emerge from stop-and-go waves — density-flow fundamental diagram
Nagel-Schreckenberg, 1992
Rules (each step):
1. Accelerate: v → min(v+1, v_max)
2. Brake: v → min(v, gap-1)
3. Dawdle: if rand < p, v → max(v-1, 0)
4. Move: advance v cells

Phantom jams form above critical density even without obstacles. Stop-and-go waves travel backward.