NaSch Traffic Model

Nagel-Schreckenberg Model (1992): Each cell is empty or has a car with velocity v∈[0,v_max]. Each step: (1) accelerate: v←min(v+1,v_max); (2) decelerate: v←min(v,gap−1); (3) randomize: with prob p, v←max(v−1,0); (4) move: x←x+v. Despite its simplicity, the model reproduces jam formation, the fundamental diagram (flow vs. density), and metastable states. The "ghost jams" that propagate backward are a hallmark — jams exist even without accidents. The flow peaks near ρ≈1/(v_max+2) and drops as density increases beyond the critical point.