Phantom traffic jams

▸ Laying a 220-cell ring road — no obstacle, no lights…

▸ Spawning cars at the target density

▸ Loading the Nagel–Schreckenberg rule (4 steps)

▸ Enabling random slowdown noise (p) — the phantom-jam seed

▸ Calibrating the space-time plot

▸ Ready — Online. ✅

Flow gauge

🚗 Chạy ổn

arc = flow · needle = density

Density—

Mean speed (cells/tick)—

Flow (cars/min)—

Jam waves—

Slowdown probability p—

Cars—

The idea

No accident, no red light — yet a jam still EMERGES. One car brakes a bit hard, the car behind harder: the chain piles into a "wall of cars" drifting backward against traffic. That is a phantom jam.

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Car color by speed: red = jammed · green = fast · bottom strip = space-time plot (tilted black stripe = backward jam wave)

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Flow & mean speed over time flowmean speed