Phantom traffic jams

Crawling for kilometres and then, with no accident or roadworks in sight, suddenly running free again. The Nagel–Schreckenberg model of 1992 rebuilds exactly that from four steps per tick: accelerate, brake to the gap ahead, slow down at random with probability p, then move. That third step is the soul of the phantom jam; drop p and the jams vanish. On a space–time plot the jam shows up as a slanted black stripe: the wall of cars drifts backwards against the flow while every single car is still moving forwards.

▸ 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

About Traffic Jam