🚗 Phantom Traffic Jams: Stop-and-Go Waves

About this simulation

In 2008, researchers at Nagoya University put 22 drivers on a single-lane ring road and told them only to avoid hitting the car ahead. Within minutes a jam appeared out of nowhere and rotated backward around the ring — proof that congestion can be a pure, self-organizing property of car-following behavior, with no crash or bottleneck required. This simulation reproduces that ring-road experiment with a real car-following model.

How it works

• Each car tracks the gap to the car ahead along the ring and keeps a safety distance that scales with its own speed and its driver's reaction time: safeGap ≈ speed × reactionTime.
• If the gap is comfortably larger than the safe distance, the car accelerates toward the free-flow speed; if the gap shrinks below it, the car brakes — matching the speed of the car ahead.
• The reaction-time delay means braking is always a little late and a little too strong. That overcorrection passes down the line of cars, amplifying into a self-sustaining stop-and-go wave that travels backward through the traffic even though every car is moving forward.
• Car color encodes speed: green near free-flow, through yellow, to red near a standstill — watch a red cluster form and drift backward around the ring.

Controls

• Vehicles on ring — sets traffic density. More cars packed onto the fixed-length ring pushes density past the critical point on the fundamental diagram.
• Reaction time — the delay between perceiving a change and reacting to it. Longer reaction times make the traffic stream more unstable and waves appear more easily.
• Free-flow speed — the speed drivers aim for when they have room to accelerate.
• Anticipate 2 cars ahead — toggles a simple form of cooperative driving that looks two vehicles ahead instead of one, damping the amplification that produces waves.
• ⚡ Brake one car — manually seeds a single braking event to show how a tiny disturbance can grow into a full wave.
• ↺ Reset ring — respawns all vehicles evenly spaced. Drag to rotate, scroll to zoom.

Did you know?

Real stop-and-go waves on congested highways travel backward at a strikingly consistent 15–20 km/h (about 10–12 mph) almost regardless of the road's speed limit, because the wave's speed is set by human reaction time and following behavior, not by how fast anyone is allowed to drive.