Traffic Light Green Wave (2D)

Green-Wave Design Speed

Signals timed for 50 km/h

Your Driving Speed

Speed you actually drive 50 km/h

Signal Timing

Cycle length 40 s

Green share 50%

Number of signals 5

Cars per minute 10

Set your speed equal to the design speed to ride the green wave.

Live Readout

Non-stop cars

Avg. speed

0 km/h

Stops / car

Cars on road

How it works

A green wave is a chain of traffic signals whose green phases are staggered so a driver moving at one specific design speed reaches every signal exactly as it turns green. The offset given to signal i, sitting at distance d_i from the start of the road, is simply offset_i = d_i / v_design (taken modulo the cycle length) — the time a car at the design speed needs to reach it.

The space-time diagram below plots distance along the road on the horizontal axis and time flowing downward on the vertical axis. Each signal draws its green windows as a repeating band at its own column; because the offsets above are all derived from one shared speed, those bands line up into a diagonal corridor — the "wave". The dashed diagonal lines show that corridor: any trajectory that stays parallel to them and inside the bands never meets a red light.

Cars in the road view follow the Intelligent Driver Model, braking smoothly for a red signal exactly as they would for a stopped car ahead. Set "Your driving speed" away from the design speed and watch their trajectories drift out of the green corridor and start clipping red bands — which is exactly what forces real stop-and-go driving on a badly matched arterial.

Green Red Your car

Space-time diagram — distance → , time ↓