Why do traffic jams appear out of nowhere?

You crawl through a highway slowdown for ten minutes. Then the traffic opens up, and there is nothing there. No crash, no lane closure, no merging ramp. These are called phantom traffic jams. In dense traffic, a small disturbance can be enough to start one. Wikipedia: Traffic wave.

How can a small slowdown become a jam?

Every driver reacts to the car ahead. When that car slows, you slow too, a moment later. With a big gap in front, you can ease off gently and let the gap shrink. The slowdown fades before it reaches the driver behind you.

With a small gap, there is no room to absorb it. You must slow as much as the car ahead, or more. Then the driver behind you does the same. The slowdown passes backward from car to car, and it can grow into a full stop.

Through it all, no car ever drives backward. Cars leave the front of the jam as new cars arrive at its back. So the jam itself slides backward, against the traffic. This is called a traffic wave. Wikipedia: Traffic wave.

▶ Play with this now in Phantom Traffic Jam: slide the density to Busy and watch the jam drift backward.

What did the model show?

Our model puts cars on a one-lane ring road divided into 300 cells. It follows rules published by Kai Nagel and Michael Schreckenberg in 1992. Each step, a car speeds up if it can, but never past the empty cells ahead. Wikipedia: Nagel–Schreckenberg model.

We ran the same test on a quiet ring and a busy one. Nobody slowed at random. Car 1 stopped for three steps, and only the number of cars changed.

With 30 cars, each gap was 9 cells. The slowdown changed the speed of 7 cars, then faded within about a dozen steps. With 75 cars, each gap was only 3 cells. The same tap reached 49 cars within 48 steps and left a small jam behind. That jam drifted backward one cell every step, for the whole run. In time, the slowdown touched all 75 cars.

These are results from one seeded run, counted in cells and steps. They are not real distances or times.

Real drivers do this too. In 2008, Yuki Sugiyama and colleagues had 22 drivers circle a 230-meter track at about 30 km/h (19 mph). With no bottleneck at all, a jam formed. It traveled backward at roughly 20 km/h (12 mph). Sugiyama and colleagues (2008).

What does the model leave out?

Phantom Traffic Jam is a simplified one-lane following model. It is not calibrated to any road and is not a traffic forecast. It leaves out:

• Road features. Extra lanes, lane changes, ramps and bottlenecks. The ring removes them on purpose.
• Different drivers. Every car follows the same rules, with whole-number speeds from 0 to 5 cells a step.
• Real distance and time. The model counts cells and steps, and the animation plays six steps each second.

The outcome also depends on the settings. A busier road does not guarantee a lasting jam every time. That is why the interactive measures each run instead of assuming the answer.

Can you make a traffic wave with people?

You need at least five people and some open space, such as a yard or a park. These steps are a suggestion, so adapt them to the children with you. Walk, never run, and leave room to stop.

Predict. Make a big circle, one person behind another, all facing the same way. Agree that one walker will stop for a count of three, then walk on. Ask: will the stop stay with that walker, or travel? Which way will it go?

Try. Walk slowly with about three big steps between people. Have the chosen walker pause for three counts. Then close the gaps to one small step, and repeat the same pause. If you can, ask a helper outside the circle to watch where people stop.

Explain. With big gaps, the people behind slow a little, and the pause fades. With small gaps, each person must stop in turn. The stop passes backward around the circle while everyone walks forward. That is the model's jam, made of people.

Next time you meet a jam with no cause in sight, look for the wave. For the next question, explore Ryan Sael's Who Gets the Green? It compares ways a traffic light can decide who goes.

Phantom Traffic Jam is an ExplainerTools Original. Its rules come from the Nagel–Schreckenberg model. Its ring road echoes the 2008 experiment by Sugiyama and colleagues.