# A Mathematician Has the Perfect Explanation For Why Traffic Jams Happen

Sitting in traffic is the worst way to spend Labor Day weekend. What’s even more frustrating is realizing there was no reason for a traffic jam in the first place.

Why does traffic happen where there seems to be no accidents and no construction work interfering with the flow of cars driving in one direction?

According to Vox, researchers used mathematical calculations on real-world cases and discovered a cause for phantom traffic jams. They found that with enough people on the road, the simplest interruption in traffic flow causes an amplified domino effect. When one car brakes slightly, the person behind them brakes slightly harder to avoid an accident, and the car behind that one breaks even harder, etc. Eventually this chain reaction creates a wave effect of completely stopped or slowed traffic.

Benjamin Seibold, a mathematician at Temple University, described the effect:

“These traffic waves arise from small perturbations in a uniform traffic flow, like a bump in the road, or a driver braking after a moment of inattention.”

What’s surprising is that even when the cars that initiated this traffic leave, the traffic wave doesn’t disappear. Instead the ripple effect travels backward against the direction of traffic. Seibold explained:

“It’s typically 100 to 1000 meters long, and it usually begins with vehicles running into a sudden increase in density at the start, and a drop in velocity. Then, after that, they slowly accelerate again.”

Seibold and his colleagues call these wave “jamitons” and applied computer algorithms to simulate the driving behavior during traffic:

According to this model, the people to blame for these phantom traffic jams are those who drive as fast as humanly possible and brake to stop themselves from hitting the vehicle in front of them. However, Seibold says jams can be prevented by drivers:

“If people anticipate higher traffic densities ahead, and take their feet off the gas earlier and leave more room in front of them — instead of waiting until they have to brake — that can prevent traffic jams from arising.”

The researcher explained that engineers can assist with short-term solutions by designing straighter and smoother roads. Another way to help with phantom traffic jams are to implement variable speed limits. If cars slowed down gradually rather than abruptly and all at once, this could break up waves. However, Seibold believes the long-term solution for traffic jams is the innovation of self-driving cars that can control their speeds more precisely than humans by using traffic data to foresee any jams down the road.

Feature Image via Robert Jack 啸风 Will/ (CC BY-SA 2.0)