Solving traffic congestion with help of math

Eindhoven University of Technology

How do you make sure that there are no traffic jams at traffic lights? That’s easier said than done, as anyone who has been stuck in a traffic jam at a red light knows. Researcher Rik Timmerman has applied a mathematical model to improve traffic flow. He will defend his thesis on January 28th at the department of Mathematics and Computer Science.

You drum your fingers on the steering wheel, wobble in your seat and clench your fists. Driving on is impossible during congestion. At last, the light turns green! But driving is impossible because the person in front of you is lost in his cell phone. Traffic lights often cause congestion. “They create a difficult problem to solve,” says Rik Timmerman of the Stochastic Operations research group. “You’re dealing with a lot of different factors, and chance.” He investigated how to prevent congestion at traffic lights as much as possible with mathematics.


At traffic lights you have to deal with many different elements. Like the amount of vehicles, the weather, driving behavior, accidents, and the different types of traffic participants. “But chance also plays a role,” says Rik Timmerman. “Sometimes there are two cars at a traffic light, at other times ten. And if an older person crosses at the same time, that also has an effect.”

Rik Timmerman
Rik Timmerman

The researcher tried to capture all these elements in a queuing model, the Fixed-Cycle Traffic-Light (FCTL) queue. These types of queueing models are used to discover a pattern in the chaos of traffic to provide better flow. He analyzed different traffic scenarios, such as where pedestrians block vehicles because they are given a green light at the same time. “When you analyze traffic lights, you’re looking at situations that have happened before. In this way, you capture chance, as it were.”

Better traffic flow

His mathematical model cannot promise that traffic jams will never occur. But Timmerman can promise better traffic flow. “If you can predict the average number of cars waiting at a traffic light and how fast the traffic will flow, then you can reduce the waiting time. Even if it’s a few seconds, it works its way back into the rest of the traffic. And that already is a gain.”

The researcher also looked at the effect of self-driving cars on congestion at traffic lights. “If you get those cars to respond intelligently to traffic lights, that also saves time,” he said. That’s because they can react faster, drive faster at traffic lights and are able to cross an intersection in groups. A future with more self-driving cars therefore also means less congestion, according to the model. “Unless, of course, more and more people get in their cars.”

Saving time

His thesis research is a popular conversation topic during birthday parties, says the researcher. “Everyone always wants to know how they can avoid ending up in a traffic jam.” He also likes to apply the theory himself in practice. “Through my research, I know that it’s best to approach at a slightly higher speed when the traffic light is still green, rather than slowing down. And that it’s smart to drive on quickly when you know it’s almost green. If everyone does that, it will save a lot of time and reduce traffic irritation.”

Rik Timmerman will defend his thesis on 28 January for his dissertation entitled: Performance analysis at the crossroad of queueing theory and road traffic. Supervisors: Ivo Adan, Johan van Leeuwaarden and Marko Boon.

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