Scientists have explained why a car you overtake catches up with you again

It's about a simple mathematical pattern.

Details

A researcher from Dublin City University has modelled a situation involving two cars.

The model takes into account

• speed differential
• the time advantage after overtaking
• the traffic light cycle (red and green)

The key factor is the moment at which the driver approaches the signal.

The analysis showed:

• the small time gain easily disappears on red
• the longer the red signal, the greater the chance of the second car catching up
• the probability depends on three parameters: the time gain, the cycle length and the proportion of red light

Why it matters

The results explain why overtaking in the city often doesn't have the expected effect.

The scientists point out:

• these situations occur regularly, not randomly
• the effect is stronger on roads with frequent traffic lights
• this can be taken into account when modelling urban traffic

Background

Such behaviour has been observed by drivers for a long time, but previously it was explained by subjective perception.

The study describes this effect as "Voorhees' law" - by analogy with a character in films who inevitably catches up.

Source

The study is based on a probabilistic model of two-car traffic, taking into account the random phase of a traffic light. The work has been published in Royal Society Open Science (2026).