A new study published in Royal Society Open Science explains a common driving experience where a slower car catches up after being overtaken.
The research, led by Conor Boland at Dublin City University, uses a mathematical model to show how traffic signals play a key role in this outcome.
A Simple Model of Two Cars
The study focuses on interactions between two vehicles traveling at different constant speeds.
While it is generally expected that a faster car will stay ahead, the model shows that traffic lights can change this outcome. The timing of signals is treated as random, meaning drivers cannot predict whether they will encounter a red or green light after overtaking.
Role of Traffic Signals
Boland’s model calculates the probability that a slower car catches up at the next red light.
This probability depends on three factors: the time advantage gained during overtaking, the total duration of the traffic light cycle, and how much of that cycle is red.
If the faster driver reaches a red light, the slower car can close the gap despite traveling at a lower speed.
The “Voorhees Law of Traffic”
The study introduces what Boland calls the “Voorhees law of traffic,” referencing the fictional character Jason Voorhees, known for catching up to faster-moving victims.
The law suggests that when the time advantage from overtaking is small, the chances of the slower car catching up increase significantly. When the advantage is larger, the likelihood of this happening drops.
Impact Over Multiple Signals
The research also shows that the probability of a catch-up increases when multiple traffic lights are involved.
Over longer urban routes with several signals, the chances of at least one catch-up event become much higher, which explains why the experience feels common to drivers.
Broader Implications
Beyond explaining a familiar driving scenario, the findings could improve traffic modeling by incorporating how individual vehicles interact with signals.
The study also suggests that these events are statistically common, which may explain why drivers often remember them clearly.
