The Voorhees law of traffic: a stochastic model explaining why the car you passed always returns
Year: 2026
Type: article
Abstract: Every driver knows the paradox: after overtaking a slower car and gaining a clear lead, you find the same car mysteriously behind you at the very next red light. Like Jason Voorhees from Friday the 13th, their supernaturally slow pace seems to lead to scenarios where their hastier victim is caught. Here, a simple mathematical model provides a tractable analytical framework for pairwise vehicle interactions under a fixed-time traffic signal control. The model shows that the probability of catch-up depends on the overtaking time advantage t, the signal cycle length C and the fraction of the cycle that is a red light r. Specifically, the chance of reappearance is max(r−tC,0). While framed humorously, the analysis is mathematically consistent with classical traffic signal and queueing theory. The work introduces a new, two-vehicle stochastic framework for overtake–reset dynamics, linking overtaking kinematics to signal-phase statistics, which to the author’s knowledge, has not been modelled before. It is argued that everyday traffic obeys not only Newtonian mechanics, but perhaps also a cinematic law of inevitability.
Source: Royal Society Open Science
DOI: 10.1098/rsos.260310
Author: Conor S. Boland
Institution: Dublin City University
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,471
OpenAlex ID: W7147089794