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The Voorhees law of traffic: a stochastic model explaining why the car you passed always returns
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DOI：10.1098/rsos.260310.png)
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Abstract
En 中文
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.
Keywords:
stochastic reset
traffic flow
reliability theory
perception bias
everyday physics
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775
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