Traffic Light Queues and the Poisson Clumping Heuristic

TL;DR

This paper analyzes the maximum queue length of cars at traffic lights with alternating red and green phases, providing probabilistic asymptotics for specific cycle lengths.

Contribution

It introduces a novel application of the Poisson clumping heuristic to model and analyze queue lengths at traffic lights with fixed cycle lengths.

Findings

Derived asymptotic distributions for maximum queue length

Validated conjectured probabilistic behaviors for specific cycle lengths

Extended the Poisson clumping heuristic to discrete-time traffic models

Abstract

In discrete time, $\ell$-blocks of red lights are separated by $\ell$-blocks of green lights. Cars arrive at random. We seek the distribution of maximum line length of idle cars, and justify conjectured probabilistic asymptotics for $2 \leq \ell \leq 3$.