Traffic Light Queues and the Poisson Clumping Heuristic

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 $2\le \ell \le 3$.

23 pages; 5 endnotes (re pp 7,8,9,13,21) added in v 2; further corrections & 1 additional endnote in v 3

References in corpus (2)

• The Maximum of an Asymmetric Simple Random Walk with Reflection
• Conjectures about Traffic Light Queues

Cited by in corpus (4)

• Conjectures about Traffic Light Queues
• Geo/Geo/2 Queues and the Poisson Clumping Heuristic
• M/M/$c$ Queues and the Poisson Clumping Heuristic
• How Long Might We Wait at Random?