Traffic light problem

The traffic light problems are a type of mathematical problems involving several distant traffic lights out of phase and a car moving at a constant speed.^[1]^[2]

Example

Imagine a 1-meter road, with a traffic light in the background that changes from red to green every 10 seconds. If the car travels at 1 meter per second, we can guarantee that unless it starts in second 9 of being green, it will always have to wait less than 10 seconds.

References

↑ McNeil, Donald R. (1968-12-01). "A solution to the fixed-cycle traffic light problem for compound Poisson arrivals". Journal of Applied Probability. 5 (3): 624–635. doi:10.2307/3211926. ISSN 0021-9002. JSTOR 3211926. S2CID 123732627.
↑ Gaspard, Mallory E.; Vladimirsky, Alexander (2022-01-12). "Optimal Driving Under Traffic Signal Uncertainty". arXiv:2201.04521. {{cite journal}}: Cite journal requires |journal= (help)

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[1] McNeil, Donald R. (1968-12-01). "A solution to the fixed-cycle traffic light problem for compound Poisson arrivals". Journal of Applied Probability. 5 (3): 624–635. doi:10.2307/3211926. ISSN 0021-9002. JSTOR 3211926. S2CID 123732627.

[2] Gaspard, Mallory E.; Vladimirsky, Alexander (2022-01-12). "Optimal Driving Under Traffic Signal Uncertainty". arXiv:2201.04521. {{cite journal}}: Cite journal requires |journal= (help)

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