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arXiv · 1802.04621

Maximum Queue Length for Traffic Light with Bernoulli Arrivals

Steven R. Finch
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Abstract

Cars arrive at an intersection with a stoplight, which is either red or green. The cars all travel in the same direction, that is, we ignore cross-traffic & oncoming traffic. Assume that the intersection is initially empty. Assume that, at every second, there is a probability p that one new car will arrive at the light, and the outcome is independent of past & future. Let L>=1 be an integer. A red light lasts L seconds; likewise for green. If the light is red, no cars can leave the intersection. If the light is green, cars will leave the intersection at a rate of one per second. Over a time period of n seconds, determine the (random) maximum queue length M of cars at the intersection. What is the distribution of M, as a function of (p,L,n)? We answer this question for the special case L=1 and introduce a conjecture for L>1.

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Steven R. Finch. 2018-02-13. Maximum Queue Length for Traffic Light with Bernoulli Arrivals. https://arxiv.org/abs/1802.04621

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