  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.
