Friday, January 16, 2009

Men's Room Problem

There are N urinals; men prefer to stand away from others and they come in following a Poisson process and occupy one urinal for a fixed amount of time. How many flushes each of the urinals would get for each day?

COMMENT: this problem gets interesting when N is larger than 3 and the restroom is relatively crowded (say always slightly more than half occupied). Say N=2^n+1, the # of flushes is not a monotonous function from one side to the other; instead as n goes to infinity, it could very well have an asymptotic form like the Weierstrass function (not proved)...
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1 comment:

Danyan said...

I know I don't answer to you question. Just FYI. From a psychologist's point of view, most men would prefer the urinals on the side in stead of those in the middle just for the privacy. Nobody likes to be sandwiched by two other men in this restroom scenario. In fact, I suppose nobody likes the center seats in those international flights for a somewhat similar reason. In human, we call it guarding privacy. In animals, we strip the psychology down to the open-field anxiety that comes from hanging out in the center. Rats prefer walking the sidelines :D cuz I think it gives them the sense of security to know that they can always find a hole along the wall somewhere more quickly than dashing from the center to nowhere.

January 18, 2009 at 3:40 PM

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