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 Waiting, waiting... (Posted on 2004-08-07)
You are outside a well known restaurant, waiting in queue, with 18 couples in front of you. You know there are forty tables inside, and you think an average meal will take one hour.

How long will you have to wait, on average?

PS. This problem comes from queueing theory, but you don't have to know anything about it to find the answer!

 See The Solution Submitted by Federico Kereki Rating: 3.2857 (7 votes)

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 Realistically Comment 19 of 19 |
Assumptions have to be made about a lot of things to come up with an answer for this problem.

Here's another issue that is realistic although I will take it to the extreme for clarity.

The time remaining for the seated people is not random.  Good restaurants tend to have a dinner rush.  Say 58 couples show up at the same time.  40 of them will be seated at once and the rest will have an hour wait (also assuming the service can cope with this rush.)  Actually the wait for the others is highly dependent on the distribution of individual tables.  The 41st couple will only have to wait as long as the quickest of the 40 preceding people.  The 58th will have to wait as long as the 18th quickest, or a little less if one of the 41st through 57th has a quick turn around.

If everyone takes precisely one hour, the wait for everyone from 41 to 80 will be one hour.

So again, the wait time has everything to do with the distribution of the individuals.  This question cannot be answered without knowing it.

 Posted by Jer on 2015-06-16 08:57:44

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