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posted by Fnord666 on Monday May 08 2017, @09:39PM   Printer-friendly
from the wait-your-turn dept.

It seems obvious. You arrive at the checkouts and see one queue is much longer than the other, so you join the shorter one. But, before long, the people in the bigger line zoom past you and you've barely moved towards the exit.

When it comes to queuing, the intuitive choice is often not the fastest one. Why do queues feel like they slow down as soon as you join them? And is there a way to decide beforehand which line is really the best one to join? Mathematicians have been studying these questions for years. So can they help us spend less time waiting in line?

The intuitive strategy seems to be to join the shortest queue. After all, a short queue could indicate it has an efficient server, and a long queue could imply it has an inexperienced server or customers who need a lot of time. But generally this isn't true.

[...] Once you're in the queue, you'll want to know whether you made the right choice. For example, is your server the fastest? It is easy to observe the actual queue length and you can try to compare it to the average. This is directly related to the mean and standard deviation of the service time via something called the Pollaczek-Khinchine formula, first established in 1930. This also uses the mean inter-arrival time between customers.

Unfortunately, if you try to measure the time the first person in the queue takes to get served, you'll likely end up feeling like you chose the wrong line. This is known as Feller's paradox or the inspection paradox. Technically, this isn't an actual logical paradox but it does go against our intuition. If you start measuring the time between customers when you join a queue, it is more likely that the first customer you see will take longer than average to be served. This will make you feel like you were unlucky and chose the wrong queue.

So, before you choose a queue to join, put the screaming kids down and carefully note the average serving time in each queue, measure the queue length, and then project which will get you through to a completed transaction quickest.


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  • (Score: 2) by bob_super on Monday May 08 2017, @11:17PM

    by bob_super (1357) on Monday May 08 2017, @11:17PM (#506659)

    Does the trick of having your girlfriend put a pillow under her dress still work, or are people now Candy-crushing too much to even notice?

    Queues are when other people check their FB one more time, just in case the 20 minutes in the supermarket made them missing some life-changing event. Which of course makes them unprepared when their turn comes, slowing down the queue...

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