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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 Rosco P. Coltrane on Monday May 08 2017, @10:46PM (1 child)

    by Rosco P. Coltrane (4757) on Monday May 08 2017, @10:46PM (#506641)

    Those 3 things are quick and easy to assess too:

    1/ Is the cashier quick when they ring items?

    Z/ Is the cashier the kind who just does their job, or the chatty type who likes to socialize a bit with each customer who passes through? Because the socializing can be nice when it happens with you, but it slows you down when it happens with customers before you.

    3/ Is the line composed of 3 people with 20 items each, or 6 people with 3 items each? Logic would dictate that you should pick the latter (only 18 items total), but I always go for the former because what usually takes forever is customers paying (you know, counting their cash, producing a million vouchers, looking for another credit card because the first one is maxed out, etc). The paying phase is pure overhead in the process - not to mention the chit-chat time that usually happens at the same moment, if the cashier is the socializing type - so you're better off waiting for fewer customers who have a lot more items to ring through.

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  • (Score: 1) by Ethanol-fueled on Monday May 08 2017, @11:02PM

    by Ethanol-fueled (2792) on Monday May 08 2017, @11:02PM (#506650) Homepage

    I've already described how I handle 3, but there is also a way to address 1 and 2 by speeding up the checker (and by extension, the line).

    Look really fucking uncomfortable. Put your hands in your pockets, dart your head to different things around you but never directly at anybody, maybe glance upward at the ceiling and get a nice look at those loss-prevention cameras, breathe deeply and irregularly, shuffle around and tap your fingers. Look at all the stuff the people behind you are buying and eyeball it judgmentally. I guarantee the checker will pick up on it and speed things up just to get your awkward uncomfortable ass the fuck out of the line.

    Super-autists and OCD types are naturally gifted with this ability, though they may not even realize it.

    The only downside to this approach is that there is collateral damage, you will make everybody else uncomfortable as well. They will start to shift and fidget and mirror your actions.