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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.
(Score: 2) by nobu_the_bard on Tuesday May 09 2017, @12:23PM
It helps to know a couple of things, like the priority of the store in selecting cashiers.
Wal-Mart's priority, for example, is that all queues appear to move at the same speed, or as close to it as possible, so that customers don't feel like they picked the wrong line. Tricks they use to try to do this include having the slowest cashiers in the express lanes; faster cashiers typically operate specialized registers (like ones with access to cigarettes). There's problems with Wal-Mart's implementation of course - most of the COS (front-end supervisors) don't do their jobs properly and manage the queues to maintain these objectives. They're usually ghosts or staring vacantly into space back at their station hidden out of sight until called. Sam's Club ones are a little better about this; they are more likely to be proactive, partly because they are paid better, partly because the working environment is more positive in those places.
You see different things at places like Target. They're laid out to confuse queue lengths to customers. It removes the need to micromanage things that Wal-Mart has.
The one-queue-multiple-registers thing that Kohl's does really seems to work pretty okay for them. These other stores should try figuring that out sometime; I'm not sure it scales up to the size that Wal-Mart operates at though without the COS doing their jobs.