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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: 0) by Anonymous Coward on Tuesday May 09 2017, @01:13AM
Plus truck drivers are going to know what the fsck they're doing. When I used to drive truck and headed through Chicago on a near weekly basis, I pretty much had every toll memorized and the cash ready to go. No fishing for wallets, spare change, screaming kids in the back, etc etc. Just hand the lady (or dude) in the toll booth some bills or exact change if I had it, get the receipt to claim the expense, and go.
Of course these days all the big trucks have an I-Pass or whatever it's called for Chicago. I think they were integrating it with some other toll systems out East when I moved on from that job. Was an interesting lifestyle, definitely had its perks, but just not the career for me.
Going way off on a tangent, I still wish I could give it another go one last time before truck drivers become a thing of the past, but these days I'm one of the people automating that career away for good. Kinda sad in a way, but this pays better and I've got obligations now, etc etc. You only get to be a free-wheeling 20-something once.