“One line to rule them all”?

Jane Galt writes:

Everyone knows the unified queue is the best way to move checkout traffic. So how come every time customers in a crowded drugstore try to form a single queue, the cashiers force us to line up at the registers? Do they get some kind of psychic job from knowing in advance which customer they’ll check out?

You might try to argue that the indirect utility function is convex (risk-loving) in prices, and that people, when they realize that their personal line-choice algorithms result in shorter (longer) waits, make more (fewer) trips to the store.  Samuelson once proved a theorem about that in the QJE.  The intuition is that consumers can take advantage of price variability, in this case "time price" variability, and come out ahead.  Admittedly the notion of "going to the store more often when your innate line-choosing algorithm turns out to be good" requires a mental stretch.

People also might like knowing that the end to waiting is in sight.  On the phone they put you on hold and tell you the expected wait time, or they should.  At least five times in my life I’ve bolted a supermarket and abandoned the groceries, simply because the lines appeared too long.  It is harder to estimate how long a single line will take, and it is harder to compare single lines across supermarkets.

And might there be "line price discrimination"?  Hurried people like me can scout out the best lines (don’t you have visual algorithms for speedy cashiers?…young girls are best), whereas the conversation-starved, check-writing old ladies might even prefer a slower line.

There are thousands of papers on queuing theory, but I’ve never seen a good study of when single lines are to be preferred.  How sad indeed is my profession…


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