Good point, well made. In reality, the situation in your example of a multi-line queue is not usually as dire as your example portrays, because the delayed people in queue #1 are likely to jump ship sometime after the other two queues. have cleared. Nonetheless, this queue-jumping behaviour confuses the circulation pattern and causes congestion in the vicinity of the tills, which itself slows down the throughput. There's no doubt that a single-file call-forward queue is more efficient for both the customers and the shop.

One point I didn't see made in the article: single-file queues are also a fair amount more space-efficient, which has value to retailer that is separate from the issue of throughput. This spatial opportunity cost is something that also needs to be considered when designing a queuing system.

I've seen subtle & sophisticated studies which do say that customers prefer multi-line queues to single-line queues, but I rarely see any that bring the other factors into play. Retailers really should base their decisions on the following formula:

average revenue per customer * (% improved customer throuhgput - % of customers you'll lose because of multi-line queues) + extra retail m^2 * average revenue per m^2

In most cases, you'll find that that the value of a single-line queue is a good deal greater than the value of a multi-line queue. So this is one of those cases where it's likely a good idea to not cater to customer preferences.

(I'll also note that single-line queues are much more common here in the UK than in the US; I've become quite accustomed to them and in fact dread multi-line queues and the inevitable idiots that I get stuck behind in them. It seems likely to me that a large part of the American aversion to them is simply a bias against the unfamiliar; this is likely to subside as they become more accustomed to it.)

The problem with your first example is that in real life the queues will rebalance. The two people behind the first guy won't just stand there for 10 minutes with the other two checkouts empty; they'll switch lines.

If they do that, they'll each wait for 3 minutes, giving the same distribution as in the single line.

Ah, you say, but what if other people have entered those lines already? Then you have to count their wait times too, which will be shorter in the three-line case than the one-line case.

Using one line doesn't reduce the mean wait time; it's always the number of people waiting divided by the throughput. What it reduces is the variance in wait times, making the system more fair.