Columnist Lawrie McFarlane on the mathematics of checkout queues

I f you believe statisticians, adults spend an average of five to six hours a month waiting in queues, most often in supermarkets. A small but aggravating factor in this misery is the sheer mutton-headed behaviour of certain individuals.

You know the sort of thing. A customer in front of you who’s apparently outfitting a trip to Nepal is finally presented with a bill. Only then does she start rummaging in her handbag for money. Now look, you’ve just bought half the store. You must have known they were going to want payment.

Then there’s the person who rushes off in search of a forgotten item even as the teller is bagging things up. Or the joker who misleads you into joining his line because he has a mere handful of purchases, then spends 20 minutes negotiating with the clerk over gambling pull-tabs.

Or the visitor from another planet who insists a certain item is 20 cents off, and holds up the entire line while a geographically challenged employee sets out to find the Franklin expedition.

Now, you might say, this is just one of the inevitable irritants of life. Yet there is a fluky branch of science called queueing theory that disputes this pessimistic view.

Basically, it turns out that the length of time you wait in a lineup is affected by factors that, on the face of it, appear hugely disproportionate to their impact. An example: The local muffler store has only one bay. If two cars arrive per hour, the average wait time is 40 minutes.

Now, double the number of bays, and you might expect the wait time to drop by half — i.e. 20 minutes. But it doesn’t. Instead, the average wait time falls to just 2.5 minutes.

That’s one reason why, although there might be huge lineups at a store when you arrive, they often disappear before you leave. The store merely had to open one additional checkout to shorten the queues dramatically.

A second factor also plays a role. Say your supermarket has three checkout points, and customers form lines behind each. It turns out this is hugely inefficient.

Better, by far, to have just one lineup. You see this system in banks, where customers form a single queue and proceed, in order, to whichever teller comes open next.

It seems implausible. If you have the same number of checkouts, and the same number of customers, why should it matter how many lines there are?

But it does. A single queue served by three tellers will move roughly three times as fast as three queues.

The reason is that with multiple lanes, a really slow customer will hold up everyone to the rear. With just one queue, the time our slow customer wastes is spread evenly among all the shoppers. On average, they move faster.

Unfortunately, most stores are leery about adopting this method, because they fear, correctly, that customers will shy away from long, snaking lineups. But what our lying eyes tell us, and what is true, are two different things.

Take the idea, for example, that you shouldn’t join a lineup where a customer ahead of you has a packed cart. In fact, what you should avoid is a lineup with multiple customers, even if each has only a small basket of purchases.

That’s because what really holds things up is the amount of time people spend finding their credit card, fiddling with the machine, screwing up their password, chatting to the clerk, etc. It’s the number of transactions, not the volume of goods, that determines wait times.

Can anything be done? I doubt it. The impossible we do right away. The deeply counterintuitive we never do at all.

Shoppers line up with their purchases at a U.S. department store. Standing behind shoppers carrying small amounts of goods might not be the fastest way to get through the checkout.