Dear Mona,

Is the express lane in the grocery store always the fastest lane?

Barry, 44, New York

Dear Barry,

We’ve all been there. While grasping a stack of toilet paper and a carton of milk in the grocery store’s express lane, you glance to your right and see that other customers with cart-loads of produce are seamlessly drifting forward in their appealingly shorter lines. You start to contemplate whether you should stay put, switch lanes or just head home empty-handed to face dry cereal and your wet bum.

I couldn’t find much research on express lanes specifically, but one paper from Amsterdam found the reduction in wait times for express-lane customers didn’t offset the overall increase in wait times for everyone. Maybe life would be easier if the supermarket didn’t have an express lane — or, better yet, if it got rid of multiple lines altogether and had all customers join a single infinitely sprawling line where there were no winners and losers. That might sound nightmarish, but the math actually suggests it would be anything but.

That math comes from queuing theory, a subject of study that’s been around ever since Danish mathematician Agner Krarup Erlang discovered a method for managing telephone traffic in 1909. To answer your question, I’ve had to take a crash course in (more modern) queuing theory, including examining formulae that calculate how average wait times at the grocery store vary depending on the type of line you join.

There are several types of lines we could consider — textbooks classify queues according to how many servers there are, whether a customer is only served once (like at the dentist) or in multiple phases (like at a drive-through), as well as whether she gets to choose which line she joins. Since you’re interested in your grocery store, where there are almost certainly several servers and one phase of service, I’m going to focus on that last distinction: Are single lines better than multiple lines?

But to make that comparison, I’d need to know things like the number of cashiers at your grocery store, the number of items customers have in their carts and the amount of time it takes to serve each of them. There isn’t any national data we can plug in to the formula to give us answers — the numbers vary considerably by store and even within a store, and will change on a weekly, daily and hourly basis. One alternative, then, is to run a simulation — pretend that 10,000 hypothetical people are waiting in your hypothetical store and see how their wait times vary.

That’s what Wes Stevenson, a professional data analyst, did out of sheer curiosity. To test the difference between single and multiple lines, Stevenson quantified a few assumptions (10 cashiers, an average wait time of 3 minutes) and put them into his model to see what it would spit out.

He found that the wait time in single lines is more predictable (you can see that in the chart below, where there’s a narrower spread of outcomes). More importantly, though, Stevenson found that a single line is more likely to mean a shorter wait (also visible below, where the single-line chart clusters farther left than the multiple-line one, meaning that more of those 10,000 simulations produced a shorter wait time). In that respect, Stevenson’s finding concurred with well established queueing theory: One line is better than many.

“But wait a minute!” I (sort of) hear you cry, Barry. “If single lines reduce wait times by so much, why do grocery stores across the country have us queueing in separate lines for each cashier? And presumably the 830,750 Americans who work as cashiers in grocery stores would also benefit from having to deal with fewer pissed-off customers?”

One reason is that models like these overestimate the difference between single and multiple lines because they don’t take into account some human behaviors. Maybe you know your grocery store pretty well, Barry. Maybe you know who the fastest cashier is and which register has the drawers that always get stuck; maybe you can even spot that customer that always spends an age rummaging around for his wallet — and you pick your lane accordingly. Aside from careful queue selection, you might also switch lanes (known as “jockeying” in the queueing theory textbooks) or simply ditch your items and leave (“reneging”). Those behaviors, from you and other customers, reduce the average wait time in a multiple-line queueing system and bring it a little closer to a single-line system.

To be fair though, if the models underestimate human intelligence, they also fail to factor in just how mistaken we can be.

For one thing, our perceptions don’t always match up with reality, and that matters to the businesses that want us to be their customers. The longer we stand in line, the more the gap between perceived and actual wait time grows. By the time we’ve been in line for 5 minutes, we think we’ve been waiting for 10, according to Paco Underhill, who measured shoppers’ over-estimations for his book “Why We Buy: The Science Of Shopping.”

Unsurprisingly, longer perceived wait times means lower satisfaction. Or, to be more formulaic, perceptions feed into a simple equation written by David H. Maister from the Harvard Business School: S = P – E, where S = satisfaction, P = perceptions and E = expectations. One way then, Barry, to feel more satisfied with your grocery store experience (and your job, and your love life and just about anything) is to simply lower your expectations. I guess that probably doesn’t sound too appealing.

It’s not just perceived waiting times that show how we as customers don’t have perfect judgment. Imagine your reaction if your local grocery store did switch to a single line. You walk in after a long day at work, and rather than seeing 10 neat lanes with four or five customers in each, you’re now met with a winding line of dozens of bodies. It’s probably harder to gauge the rate at which the queue is moving ahead than its simple length. Maybe you’ll turn straight back the way you came. That U-turn is known as “balking” in queueing theory and, from a business perspective, it’s a store’s worst nightmare.

So, rather than simply shoving us all into one line, supermarkets are exploring a range of alternatives to reduce both our actual and perceived wait times. I spoke to Perry Kuklin, director of marketing at the queue-management consultancy Lavi Industries Inc., about the sorts of methods the firm suggests to its clients, who range from pharmacies to personnel services at U.S. army and naval bases.

Kuklin outlined three main strategies that Lavi’s clients are using to improve the queuing experience. First, customers waiting in line can have their items scanned by roaming tellers with hand-held machines, to reduce their service time once they finally reach the cashier. Second, customers can register their place in line, go away, and come back once it’s their turn. There’s nothing new about this latter strategy, really, it’s just that rather than grabbing a paper ticket from the deli counter and waiting for your number to be called, you might receive a text message saying you’re up next.

But it’s a third strategy that has really stood the test of time: distraction. “You can try to entertain customers with videos,” Kuklin said, “and in-line merchandising helps to keep them busy and distracted.” There are more cunning ways, too. After airline passengers wouldn’t stop complaining about the time they spent at baggage claim (even when more staff were added and wait times fell) a Houston airport simply moved the arrival gates so that passengers spent more of their “wait” time walking to the baggage claim. The complaints all but disappeared.

All of this shows that we who stand there desperate, tired and irritated are not perfect. But we’re also not perfectly imperfect. So, until your grocery store switches to a single-line system, my advice to you is: Be observant, and (if you don’t want to examine chewing gum and candy bars for a distraction while you’re waiting in line) take a book.

Hope the numbers help,

Mona

Have a question you would like answered here? Send it to dearmona@fivethirtyeight.com or @DataLab538.