Let’s say you and your roommate have a little side business baking rhubarb pies at home and selling them on a street corner. Folks love pie, and you’re having trouble keeping up with demand. But you can only invest so much money in the business. Where should you put your resources? Should you hire another baker? Buy another stove? Start your own rhubarb farm? You need to make a careful, data-based analysis of these options to figure out where the primary bottleneck is, and thus where you should concentrate your efforts.

Business school types have a word for this sort of analysis: operations. Operations determines how products get manufactured and how services get delivered. Improving operations can cut costs, making the things you buy cheaper. It can speed processes, getting those things to you more swiftly. It can eliminate waste, doing a favor to the environment. You can thank (or blame) operations for the manner in which you’re admitted into a hospital, screened at an airport, or served at a busy fast-food restaurant.



For the next few weeks, I will be exploring the world of operations management in a series for Slate. It is a world full of ingenuity, practicality, and even beauty. It draws on fields ranging from engineering and math to psychology and sociology. Simply put, operations is the science of making things run better. Once you start thinking like an operations geek, it can transform the way you think about everything, from your workplace to your commute to the way you make a PB&J.

One important and enduring corner of the operations world—the one we’ll be exploring today—is queuing theory. Queuing theory is the study of lines. All kinds of lines. The lines at supermarket checkouts, the lines at toll booths, the lines of people on hold waiting for someone, anyone, to pick up at the cable company’s 1-800 number.



MIT professor Dick Larson is perhaps America’s foremost scholar of queuing theory. (This distinction has earned him the Bond-villain-ish nickname “Dr. Queue.”) According to Larson, queuing theory got its start about 100 years ago in Denmark, necessitated by a booming new technology: the telephone.

If your phone connected only to one other phone, it wouldn’t be very useful. What made telephony so valuable and popular was the ability to connect to thousands upon thousands of other phones. But this required a hub-and-spoke network, with calls coming into a switchbox and then being routed on their merry ways.



Back in 1909, calls were routed by operators using switching equipment. To maximize profits, telephone companies needed to know how precisely many operators and switches were necessary to handle call volumes. Too few operators and switches, and the calls would stack up, annoying waiting customers. Too many, and the company would be wasting money on excess labor and equipment. A Dane named Agner Krarup Erlang was assigned to study the problem. The equations he devised, says Larson, still get used today in operations—any time a manager needs to calculate the probability that a queue will build up given a certain volume of tasks and a certain amount of task-accomplishing resources.

Corporate call centers these days tweak their algorithms to achieve similar but slightly more complicated goals. For instance, the highest paid service representatives at the call center are trained to handle very complex interactions with customers, while the lowest paid reps are qualified for only the most basic tasks. The call center attempts to optimize the distribution of incoming calls so that you’re sent to the lowest-paid rep who is still capable of addressing your complaint, freeing up the more expensive reps to solve the thornier problems. This is why you’re always being asked to describe your problem by punching numbers on the keyboard before you talk to a human being. Which in itself raises another operations challenge: how to get maximum information from the caller without ticking her off so much that she hangs up the phone in anger after her seventh keypad touch.



Though queuing math hasn’t changed a ton since 1909, this kind of queuing psychology has. According to Larson, since the mid-20th century, queuing theory has been more about feelings than formulas. For example: Midcentury New York featured a rush-hour crisis—not out on the roads, but inside office tower lobbies. There weren’t enough elevators to handle the peak crowds. Complaints were mounting. “One solution would have been to dynamite the buildings and build more elevator shafts,” says Larson. “But someone figured out the real problem isn’t just the duration of a delay. It’s how you experience that duration.” Some buildings installed floor-to-ceiling mirrors near the elevators and, entertained by their own reflections and by the flirting that sometimes ensued, people stopped complaining quite as much about the wait time.

There are three givens of human nature that queuing psychologists must address: 1) We get bored when we wait in line. 2) We really hate it when we expect a short wait and then get a long one. 3) We really, really hate it when someone shows up after us but gets served before us.



The boredom issue has been tackled in myriad ways—from the mirrors next to elevator banks to the TVs in dentist’s waiting rooms. Larson mentions a clever solution from the Manhattan Savings Bank, which once hired a concert pianist to play in its lobby as customers waited for tellers. “But Disney has been the absolute master of this aspect of queue psychology,” says Larson. “You might wait 45 minutes for an 8-minute ride at Disney World. But they’ll make you feel like the ride has started while you’re still on line. They build excitement and provide all kinds of diversions in the queue channel.” Video screens tease the thrills ahead, and a series of varied chambers that the queue moves through creates a sense of progress. Another solution: those buzzing pagers that restaurants in malls sometimes give you while you’re waiting for a table. Instead of focusing on the misery of the wait, you can go off and entertain yourself—secure in the knowledge that you’ll be alerted when it’s your turn.

How to play the expectations game? Studies show that we’re much more patient when we’re given an idea of how long we’ll be waiting, instead of wondering whether it will be three minutes or three hours. So, for example, some New York City subway platforms now feature digital displays featuring estimated arrival times for the next few trains. But again, Disney is the master. It posts estimated wait times next to various spots in its long queues—but, according to Larson, it pads the times so you always get to the head of the line more quickly than you’d expected: “You think, ‘We’re 10 minutes ahead of schedule!’ and so you’re happy.”



Perhaps the most emotional issue in the world of queuing is the human quest for fairness. “When we see people arrive after us and get served before us we get very angry,” says Larson. “We can remember it for days, sometimes. And there have been incidents of ‘queue rage.’ People have drawn knives and guns.”

Sometimes we will make exceptions. We seem to be OK with the idea of an express lane at the supermarket—someone buying one roll of paper towels shouldn’t be forced to wait behind someone buying a full cart of groceries. We also allow for differing priorities at an ER, with more critical cases being admitted first even if they showed up last.



But in most situations, we demand social fairness. No one is more important than anyone else, and everyone should be served in the order he or she arrived. No doubt you’ve experienced mild queue rage when you choose the wrong line at a fast food counter or a drug store, watching people in the other lines zoom ahead of you.

To solve this problem, some genius (Wendy’s, American Airlines, and Citibank are among the companies that claim to be originators) invented the serpentine line. The serpentine line funnels all customers into one big snaking queue, demarcated by ropes or barriers. When you reach the head of the queue, you are directed to the next available server, or teller, or customs official. The serpentine line isn’t always faster than a simple scrum before an array of cash registers. But it offers important solace: You absolutely never have to see someone arrive after you and get served before you.



Larson says he was once at a queuing theory conference where the hotel checkout line became quite long and was populated mainly by queuing theorists. “We insisted on forming our own serpentine line,” he says. “The lobby wasn’t designed for it and it looked extremely messy. The hotel manager was unhappy. If we’d just dispersed into six parallel lines at the checkout desk the wait might have been shorter and less chaotic. But it would have been less fair.”