The science of queuing: What robots can tell us about standing in line

​Why does standing still bring us out in sweats? Because queueing, says David Andrews, author of a new book on the psychology of waiting in line, draws on human instincts both base and complex. Here, he ponders the forces at work, from personal programming to corporate trickery.

Queue buster: research has found that by dividing a space into smaller measurable segments, our minds tell us that the wait is shorter (Getty)

A robot that stands in line is a commonplace of science fiction: Everyone knows that in the future nearly all aspects of people's jobs, homes, and lives will be outsourced to robots. You'll know you've arrived in the future when there's a robot in front of you at Starbucks, patiently waiting to place an order.

In fact, that particular robot was invented over 20 years ago, and his name is Xavier. He was constructed in 1995 by a team at the Robotics Institute at Carnegie Mellon University. Xavier is cylindrical, 2ft in diametre and stands about waist-high. He moves around on hidden wheels and sees through a pair of stereoscopic cameras mounted to his top. If R2D2 ever made love to a garbage disposal unit, their offspring might look a little like him. His creators call him a social robot, programmed to autonomously do a variety of “social” things. One of these tasks was standing in line at the coffee shop in the building where the Robotics Institute is located, where he would order a coffee.

When a person (or a robot) stands in line, she makes a series of decisions reacting to the environment around her, some not always entirely conscious. These decisions are not unlike the ones a computer program algorithmically makes by design: if A, then B. Scan the area. Is there more than one line? Then join what you perceive to be the shortest of them. Is the line too long? Then don't join it (a move researchers call balking). Is there a well-ordered line? Then line up. Is there a disorganised line? Then stand in such a position to the people in front of you that someone coming later will recognise that you are waiting. If you join a line, give enough personal space to the people around you, but not so much personal space that someone might cut in front of you. If someone looks you in the eye, then look down at your shoes. If the person in front of you steps forward, then you step forward too. If someone cuts in front of you, give him hell. If the wait takes too long (based on some internal calculation of cost versus reward), then you might even decide to step out of line (researchers call this reneging). Et cetera.

You might say each of us has been programmed to make these decisions, based on a murky combination of culture, individual circumstances, and personality. For a robot, all of these microdecisions must be made explicit; otherwise it won't know what to do. There are many challenges in training a robot to queue. How close does a robot stand in proximity to the people around it? How does a robot even recognise that a given group of people are forming a queue (not something always easy for humans to discern)? Or for that matter, how does a robot even recognise a human as such, to make sure it's not lining up behind, say, a lamp post?

Xavier, the queuing robot

Like a piece on a game board, Xavier takes the queue step-by-step, according to the algorithmic rules he was set up with. He goes into the situation knowing only a few things. He knows where the barista is (the “point of service”). He can recognise which people are in line, using a “person-detection algorithm” that also determines their body orientation (they are generally facing forward). He also knows the levels of personal space people standing in line expect, which both helps him determine which people are in line (and not just a random bystander), and tells him how close to stand next to the person in front of him. His creators determined American personal space by standing in line themselves, and testing for distances that made them uncomfortable, which they turned into an average for Xavier to follow.

To determine where the back of the line is, Xavier moves backward from the front, parallel to the line. He stops and takes a scan of the person at the head, who is ordering a coffee. Xavier moves back a space, takes another scan of the second person in line. Repeat. He does this until he makes a scan, and there's no person there. He has found the end of the line. He moves in. He continues to scan the people in front of him. If the person ahead of him steps forward, he does too. Repeat, until what he scans isn't the back of someone's legs, but the flat smooth service counter. He puts the coffee on his tab, thanks the barista, and returns the coffee to the person who ordered it.

Xavier correctly stood in line 70 per cent of the time. Occasionally he got the shape of the line wrong, standing behind someone who was only line-adjacent. He could handle a slightly curved line, but if the line bent too sharply, he got lost. Sometimes something about a person's haircut (up-dos in particular) caused him to miscalculate personal space. He was decidedly slow to assess the situation, having to stop and scan each time before deciding the next step. But overall, not bad. His creators were pleased to note that several people got in line behind Xavier, which they cited as “anecdotal evidence that Xavier is considered, in some sense, to be a social member of the community”.

The experiment with Xavier not only represents progress in the field of “social” robotics, but by comparing his own relatively simple decision-making process to our own, we see how complex ours really is. Of course, Xavier was lucky to queue in a social space where lines are short and generally easy to read, and even then he made it through only 70 per cent of the time. In real life, we are constantly encountering situations where order isn't so neatly determined. When Xavier encountered a queuing situation that was not addressed explicitly in his program, he stalled. When humans encounter a queuing situation outside our personal and cultural expectations, we become dumb and anxious. In extreme cases, sometimes we stall too.

As far as social conventions like line-standing go, humans aspire to (and often fall short of) the condition of robot. Call this the principle of mental energy conservation: we want to expend only as little brainpower as is necessary to live. Thinking burns calories. Our bodies tell us to conserve calories. If given the choice, I believe most people would choose the tightly regulated line with well-defined boundaries over the looser slightly disorganised one, because constantly looking over your shoulder to ensure your place requires thinking, however marginal the threat. In addition, the vast majority of people don't try to cut in line because that would simply require more work (the time it takes to poach a spot, the possibility that one might get into an altercation, and the need to create an alibi for why you need to cut in line all sound exhausting to me).

This, at least, is the conclusion Stanley Milgram came to in the 1980s, when he conducted a pair of experiments in which he and a group of his graduate students went through crowded New York City subway cars asking strangers to give up their seats. Later, he sent the same students out to cut in line at ticket counters. In both cases, they gave no reason for their intrusion. The findings surprised Milgram. First, people actually were willing to give up their seats about 50 per cent of the time. Around the same percentage put up no protest when the graduate students cut in line, but when people did put up a stink, they put up a more visible stink. But half the time? No response. But what was almost more interesting was the personal effect the exercise had on Milgram and his graduate students: they all found the experience to be utterly exhausting emotionally. They were anxious, sweaty, embarrassed. Milgram characterised the experience as “wrenching”.

What it comes down to, Milgram argued, is social cost. When a certain practice becomes a social convention, you must do more work to explain why you get to flout it. When a high enough percentage of people within a community recognise first come, first served as the social norm, and you don't want to stand in line, you have the burden of proof in convincing them you deserve to cut in. If there's a compelling reason why you would expend so much energy, perhaps due to an emergency, people will indeed often give way. If it's not an emergency, be willing to defend yourself. And then you might simply be sent to the back of the line, and your little misadventure has cost you that much more time.

Meanwhile, roughly half the people whom Milgram and his students cut in front of didn't say a word. Milgram believed that this also has to do with cost. The first person to be cut in front of is the most likely to complain, partly because he would have the clearest view of the incursion, and partly because he has the most to lose, at least in terms of percentage of his time. (For instance, if there are 10 people in line, and the line-cutter cuts in front of everyone, the extra cost in terms of time for the person immediately after the line-cutter doubles, but for the tenth person in line, the cost increases by only 10 per cent.) But it also costs him least to protest, because he doesn't need to step out of line to do so. At the same time, he might wonder whether it's worth complaining, when he's nearly at the front of the line himself. And say you are several people behind the line-cutter. To protest, you have to get out of line to say something to him. To do so, you risk your own place in line. If enough people protest, the line wavers and threatens to dissolve. Milgram viewed this ability of line-standers to tolerate line-cutters as part of the health and stability of the queue: it can withstand incursions, because “a system's resilience depends not only on its capacity to defend against disturbances, but also its capacity to ignore, adjust to, and tolerate them”.

Queues in a modern economy are inevitable, but they have the power to significantly sour a customer's attitude toward a place. There's a certain coffee shop and bakery in my neighbourhood that's a lovely place to hang out, but I increasingly refuse to go there because to do so is always a gamble. The cramped, crowded wait takes as much as 10 minutes sometimes. “But all I want is a simple black coffee!” I want to cry from the back of the line.

But is the line at my coffee shop really 10 minutes? I've never actually timed my ordeal, but it certainly feels like 10 minutes. And according to David Maister, a well-regarded business management consultant and professor at the Harvard Business School, that's what's important to customers. People are not great at thinking objectively about the passage of time when they are in captivity. Time is subjective, and we perceive it to be moving more slowly when we're standing still. A company can make the time seem to pass more slowly or more quickly. Why fix the problem, Maister argues, when you can fix the perception of the problem?

The trick is either to distract the customer from the fact that she is waiting or to adopt a series of tactics that make her feel more in control of her own circumstance. For instance, there is something particularly agonising about being put on hold on the phone. In most situations, you neither know how long your wait will last, nor can you come to a rough guesstimate based on a visual scan of the number of people in line. On the phone, you are blind. You could be the next caller, or you could be the 100th caller. You feel trapped. The wait takes an eternity as a result. In his tract, Maister proposed theories concerning the psychology of line-standers, and in the last decade or so, you can begin to see some of them in action. Lately I've noticed that telephone queues often feature a callback option, in which the company calls you when the queue has subsided. Sometimes a human voice will periodically punctuate the smooth jazz coming out of your headset: “There are two callers ahead of you,” she says.

Dr Richard Larson, a professor of operations research at MIT and probably the world's foremost authority on the subject of queuing – he calls himself Dr Queue – gives examples of even simpler fixes. Ever notice that there's almost always a mirror next to the elevator you're waiting for? Thank some genius working in an early Manhattan skyscraper for that. When management began getting complaints about how slow their elevators were, they couldn't exactly tear out their elevators and begin again. Instead, after some experimentation, they settled on mirrors: people could spend time fixing their hair. Another: there's a reason you have to walk through a maze of velvet ropes to get to the teller at some banks. Someone discovered that by dividing a space into smaller measurable segments, our minds tell us that the wait is shorter. We mentally break up our wait into manageable chunks. We're less reminded of how long our wait is than when we see a long uninterrupted straight line down the street.

These are fairly simple tricks of perception, and you the customer are fooled by them (and other techniques like them) on a daily basis. Best of all? Tactics that free us from waiting in a visible line at all. Consider this one of the benefits of living in a consumer-driven economy: in the 30 or so years since David Maister and Dr Queue published their findings, companies have taken the hint. New technologies are coming out every day to help measure, alleviate, streamline, and if possible eradicate the phenomenon of the physical queue. “Queue management” companies with names like Emerge Queue, Nemo-Q, QLess, Q-nomy, Q-net, Q-matic (I could go on) offer solutions that not only promise greater efficiency for the companies that use their products, but also offer the illusion that there isn't even a line. People-counting sensors, coupled with predictive algorithms, help stores know how many people will be rushing to check out at the same time. There are self-service kiosks at the movie theatre, in airports, in casinos. At the university bookstore, a smartphone app keeps a student actively informed about his place in line, while he continues to browse the book rack. When it's his turn, he gets a text message. If he's a no-show, the system quickly sends the same message to the next person in the virtual line. And who doesn't simply pay their bills online any more? One day we might look back at the queue and determine that it was a particularly 20th-century phenomenon.

The illusion that we are trapped in line is increasingly being replaced by the illusion that we aren't. Technically, people are in line as much as they ever were, but the lines are becoming invisible, virtual. But because we can't see them, who's going to complain? Fix the perception, fix the problem. There may never be a physical line-standing robot brought to market, but make no mistake: machines are taking over the act of line-standing. Xavier, my saviour! In this one area of life, at least, I welcome the coming robot takeover.

'Why Does the Other Line Always Move Faster?' by David Andrews (£9.99, Workman) is out now