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Long, leg-aching, frustrating lines.

There’s a mental game you play when deciding whether to join one, or which to select if there’s a choice. Standing in a slow-moving line, you weigh various factors before switching or leaving.

“Sometimes it’s a rational decision; sometimes it’s a spontaneous one,” said Dick Larson, a Massachusetts Institute of Technology specialist in operations research, a discipline that uses math to address real-world puzzles, such as the issues that arise from waiting in line.

Within seconds, you may ask: How long have I been standing here? How many people are in front of me? Behind me? How badly do I need what I’m waiting for? Can I afford to spend the time?

Serious line-waiters spend the night in single file for concert or playoff tickets or to be among the first to relish a Harry Potter book, “Star Wars” movie or Xbox 360 game system. Those paying final tribute to President Reagan and Rosa Parks in Washington filed in lines that wound far from the U.S. Capitol where their caskets lay.

“We wait, because we know at the end of the line there is some value for us,” said Gad Allon, professor of managerial economics and decision sciences at Northwestern University. “The more valuable the service at the end, the more you will be willing to stand in line, the more tolerable it will be.”

Maybe it’s a table at the hottest restaurant in town. Perhaps it’s the promise of big savings.

Duane Powell, 42, of Gaithersburg, Md., showed up at 3:30 a.m. at his local Kohl’s department store the day after Thanksgiving to catch early-bird specials and avoid checkout lines.

“I had to be first. … I’m not one to stand in line,” said Powell, waiting with several dozen pre-dawn shoppers who squeezed between the two sets of entry doors, seeking warmth from temperatures in the low 20s. When the store opened at 5 a.m., Powell was off, gliding swiftly through the store, selecting his merchandise. He was first at the cashiers and first out the door, at 5:05.

Those who shop before sunrise the day after Thanksgiving, while most people are still sleeping off turkey and pumpkin pie, share an experience akin to the classic concert campout.

“Sometimes a queue is a social event,” MIT’s Larson said. “It’s really cool to camp out overnight with other people who love the Rolling Stones” or who share the same affinity for the object of desire.

The line becomes part of the outing, like clamoring to get inside an exclusive dance club.

“You understand that the waiting brings more value to your entire experience,” Allon said.

But when a line is just a means to an end, businesses strive to ease the wait.

The Walt Disney Co. theme parks, researchers say, have mastered managing lines, with signs alerting visitors to wait times and television screens flashing scenes connected to the attractions. The parks keep guests informed and transform lines into introductions to the rides and shows.

It’s the art of distraction.

High-rise buildings place full-length mirrors in elevator lobbies to keep passengers busy straightening their ties or checking their hair, in effect minimizing delay. Restaurants suggest drinks in the bar during a wait to soften the downtime while boosting sales.

Management gives thought to the look and flow of lines.

“Pooling many lines to a single line – also known as forming a snake – not only decreases waiting time but also makes the line deplete faster than having multiple individual lines,” said Hyun-Soo Ahn, assistant professor of operations and management science at the University of Michigan in Ann Arbor. “It also looks fairer in the eyes of consumers, since it is first come, first served.”

But, even though such lines tend to move faster, “the sheer sight of a long, winding line may scare some customers,” Ahn said.

For all the research, a customer’s choice of line can rest on whim.

Joe Phoenix, 44, of Minneapolis, prefers “a pretty girl’s line.”

“At the grocery store I will try to find a queue that has few people in it but will avoid that line if I know the cashier to be unfriendly or ugly,” he said. “So for me it’s about the time crunch and the competence and attractiveness of the clerk.”

Time remains a top factor for many consumers.

“The value of one’s time is the key,” said Jim Cox, associate professor of economics and political science at Georgia Perimeter College in Lawrenceville. “Higher earners, busier people will tend to make other arrangements, whereas lower earners, un-busy people and those who just plain enjoy the experience … will do the waiting.”

Lisa Watson of Washougal, Wash., waits in line for other people. This year, she and her mom, Kathie Wardlaw, started a business called The Domestic Divas, which includes errands services in the Portland, Ore./Vancouver, Wash., area. They’ll pick up dry cleaning, prescriptions and groceries.

Watson said their clients include the “uber-goober rich” who “don’t have to wait in line for anything,” busy parents, and older adults unable to drive to the stores. “When you’re getting paid $25 an hour for (standing in line), it takes all the frustration out of it, wanting to shoot the person in front of you,” she said.

Some consumers opt to do business online to save time. Some adjust their schedules to visit notoriously busy venues during non-peak hours. Some just try to stay positive.

“I’m a patient person,” said Michelle Dean, 35, of Olney, Md. When she’s in a particularly slugglish line, she’ll “take a deep breath” and think, “At least I’m in line. It’ll be over soon.”

Michele M. Melendez can be contacted at [email protected].

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