How to Eliminate Airplane Boarding Lines: Use Math

There’s nothing like the airport to remind us that, despite college degrees, fancy shoes, or six-figure incomes, we need to be handled like cattle in order for the system to flow smoothly. We queue to get your ticket, wait patiently in security lines, take off our shoes and belts, step slowly through the metal detectors, put ourselves back together, and trot to the gate, where we break off into separate herds and wait to file onto the plane. It’s only once we’re left to our own devices in the airplane aisle that the pushing and shoving begins and everything seems to fall apart. Thankfully, a group of mathematicians is working out the kinks in this last bit of pre-air travel.

If you think air travel is tough in the U.S., imagine what it’s in China, where the air transportation has taken off from about 10 million passengers in 1950 to 200 million passengers at last count in 2010. China’s growing passenger air travel industry is the case example for a recent study of how to guide people to their seats most efficiently. The study, authored by a group of researchers at Beihang University in Beijing, offers a new boarding model that quantifies “passengers’ individual properties,” such as age, luggage items, check-in times and other personal factors.

A quick bit of background on modern boarding procedures: The two most common methods of arranging passengers on an airplane are 1) assigned seating and boarding rank, and 2) random boarding in which everyone fends for themselves. Random boarding, the researchers say, is a disaster. People cut each other in line at the gate desk and while queuing for seats, and there’s more congestion in the aisles on the plane. Assigned seating is better, although less-than-optimal, because it allows only the first group of people on the plane to reach “maximum efficiency” and effectively jams up the majority of passengers that follow them on.

“Our numerical results illustrate that overtaking, queue-jumping, seat conflict congestions and james may occur under the first two boarding strategies, but these phenomena do not occur under the third boarding strategy,” the researchers write in the most recent edition of Transportation Research.

The Beijing researchers, led by Tie-Qiao Tang, say they’ve found a third method that’s a lot smoother. It’s based on pedestrian flow theory (some of which is based on studies of ant colonies), which is essentially a means of evaluating patterns of movement and analyzing correlations between people’s identities and their tendencies.

Tang explains it this way:

“Each passenger has their own individual properties. For example, each passenger’s luggage has a different attribution and thus has different influences on boarding behaviour; the time that the passenger’s ticket is checked at the gate is different; the time that the passenger deals with his or her carried luggage is different; seat conflicts have different effects on the passenger. Each passenger has a different optimal speed, maximum speed and safe distance.”

The best way to line people up for a plane is to assign seat numbers based on an algorithmic analysis of their optimal speeds as they check in at the ticket counter, the researchers say. It’s hard to know exactly how this would manifest because not a single airline today uses this third method, Tang says.

The article builds on Tang’s research into how highway on- and off-ramps exacerbate stop-and-go traffic and “might destroy the stability of the main road traffic flow.” But while traffic will always remain ridiculously complex, hopefully his work will pay off with a little less brawling over the overhead bins.