Mon. Sep 26th, 2022
Physicists have shown that there really is an optimal boarding process for airplanes.
enlarge Physicists have shown that there really is an optimal boarding process for airplanes.

izusek/Getty Images

Commercial airlines often prioritize boarding for passengers traveling with small children, or for those who need extra assistance — in other words, those who are likely to be slower to pack their bags and take their seats — before boarding. boarding the faster passengers. It’s counterintuitive, but it turns out that boarding slower passengers actually results in a more efficient process and less time for takeoff, according to a new paper in Physical Review E.

Physicists have been puzzling over this specific optimization problem for years. While passengers have all reserved seats, they arrive at the gate in random order, and over the years airlines have tried all sorts of boarding strategies to make the process as efficient and timely as possible. Flight delays have a ripple effect on the complex interconnected network of air travel, often leading to additional costs and dissatisfied passengers.

In 2011, Jason Steffen, now a physicist at the University of Nevada, Las Vegas, became intrigued by the problem and applied the same optimization routine used to solve the famous traveler salesman problem for airline boarding strategies. Steffen fully expected that back-to-front entry would be the most efficient strategy and was surprised when his results showed that strategy was actually the least efficient. The most efficient, also known as the ‘Steffen method’, lets the passengers board in a series of waves. “Adjacent passengers in line will be seated two rows apart,” Steffen wrote in The Conversation in 2014. “The first passenger wave would be in order 30A, 28A, 26A, 24A, and so on, from the back.”

Field tests yielded the results, showing that Steffen’s method was almost twice as fast as stepping in backwards or rotating blocks of rows and 20-30 percent faster than random boarding. The key is parallelism, according to Steffen: the ideal scenario is more than one person sitting at a time. “The more parallel you can make the boarding process, the faster it will go,” he told Ars. “It’s not so much about structuring things as it is about finding the best way to get several people to sit at once.”

Illustration of the step-by-step advance of passenger queue during boarding (N=8 passengers).
enlarge Illustration of the step-by-step advance of passenger queue during boarding (N=8 passengers).

S. Erland et al./PR-E

Steffen used a standard agent-based particle model to represent individual agents. This latest study takes a different approach, modeling the onboarding process using Lorentzian geometry — the mathematical foundation of Einstein’s general theory of relativity. Co-author Sveinung Erland of Western Norway University and colleagues from Latvia and Israel took advantage of the known link between microscopic dynamics of interacting particles and macroscopic properties and applied it to the boarding process. In this case, the microscopic interacting particles are the passengers waiting in line to board, and the macroscopic property is how long it takes all passengers to sit in their assigned seats.

“A passenger’s ability to slow down other passengers depends on their queue positions and driving designations,” the authors wrote. “This is consistent with the causal relationship between two events in space-time, whereas two passengers are separated in time if one blocks the other and space as if they could both sit at the same time.”

Erland et al† treated the onboarding process as an iterative two-step process. The passengers move until they either reach their assigned rows or are blocked by other passengers in the aisle, and the second step is how long passengers stand next to their designated rows to stow luggage and sit down.

The passengers form a one-dimensional line that fits into a matrix of seats. The researchers predicted passenger speed based on where each person stood in line, which row they sat in, and how long it took to clear the aisle. The model calculates whether passengers will eventually meet based on how far apart they are and how far they are in line. Sitting close together but standing far apart in line (a space-like separation) means there is no interference; being far apart, but close to each other (a time difference) is more likely to cause interference.

Top row: slow-boarding subdomains chart.  Bottom row: The corresponding subdomains for the fast-first policy.
enlarge Top row: slow-boarding subdomains chart. Bottom row: The corresponding subdomains for the fast-first policy.

S. Erland et al./PR-E

The researchers came up with another counterintuitive result: It’s actually 28 percent more efficient to let slower passengers board first. In addition, “This is a universal result,” the authors wrote, “valid for any combination of the parameters characterizing the problem.” Those parameters are the percentage of slow passengers, the ratio between the turnaround times of fast and slow passengers, and the density of passengers in the aisle.

Again, it comes down to maximizing parallelism. As the boarding progresses, those at the back of the slow group will still settle in as the first influx of fast people begins to board. For example, three or four fast people can be seated in the time it takes a single slow person in the back of the plane to sit down. In effect, if all fast people board first, parallelism is minimized: the last fast passenger is seated before the first slow passenger has settled in.

To illustrate, Steffen cites the well-known analogy of trying to put rocks and sand in a pot. Put the sand in it first and there won’t be much room left for the rocks. Put the bigger rocks in there first and you can then pour in a lot of sand to fill in all the gaps around the rocks. “That’s the lesson of this [latest] result,” Steffen said. “If you’re going to pour a bunch of passengers into a craft like this, and you’re dividing them into slow people versus fast people, it’s better to get the slow people out of the way first and then let the fast people go. trickle in.”

Of course, even the best models are a simplification of an actual on-boarding process, taking into account many other factors, including human behavior. First class and frequent flyer passengers are used to preferential boarding. In an era where more people don’t check in their luggage to avoid extra costs, competition for space above the luggage compartment can be fierce – and those who get in earlier are more likely to lose valuable luggage space. Nevertheless, such studies are useful, says Steffen. “It gives you a measurable outcome to consider in policy making,” he said. “And it’s counterintuitive information, which makes it even more valuable because it shows where your intuition could lead you astray.”

DOI: Physical Assessment E2020. 10.1103/PhysRevE.100.062313 (About DOIs).

By akfire1

Leave a Reply

Your email address will not be published.