John Allen Paulos shares The Optimal Way to Board Plane Passengers — according to Jason Steffen, an astrophysicist at Fermi Lab near Chicago, who has run a few simulations:
For simplicity, his model assumes a plane with 120 passengers seated in 40 rows, each with a central aisle having three seats to the left and three seats to the right of it. It also assumes that each of the 120 passengers has an assigned seat number and carry-on baggage and that they move forward if and only if no one is directly in front of them.So, given these reasonable assumptions, what’s the best way to board? It seems intuitive that the worst way is to load those passengers seated in the front of the plane first and then those a bit further back and so on. And this is, in fact, the worst way to board passengers.
So, it might seem almost as intuitive that the standard way — loading the back rows first and then gradually rows nearer the front — should be among the best ways to board, but Steffen’s simulations indicate that this is the second-slowest way. Even random boarding is faster.
After many simulations allowing for different sets of passenger quirks and luggage-stowing times, it turns out that the best method (one of several more or less equivalent methods) calls for passengers in even-numbered window seats near the back of the plane to board first.
Passengers hefting their carry-ons into the overhead compartments are less likely to get in each other’s way if there’s an empty row between them. Moreover, they can step into the empty row if someone seated further back needs to pass.
After these passengers have boarded, passengers in even-numbered window seats in the middle of the plane board, and they are followed by those in even-numbered window seats near the front of the plane. Next, the same procedure is followed for those in the even-numbered middle seats and then for those in the even-numbered aisle seats.
Finally, after the even-numbered passengers have boarded, the same procedure (window, middle, aisle from back to front) is followed for passengers in the odd-numbered seats. These passengers may not always have an empty row to step into, but they will still be separated from entering passengers by a row of already seated even-numbered passengers.
It appears that the reason the protocol is faster is that it allows multiple passengers to simultaneously stow their baggage, the most time-consuming component of the boarding process.
This and other similar schemes Steffen discusses may seem too complicated for passengers to master, but passengers needn’t remember the seating order algorithm. They can each be assigned a zone consistent with it and enter by zones, as they presently do.
The outcome is fairly robust in the sense that it’s relatively insensitive to deviations from it, say, because of couples or families being seated together.
Airlines should, of course, supplement these theoretical conclusions with empirical investigations.
I’m glad he included that last line.