After hours of delay, your red-eye flight is finally boarding and your long-awaited nap is within reach.
But as the line grinds to a halt, you can't help but think, "There must be a faster way to board this plane." You are not alone.
Mathematicians have been studying this problem for years, devising a range of different boarding methods and testing them with computer simulations.
These models are designed to consider the two biggest plane-loading bottlenecks.
The first is seat interference, when someone in a seat closer to the window is blocked by people already in their row.
And the second is aisle interference, when passengers seated in the back of the plane are stalled by folks in earlier rows stowing their bags and settling in.
Different boarding methods try to tackle these problems in different ways, but the most commonly used approach is called back-to-front boarding.
It seems logical.
Board the back of the plane first, so passengers don't need to pass others to reach their seats.
And in simulations using a 156-passenger Airbus A320 where every person has a carry-on, back-to-front boarding takes around 23 minutes.
