The Steffen Boarding Method
Boarding an airplane is no fun. Usually, it's done by airline status or back-to-front. In a wildly unprofitable industry where time is the major constraint – isn't there a quicker boarding method? A survey of queuing algorithms.
Front-to-back: This is essentially boarding the plane serially – the remainder of the plane is always empty while you wait for a few passengers to stow their luggage and find their seats.
Back-to-front: Back-to-front means that Mythbusters (2014) found that this is actually the slowest method other than front-to-back. People might have to get up to provide access to the window and aisle seats. Some are standing waiting for to other passengers to stow their luggage (for which there might not even be room).
Random ordering: Easiest to implement. Performs fairly well in all of these tests and simulations that I've read online. The fact that it does so well gives me hope that there's probably a much more optimal method.
Out-to-in: Board window seats first, then middle seats, and finally aisle seats.
Out-to-in (staggered): The Steffen method (2008) follows the out-to-in strategy but alternates between odd-numbered and even-numbered seats (e.g., window odd, window even, middle odd, middle even, etc.). Steffen used a Markov Chain Monte Carlo model to test different methods. The model assumes that stowing luggage is the major constraint in boarding.
Out-to-in, back-to-front: Also known as the reverse pyramid, this method was developed by some researchers at Arizona State University in 2006. You can read an article about it here.
Slow/Fast: This paper (Lorentzian-geometry-based analysis of airplane boarding policies, 2019) find that boarding slow passengers first is the most effective. They offer a categorization of "slow" passengers as those who require extra assistance (e.g., elderly or children) or those with overhead bin luggage.
Of course, there are other considerations with these boarding methods:
Temporarily splitting up families and passengers traveling together
Intentionally unfair – consideration for airline status
Fair distribution of overhead bin space (who gets it when it's limited?)
No incentive to optimize – weak market forces in a government-subsidized industry with enormous barriers to entry.
While queueing algorithms are fascinating (not as much as elevator algorithms), maybe there's an outside-of-the-box solution.
Boarding times increased as airlines increased prices for checked luggage. Fewer passengers bringing carry-on luggage means faster boarding times.
Different algorithms are currently enacted by seat block – it wasn't practical to call out specific passengers or seat numbers to board. Now, we have the technology to notify individual passengers via mobile. This could be used to increase the granularity of how the algorithms are used.
Would the flight crew be faster at stowing luggage than passengers? Can carry-on luggage be stowed ahead of time?
Assigned seats vs. unassigned seats (e.g., Southwest)