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.
The simulations suggest that using something like the above protocol would reduce boarding time to 1/6th of that required by the standard procedure! Multiply the average number of passengers per plane trip by the approximate number of trips by the number of minutes saved per boarding, and the number of man hours saved would be more than considerable.
There must be faster, more rational ways to go through security, as well, but, alas, "Zone 4 is now boarding."
John Allen Paulos, a professor of mathematics at Temple University, is the author of the best-sellers "Innumeracy" and "A Mathematician Reads the Newspaper," as well as of the just-released "Irreligion: A Mathematician Explains Why The Arguments for God Just Don't Add Up." His "Who's Counting?" column on ABCNews.com appears the first weekend of every month.