Saturday, 21 January 2012

Just hurry up and sit down!

As a semi frequent flyer, and incredibly impatient stand-behinderer I couldn't resist linking to this - Time needed to board an airplane: A power law and the structure behind it from a Norwegian group, Vidar Frette and Per Hemmer.

Boarding strategy is of great importance to airlines, where the turn around time of planes – especially short haul – can make a real dent in profits. For the authors of this paper, however, it seems they just think it's a neat model to test out 1D problems where the particles are distinguishable, rather than the more common indistinguishable particles. In a traffic model the cars are usually identical, whereas here the passengers have a specific seat booking. Statistically this makes a difference.

Of course many people do look at specific strategies. For example here, it seems that it's difficult to think up a strategy that beats random loading. One would think that loading back-to-front would be better but this is not the case. A quick google search finds this nice page from Menkes van den Briel. There you can see videos of all the different strategies.

Unfortunately the best strategy seems to involve seating people in order of window/middle/aisle. Not great if you're sitting next to your kids.

All of which did remind me that it is much quicker boarding when you don't have seat bookings. When I fly to England using a certain orange-themed airline, that doesn't book seats, there's an initial mêlée followed by reasonably rapid sitting down. On a certain royal blue-themed airline it takes forever for a plane half the size to get sat down.

My suggestion is that I should be allowed to starting poking, with increasing frequency and verbal abuse, anyone that I deem to be taking too long to put their bag away.


  1. Dear Douglas
    Unfortunately the paper you refer to is completely wrong. The authors discuss a classical mathematical problem known as the increasing subsequence problem or Ulam's problem. There are plenty of survey paper which give the correct result, by Aldous and diaconis, by Deft and by Stanly among many others. The Norwegian team is way off, actually way way off. At a macroscopic level airplane boarding is related to relativity theory (described by Lorentzian geometry), while at a microscopic (second order corrections) level its related to the Kardar-Parisi-Zhang universality class, with another unexplored regime after a certain phase transition. Please see my JPA paper for a few more details.

    eitan bachmat

  2. Hi Eitan, thanks for the info. I must admit I wasn't aware that this was such a rich problem. For anyone interested I think this is the JPA you mentioned.