00:00 25-04-2006

We analyse airplane boarding times. We attach to the boarding process a Lorentzian metric defined on the unit square which depends on parameters of the boarding process such as airline boarding policy, dis- tance between rows, number of passengers per row and average aisle length occupied by passenger. The asymptotics of the boarding process (as the numbers of passengers tends to infinity) are described by the geometry of the resulting space-time. In particular, the total boarding time is given (up to a normalisation) by the length (proper time) of the maximal curve. The model describes the asymptotics for an infinite number of passengers while realistic numbers are 100-200 passengers per aisle. The discrepancy between the infinite and finite population calcu- lations is closely related to the Tracy-Widom distributions for GUE and GOE when passengers are very thin. At some point there is a phase trans- ition into a new regime. When passengers become a bit thicker there is another transition in which previously good airline policies become bad and vice versa. As it turns out, airline policies are implicitly desig- ned for cardboard thin passengers while actual passengers are on the other side of the phase transition. (Joint work with D. Berend and L. Sapir of BGU and S. Skiena of SUNY at Stony Brook)

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