October – 2004 ^November

We introduce a new discrete random process which models airplane boarding. The parameters for the process are related both to airplkane design {leg room, #passengers per row} and to airline boarding policies {"passengers from row 40 and above may now board"}. Given the parameters we construct a two dimensional space-time, i.e., a two dimensional domain {manifold with boundary and corners} and a Lorentzian metric on it. Quantities of operational interest such as total boarding time can be expressed naturally in terms of the geometry of the space-time.We use the geometry to study the effect of boarding policies and airplane design on boarding time.

We can use the same methods to study patience sorting, optimal scheduling of I/O to a disk drive, and certain growth processes from physics.

Joint work with D.Berend, L.Sapir and S.Skiena