Abstract:

We show that airplane boarding is one of several discrete random processes, which can be asymptotically analyzed via 2 dimensional space-time (a.k.a Lorentzian) geometry. We use the geometry to study the effectiveness of airline boarding policies as implemented by announcements of the form "passengers from row 40 and above are now welcome to board the plane", often heard around airport terminals. We will show that the effectivness of such policies depends crucially on a parameter which is related to the interior design of the airplane (leg room, number of passengers per row). As the parameter increases the boarding policy experiences a phase transition in which it passes from being effective to being detrimental. Unfortunately we seem to be on the wrong side of the phase transition.

We will also explain briefly the relation between fluctuations in airplane boarding time and random matrix theory.

If time permits we will discuss other examples of discrete processes which can be modeled via Lorentzian geometry including scheduling of I/O requests to a simplified model of a disk drive and the polynuclear growth model which is a 1+1 dimensional surface growth model in the Kardar-Parisi-Zhang universality class.

No knowledge of space-time geometry is needed (the speaker himself hardly knows anything about it).

Joint work with Danny Berend, Luba Sapir and Steve Skiena.