Lorentzian geometry and variability reduction in airplane boarding: Slow passengers first outperforms random boarding.

Airlines use different boarding policies to organize the queue of passengers waiting to enter the airplane. We analyze three policies in the many-passenger limit by a geometric representation of the queue position and row designation of each passenger and apply a Lorentzian metric to calculate the total boarding time. The boarding time is governed by the time each passenger needs to clear the aisle, and the added time is determined by the aisle-clearing time distribution through an effective aisle-clearing time parameter.

Lorentzian-geometry-based analysis of airplane boarding policies highlights "slow passengers first" as better.

We study airplane boarding in the limit of a large number of passengers using geometric optics in a Lorentzian metric. The airplane boarding problem is naturally embedded in a (1+1)-dimensional space-time with a flat Lorentzian metric. The duration of the boarding process can be calculated based on a representation of the one-dimensional queue of passengers attempting to reach their seats in a two-dimensional space-time diagram.

Scaling behavior of an airplane-boarding model.

An airplane-boarding model, introduced earlier by Frette and Hemmer [Phys. Rev. E 85, 011130 (2012)], is studied with the aim of determining precisely its asymptotic power-law scaling behavior for a large number of passengers N.

Probabilistic description of traffic breakdowns.

We analyze the characteristic features of traffic breakdown. To describe this phenomenon we apply the probabilistic model regarding the jam emergence as the formation of a large car cluster on a highway. In these terms, the breakdown occurs through the formation of a certain critical nucleus in the metastable vehicle flow, which enables us to confine ourselves to one cluster model.