A statistical mechanics model for free-for-all airplane passenger boarding

TL;DR

This paper introduces a statistical mechanics model for free-for-all airplane passenger boarding, using principles like Boltzmann statistics to predict seat occupancy and compare with assigned seating models, offering industry and educational insights.

Contribution

It presents a novel physics-based model for passenger boarding dynamics, incorporating seat preferences and probabilistic seat selection, which has not been previously modeled in this way.

Findings

Predicts seat occupancy probabilities during boarding

Provides qualitative comparison with assigned seating models

Offers a pedagogical example of statistical mechanics applications

Abstract

I present and discuss a model for the free-for-all passenger boarding which is employed by some discount air carriers. The model is based on the principles of statistical mechanics where each seat in the aircraft has an associated energy which reflects the preferences of the population of air travelers. As each passenger enters the airplane they select their seats using Boltzmann statistics, proceed to that location, load their luggage, sit down, and the partition function seen by remaining passengers is modified to reflect this fact. I discuss the various model parameters and make qualitative comparisons of this passenger boarding model with models which involve assigned seats. This model can also be used to predict the probability that certain seats will be occupied at different times during the boarding process. These results may be of value to industry professionals as a useful description of this boarding method. However, it also has significant value as a pedagogical tool since it is a relatively unusual application of undergraduate level physics and it describes a situation with which many students and faculty may be familiar.