A statistical mechanics model for free-for-all airplane passenger boarding Page: 3 of 18
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statistics. As the airplane fills, the partition function is updated to reflect the evolving state
of the aircraft cabin. Thus, the free-for-all boarding process can be studied as a sequence of
passenger decisions modeled by statistical mechanics considerations.
In addition to studying the boarding process we may study the outcome or final seating
arrangement of the aircraft for airplanes that are only partially filled (the seating arrange-
ments of full flights are trivial) or the seating arrangement at any time during the boarding
process. Instead of modeling the seat selection of each passenger during boarding, we deter-
mine the probability that a particular seat will be occupied by a passenger at the time of
interest by treating the passengers as a fermion gas.
The discussion proceeds as follows. I discuss in Sec. II the model of the airplane and the
statistical properties of the passengers. I then discuss the application of passenger model
to the boarding process, including how passengers move within the airplane. I discuss in
Sec. III the airplane boarding times given by the model and the effects of changes to the
model parameters (Sec. III A). Section III B gives a brief comparison of the results of this
model to the results of the assigned-seating model used in Ref. 4. Section IV discusses
the final states of a partially filled aircraft using Fermi-Dirac statistics to determine the
occupancy of the seats at the end of the boarding process (or at any instant during the
boarding process). Finally, I discuss the utility of this model for various classes of people
including students, educators, and airline executives.
II. DESCRIPTION OF MODEL
The airplane model and algorithm has three components: the geometry and characteris-
tics of the airplane, the movements of the passengers inside the airplane, and the decision-
making process of the passengers. The first two components are largely details and are less
important in terms of the behavior of the model. The third component is where statistical
mechanics plays its major role; the decisions of the typical passenger is modeled here.
A. Decisions, energy, and temperature
Each seat in the airplane is assigned an energy which characterizes how desirable a seat
appears to the average passenger. If a seat has a small energy or a large negative energy,3
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Steffen, Jason H. A statistical mechanics model for free-for-all airplane passenger boarding, article, August 1, 2008; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc897423/m1/3/: accessed April 22, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.