Synopsis: Now Boarding All Rows

Time needed to board an airplane: A power law and the structure behind it

Vidar Frette and Per C. Hemmer

Published January 19, 2012

The next time you are getting ready to board an airplane you might want to time how long it takes to get to your seat. Two Norwegian researchers, reporting in Physical Review E, have calculated how the average boarding time depends on the number of passengers. Their results call into question the practice of dividing passengers into groups that board separately.

For many airlines, passengers have specific seat assignments, which drastically increases the number of initial configurations modelers have to consider. Scientists have typically turned to computer simulations in order to study the dynamics of airplane boarding, but these analyses do not explicitly show how the parameters are related.

Vidar Frette of Stord/Haugesund College and Per Hemmer of the Norwegian University of Science and Technology have calculated the boarding time analytically in terms of the passenger count. Their simple model assumes that each row on the airplane has only one seat, and passengers file in randomly. When someone reaches his or her seat, everyone in the aisle behind has to wait while this passenger gets settled.

Naively, boarding time should vary linearly with the number of passengers, such that twice the passenger count should take twice the time. However, more passengers increases the chance that some people will fortuitously line up in a time-saving order. Frette and Hemmer’s calculations show that twice the passengers only takes $1.6$ times longer. This suggests that letting, for example, rows $16$ through $30$ go before rows $1$ through $15$ may prolong boarding times. – Michael Schirber