Queuing and a slow shuffle through the boarding platform is often followed by the inevitable irritation of being stuck behind someone who can’t get their carry-on into the overhead compartment. Boarding a plane is always a test of people’s patience but now a new research paper has proven the most effective way to load passengers onto a plane, using maths.
This optimization issue has plagued airlines, with a few tactics employed including boarding from two different doors or creating boarding clusters by seating. These may have improved things slightly but haven’t really cracked the code of efficiency.
Now, researchers from Latvia and Israel have used Lorentzian Geometry to solve this issue.
The authors used the well-known connection between microscopic dynamics of interacting particles and macroscopic properties and applied it to the boarding process. With the microscopic interacting particles being the passengers waiting in line to board, and the macroscopic property is how long it takes all the passengers to settle into their assigned seats.
They looked at this issue as a two-step process. The first step being the passengers moving down the aisle to their seats and the second step being how long they stand next to it until they sit down.
The passengers form a one-dimensional line to fit into a matrix of seats in a two-dimensional space-time diagram. The researchers predicted passenger speed based on where each person was in line, which row they were seated in, and how long it took to clear the aisle. The model calculates whether passengers will eventually run into one another based on how far apart they are sitting and how far apart they are standing in line. Seated close together but standing far apart in line (a space-like separation) means there will be no interference; seated far apart, but standing close together (a time separation) is more likely to lead to interference.
The results showed that it was 28% more efficient to let slower passengers board first. This is because slower boarders would be just finished settling in as the first wave of fast boarders enters the plane. For example, a slower person from the end of the grouping who is seated at the back of the plane would finish getting settled in the time that three fast people from the next group have taken their seats.
While this may be proven the most efficient, it is possible that airplane norms, like priority boarding might make implementing such a plan unpopular.