Let the fast passengers wait: Boarding an airplane takes shorter time when passengers with the most bin luggage enter first

Airlines usually organize the passenger queue by letting certain groups of passengers enter the airplane in a specific order. The total boarding time of such airplane boarding policies can be estimated and compared by a Lorentzian metric based on the one used in Einstein’s theory of relativity. The metric accounts for aisle-clearing times that depend on the passengers’ queue positions, in particular when passengers in the back of the queue with increasing probability will have to wait for already seated aisle or middle seat passengers to rise up and let the others pass to a seat closer to the window. We provide closed-form expressions for the asymptotic total boarding time when the number of passengers is large, and prove that the best queue ordering with low congestion is according to decreasing luggage-handling time. The effect of seat interference amplifies the previously shown superiority of slow first vs. random boarding and fast first. That this ranking of policies also holds for realistic congestion is illustrated by both analytical methods and simulations, and parameters are taken from empirical data. However, the result is non-trivial, as the ranking shifts for unrealistically high congestion. Based on the analytical results, we demonstrate that the slow-first policy can be improved by dividing the passengers into more than two groups based on their number of bin luggage items, and let the slowest groups with the most luggage items enter the queue first.