  Airlines use different boarding policies to organize the queue of passengers
waiting to enter the airplane. We analyze three policies in the many-passenger
limit by a geometric representation of the queue position and row designation
of each passenger and apply a Lorentzian metric to calculate the total boarding
time. The boarding time is governed by the time each passenger needs to clear
the aisle, and the added time is determined by the aisle-clearing time
distribution through an effective aisle-clearing time parameter. The
non-organized queues under the common random boarding policy are characterized
by large effective aisle-clearing time. We show that, subject to a mathematical
assumption which we have verified by extensive numerical computations in all
realistic cases, the average total boarding time is always reduced when slow
passengers are separated from faster passengers and the slow group is allowed
to enter the airplane first. This is a universal result that holds for any
combination of the three main governing parameters: the ratio between effective
aisle-clearing times of the fast and the slow group, the fraction of slow
passenger, and the congestion of passengers in the aisle. Separation into
groups based on aisle-clearing time allows for more synchronized seating, but
the result is non-trivial, as the similar fast-first policy -- where the two
groups enter the airplane in reverse order -- is inferior to random boarding
for a range of parameter settings. The asymptotic results conform well with
discrete-event simulations with realistic number of passengers, and both the
slow-first and the fast-first policies have the ability to perform unboundedly
better than random boarding. Parameters based on empirical data, with hand
luggage as criteria for separating passengers into the slow group, give a 13\%
reduction in total boarding time for slow first compared to random boarding.
