Analytical models preceded viable simulation tools by
about 20 years. In a landmark paper, Blumstein (1959)
defined the capacity of a runway as the expected
number of movements (landings and takeoffs) that
can be performed per unit of time—typically one
hour—in the presence of continuous demand and
without violating air traffic control separation requirements.
He also presented a model for computing the
capacity of single runways used for arrivals only,
for departures only, and for strings of arrivals followed
by strings of departures. Subsequent generalizations
included the possibility of inserting departures
between successive arrivals, possibly by increasing
(“stretching”) the separation between arrivals
(Hockaday and Kanafani 1972) and the treatment of
some of the parameters of Blumstein’s (1959) models
as random variables, instead of constants (Odoni
1972).