OPTIMUM LANDING ORDER OF PLANES

The report considers optimization of landing order with respect to runway acceptance rate and total delay for planes desiring to land at the same one-runway airport.Two cases determined by the character of the mirvinniTn landing separation are recognized: (a) constant landing separa tion time and (b) variable landing separation time.For constant separa tion time, it is shown that the first-come-first-served landing order both maximizes the runway acceptance rate and minimizes the total delay.For variable separation time, a class of permutations allowing maximum runway acceptance rate is defined and rules for selecting a permutation yielding minimum total delay are given.R-ite/i In developing a logic for automatic air traffic control1 there arises the problem of establishing a general procedure for setting the order of landing.In principle, an order optimizing any arbitrarily selected cri terion can be determined by examining all possible permutations and sel ecting one that yields the optimal criterion value.In practice however, when the number of permutations is large, such a method takes too much time.This note gives a simplified, time-saving procedure for optimizing 2 the landing order with respect to one or both of the selected criteria.1. THE CRITERIA 5 The two criteria arbitrarily selected for consideration are total delay (the sum of the amounts of time each aircraft is kept waiting), and runway acceptance rate (number of planes landing on a given runway per unit time).If planes P , PQ, P ,... desire to land at the same one-runway t t p V . . .airport, it is assumed that each plane needs a minimum time t^, t^, •.. to land in absence of any other planes, and that the planes are required A to land so as to maintain a minimum time separation t .between planes J 1 P^ 1 and P^ landing in succession. 1 Preliminary work on automatic air traffic control carried out at the Coordinated Science Laboratory will be described comprehensively in reports R-1^5 and R-l^-6. 2 Duane Cooper and Linton.Kypta of the Coordinated Science Laboratory read a draft of the report and offered helpful suggestions.5 Some other possible criteria are maximum delay of a single plane, maximum fuel consumption of a single plane while waiting, total fuel consumption of all planes while waiting, etc.