Some Mathematical Aspects of Air Traffic Systems

Abstract

In this paper, which was presented at a meeting of the Institute in London on 26 January 1977 with Group Captain H. L. Sheppard in the Chair, Mr. Attwooll, Head of the Air Traffic Studies Division at the Royal Aircraft Establishment, discusses the application of the theory of queues to air traffic control. He shows the importance of random perturbations due to late arrival of aircraft, and how traffic schedules in an airway network can best be adjusted to minimize delays due to congestion on certain routes. Much of this study was carried out on behalf of the Civil Aviation Authority but the opinions expressed do not necessarily reflect the policy either of the CAA or the Ministry of Defence

Applications of Operations Research in the Air Transport Industry

“…The first stage involved problem definition and development of large-scale mathematical optimization models of an aggregate scope. Attwool (1977) was the first to cast ATFM issues in mathematical terms, while Odoni's (1987) detailed description of the singleairport ground holding problem (GHP) as a dynamic and stochastic optimization problem stimulated much of the subsequent work. Important advances in modeling and solving the GHP are marked by the stochastic programming models of Richetta and Odoni (1993), the extension to a multiairport setting by Vranas et al (1994), and the inclusion of en route constraints and rerouting options by Bertsimas and Stock (1998).…”

A Comparison of Formulations for the Single-Airport Ground-Holding Problem with Banking Constraints

“…• By using a polyhedral projection (see [3] and [6] for background), we will show that XSS and XGF are equivalent in strength. Let P 1 be a polyhedron defined over variable set x and let P 2 be a polyhedron defined over variable set (x, z) .…”

“…Since that time, GHP has been treated on a stochastic level by Odoni, Andreatta and Richetta in [9] and [10]. Both GH and traffic flow management in general have been treated on a network-wide level (taking multiple airports and flight connectivity into account) in Attwool [3], Sokkapia [11], Andreatta and Romanin-Jacur [1], Wang [15] and by Vranas,et. al.,in [13] and [14], and, more recently, by Bertsimas and Stock [5].…”

Conflicts between Random Flights in a Given Area

“…A conflict in any class can exist in the horizontal plane, the vertical plane, or both; these latter will be termed 'composite' conflicts. For each situation we require N b , P h , N Y and P T as defined in connection with equation (1).…”

“…Attwooll 1 gives a good discussion of queueing problems in ATC, the problems of separating traffic in time. The present paper is concerned with segregating traffic in space, dividing up the available sky to minimise conflicts between the various users.…”