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

1. Introduction. An air traffic control system maintains adequate separation between aircraft by requiring some aircraft to deviate from the paths which they would otherwise follow. In the absence of such deviations it must be assumed that civil transport aircraft would choose to operate at the most economical combination of airspeed, track and altitude (within the limits set by inaccuracies of weather prediction); A.T.C. deviations therefore involve economic penalty to the operator. It is important to assess the magnitude of such penalties for two reasons:(a) To provide a yardstick by which to compare different A.T.C. systems.(b) To give a measure of how much might justifiably be spent on new systems and equipment, to enable separation standards (and hence the penalty of deviations) to be reduced without reduction in safety.

1. INTRODUCTION. The North Atlantic air traffic system is the busiest and most important long-range system in operation today with a current total of 127 000 flights“annum. The combined effects of the total flight time and the difference in time zones on either side of the Atlantic makes it desirable for most passengers to fly westward in the day-time. Conversely, it is most convenient (or least inconvenient!) to fly eastbound during the hours of darkness. Thus the Atlantic traffic system is strongly tidal with the flow predominantly (though not entirely) westbound during the day and eastbound overnight. Currently the central core of the traffic in the busiest hours is organised into a parallel track structure – the Organized Track Structure (OTS), though nearly half the aircraft operate so-called random routes clear of the OTS.

This is the third article of a series of three describing the methods developed at the Royal Aircraft Establishment for costing the effect of air traffic control deviations in long range systems. The first two discussed the general principles of costing and their application to the current and future systems for subsonic aircraft over the North Atlantic. The present paper considers systems for the S.S.T.The characteristics and mode of operation of the supersonic transport are untested, and it will operate at an altitude for which information is relatively scanty. This means that the results obtained for the cost penalties in a supersonic traffic system must be regarded as tentative. On the other hand, because we are considering traffic systems for aircraft at such an early stage of development, the situation can be analysed in a more fundamental way, with particular emphasis on the effect of the system on the aircraft design.

The first point to note about the North Atlantic air traffic system is the diurnal pattern of flow. This is strongly tidal, with westbound flow predominant during daylight hours and eastbound flow overnight. There is some traffic which flows against the main stream, particularly during the day, but the strong tendency for one-way traffic results from the difference in local times on opposite sides of the ocean, together with the transit times of flight at current speeds. This means that the general pattern will probably persist, unless and until aircraft speeds change radically.