A generalized model for the prediction of controller intervention rates in the en route air traffic control system

Abstract

A generalized model of the domestic en route air traffic control system is constructed, which can be used to predict the rate at which controllers will need to intervene in the flow of radar-controlled traffic to prevent the violation of minimum horizontal separation standards. The model considers both crossing and overtaking conflicts, and includes both on- and off-airway traffic. Further, the model is able to incorporate complex airway intersections, including those involving more than two crossing airways, as well as those which permit aircraft to change airways at the intersection. A delayed negative exponential distribution on aircraft interarrival distances is used to reflect the traffic separation efforts of controllers in neighboring sectors. The model is initially presented in a two-dimensional form and then extended to three dimensions by the use of traffic "sources" and "sinks" to represent climbing/descending aircraft which appear and then disappear in successive flight levels. The three-dimensional version is not extended to Terminal Control Areas, due to the decidedly non-random-traffic flow into and out of large airports. Monte Carlo simulations of simple airway intersections and single airway segment overtaking situations are used to confirm the expected intervention rates predicted by the analytic model. The simulations also serve to illustrate the significant variation to be expected about the mean intervention rate. An expression for the variance about the mean intervention rate at simple intersections is derived by conditioning on the actual (as opposed to expected) traffic density and then using well known results for the variance of binomial random variables. An extensive sensitivity analysis is performed on several of the model's key assumptions. The model is found to be particularly sensitive to assumptions about steady state behavior in mean traffic flow rates and somewhat less sensitive to errors in aircraft velocity distributions.