Decision analysis and optimality in air traffic control conflict resolution: II. Optimal heading (vectoring) control in a linear planar configuration

This manuscript is concerned with the effects of a heading advisory dispensed by an air traffic controller on a resolution of a pending or an in-progress potential aerial conflict. It is assumed that the aircraft traverse two linear, planar, intersecting air routes with fixed velocities. A potential conflict is defined as a violation of a given safety distance between two airplanes traveling different paths. The controller, upon discerning that the two craft are in potential conflict or about to enter one, issues, at the appropriate instant, corrective vectoring to them in order to obtain an effective dissolution of the conflict. The interpretation of "effective" in this paper is construed as either of the following: a new direction is put forth by the controller so as to maintain an inviolable separation between the two planes while introducing a minimal disturbance to their flight paths, or alternatively, while minimizing the duration of the potential conflict. An analysis of the impact of the controller's instructions on a single conflict involving two planes only, accompanied with illustrative numerical examples, is carried out under two pilot response suppositions. The first stipulates that pilots execute precisely the controller's remedial commands whereas the second allows for a built-in randomness in their response time.