On the properties of the sum of durations of perceived conflicts in air traffic control

A perceived conflict is a configuration of two airplanes en route which is regarded by the ground controller as a potential conflict. The frequency of perceived conflicts per shift is a customary and widespread measure of the work load induced upon the air traffic controller and was thus extensively studied. The inherent assumption behind this approach is that perceived conflicts are sufficiently homogeneous to the extent that their frequency is an adequate representative of their cumulative effect. There are, though, observations to the contrary. Friedman [3] has suggested the duration of a perceived conflict, if only monitored by the ground controller, as a gauge for its intensity. A substitute measure of the work load induced upon the controller, under the more elaborate supposition that perceived conflicts are heterogeneous events, is the sum of their durations per shift. Within the framework of a model that assumes two crossing air routes with identical altitude, the present paper derives the expectation and variance of the sum of durations of perceived conflicts per shift and compares them to the corresponding moments of the frequency of perceived conflicts as obtained by Schmidt [6].