A geometric approach to air traffic complexity evaluation for strategic trajectory management

In the prospective next generation Air Traffic Management systems, aircraft will be endowed with part of the responsibility for separation maintenance, and traffic complexity reduction functions will play an important role in avoiding to overload the on-board conflict resolution system. In this work, a method for assessing air traffic complexity in the long term is presented, that may be used to detect critical situations with limited aircraft manoeuvrability in the time/space coordinates, and provide support to the flow/strategic trajectory management functions. The method is based on the concept of `influence zone´ of an aircraft, which accounts for both the direction and velocity of the aircraft, and can be regarded as the set of possible locations reachable by an aircraft through local deviations from its intended trajectory. Complexity is then related to the presence and magnitude of intersections between influence zones of different aircraft. The influence zones (as well as other regions of the airspace to be avoided) can be approximated with polyhedra, and their interaction analyzed using efficient tools borrowed from computational geometry.