In the perspective next generation Air Traffic Management (ATM) systems, aircraft will be endowed with part of the responsibility for separation maintenance, and traffic complexity reduction functions are envisaged to play an important role in avoiding to overload the on-board conflict resolution system. In this work, we introduce a method to assess air traffic complexity in the long term, with the goal of pointing out the presence of 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 airc...