In this paper, we propose a new method to evaluate air traffic complexity in 3-D airspace through a probabilistic measure of the airspace occupancy. The key novelty of the approach is that uncertainty in the future aircraft positions is explicitly accounted for when evaluating complexity. Analytic-though approximate-expressions of the complexity measure are derived.Prospective applications for the proposed complexity metric include the timely identification of those multi-aircraft conflict situations that would be difficult to solve because of limited maneuverability space, and the design of trajectories so as to avoid congested regions that would require many tactical maneuvers to pass them through. Numerical examples are provided to illustrate the approach.

In this paper we study the issue of characterizing the complexity of air traffic to support Air Traffic Management (ATM) operations. We discuss, in particular, the features of a complexity metric that are relevant for application to future ATM systems where part of the responsibility for separation assurance and trajectory management operations is distributed on board of the aircraft. We then describe a probabilistic complexity metric that meets all those features and is amenable for supporting onboard conflict detection and resolution and trajectory management operations. A numerical example illustrates its possible use in a fully automated self-separation context.

A generalized notion of the input-to-state L2-gains of discrete-time switched linear systems is proposed in this paper. Such gains are then characterized using the radii of convergence of a family of suitably defined functions called the generating functions. Properties of the generating functions are studied and their numerical computation algorithms are developed. Some numerical examples are presented.

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