Abstract : This paper presents a new air traffic complexity metric based on non-linear dynamical systems. Previous work has shown that the structure and organization of traffic are important factors in the perception of the complexity of an air traffic situation. The new metric captures these important aspects of complexity by identifying the organization of trajectories in a traffic pattern. This paper investigates only the features of this new metric without quantifying directly the connection between complexity and the metric. Authors of previous work in this area have proposed metrics that generally have not explicitly addressed the effects of organization in the traffic flow on complexity. In order to capture the effect of organization, the metric is based on a dynamical system which fits as closely as possible the observations given by the aircraft positions and speeds. Two approaches are presented. The first one is based on a linear dynamical system and produces an aggregate complexity metric. The second approach, uses a non-linear dynamical system model that fits the observations without error. This metric can be used to identify high (or low) complexity areas on a map, and, by capturing the organization properties of the traffic, captures some of the key factors involved in ATC complexity. A complexity map for the northwest area of France is shown as an example of the application of the model to real radar data. Such maps are an example of the usefulness of these methods for comparing the relative complexity of different regions of airspace.
