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There has been extensive research in formalising air traffic complexity, but existing works focus mainly on a metric to tie down the peak air traffic controllers workload rather than a dynamic approach to complexity that could guide both strategical, pre-tactical and tactical actions for a smooth flow of aircraft. In this paper, aircraft interdependencies are formalized using graph theory and four complexity indicators are described, which combine spatiotemporal topological information with the severity of the interdependencies. These indicators can be used to predict the dynamic evolution of complexity, by not giving one single score, but measuring complexity in a time window. Results show that these indicators can capture complex spatiotemporal areas in a sector and give a detailed and nuanced view of sector complexity.

One of the main missions of air traffic management is to guarantee en route safety. This safety is quantified through some minimum separation distance between pairs of flying aircraft. Current systems are human-based, i.e., have human air traffic controllers assuring minimum separation is maintained and in cases a loss of separation is predicted, they take actions to prevent the occurrence of such events. The constant and rapid increment of the air traffic demand is pushing current air traffic control systems to their limits. Development of automatic decision support systems, which can be used to automate, or support aircraft conflict detection and resolution, is considered a possible solution. However, the combinatorial nature of the problem poses several challenges for such a task. Metrics or various analytical procedures to produce information about the complexity of given scenarios can be used to guide the solution search process. In this paper, we present a complexity analysis based on the spatio-temporal interdependencies identified by the use of spatio-temporal regions constructed around the aircraft conflicts. INDEX TERMS Aircraft conflict, complexity metrics, continuous space-time regions.

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