Analytical relationships between conflict counts and air-traffic density

Semi-empirical random variable models of the expected number of air-traffic conflicts as a function of airtraffic density are derived. Model parameters are determined from analysis and simulation of real air-traffic data. These models are applied to simulated air-traffic scenarios to analyze conflict properties in various conflict resolution strategies. It is shown that under free routing conditions (approximated by great-circle routes in zerowind conditions) the expected number of conflicts is well represented by a binomial random variable model. Using this model, it is further demonstrated how conflict resolution can cause a chain reaction, leading to an increased number of conflicts for all aircraft, and how the model can be used to predict the airspace capacity for a given conflict resolution strategy. In a separate study, it is shown that for an iterative horizontal-plane conflict resolution strategy, a random variable model with the geometric distribution closely matches empirical data. This model also predicts the aircraft density at which the airspace becomes saturated. It is shown how analysis of conflicts in the horizontal plane can be scaled and applied to the analysis of conflicts in three-dimensional airspace.