Lagrangian delay predictive model for sector-based air traffic flow

A control theoretical model of sector-based air traffic flow is derived using hybrid automata theory. This model is Lagrangian, because it models the properties of the system along its trajectories. A subset of this model is used to generate analytic predictions of air traffic congestion: A dynamic sector capacity is defined and derived that is used for predicting the time it takes to overload a given portion of airspace. This result links the Lagrangian approach with Eulerian models, which account for temporal variations of parameters in a fixed volume. To determine the accuracy of predictions, an air traffic flow simulator is designed and validated. The simulator is then used to show that flow scheduling and conflict resolution may be decorrelated by reducing aircraft density.