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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, whichdoi:10.2514/1.15242 fatcat:7imkmtkssbhedixuk5gppje3gq