Optimally and equitably distributing delays with the aggregate flow model

Abstract

The aggregate flow model is used to determine how to distribute predeparture delays among air traffic control centers and across time to optimally satisfy constraints on airspace capacity and departure rates. To do so, a quadratic cost on cumulative departure delays is introduced, resulting in an optimization problem that can be quickly solved using convex optimization tools. Simulations using the model demonstrate the behavior of the national airspace system (NAS) when implementing optimal departure delays for a particular constraint scenario. These results show that capacity-constrained air traffic control Centers suffer the highest delays. Three approaches for increasing the equity of the distribution of delays across the NAS are investigated. The first involves setting an upper bound on the Gini coefficient, a quasi-convex measure of inequality. Another is to make delays in some centers more costly than in others. The last approach is to put an upper bound on the delay per departure for each center. Simulation results demonstrate that bounding delay per departure effectively reduces the delays for the constrained center. Enforcing an upper bound on the Gini coefficient and increasing the weight on delays in some centers may impose large delays on other centers when reducing the delays in the constrained center.