The U.S. National Airspace System (NAS) is inherently highly stochastic. Yet, many existing decision support tools for air traffic flow management take a deterministic approach to problem solving. In this study, we focus on the flight departure delays because such delays serve as inputs to many air traffic congestion prediction systems. Modeling the randomness of the delays will provide a more accurate picture of the airspace traffic situation, improve the prediction of the airspace congestion and advance the level of decision making in aviation systems.

We first develop a model to identify the seasonal trend and daily propagation pattern for flight delays, in which we employ nonparametric methods for modeling the trends and mixture distribution for the residual errors estimation. This model demonstrates reasonable goodness of fit, robustness to the choice of the model parameters, and good predictive capabilities. We emphasize that a major objective is to produce not just point estimates but estimates of the entire distribution since the congestion estimation models envisioned require delay distribution functions, e.g. to produce probability of certain delays or expected traffic levels for arbitrary time intervals.

Local optima problems are typically associated with mixture distribution estimation. To overcome such problems, we develop a global optimization version of the Expectation Maximization algorithm, borrowing ideas from Genetic Algorithms. This optimization algorithm shows the ability to escape from local traps and robustness to the choice of parameters.

Finally, we propose models to estimate the so called "wheels-off delays" for flights within the NAS while incorporating a dynamic update capability. Considering that our objective is to estimate delay distributions, we evaluate alternate approaches in terms of the variance of the distribution they produce. That is, new approaches are evaluated based on their ability to reduce variance and their predictive accuracy. We first show that how a raw histogram can be misleading when a trend is present and how variance can be reduced by trend estimation. Then, various techniques are explored for variance reduction. The multiple seasonal trends method shows great capability for variance reduction while staying parsimonious in parameters. The downstream ripple effect method further enhances the variance reduction capability and makes real-time prediction practical and accurate. A rolling horizon updating procedure is described to accommodate the arrival of new information. Finally different models are compared with the current model adopted by the ETMS systems and the predictive capabilities of all models are shown.

Our data have been derived from Airline Service Quality Performance (ASQP) and Aviation System Performance Metrics (ASPM) databases provided by the FAA.