Modeling Probability Distributions of Primary Delays in the National Air Transportation System

Flight delays impose enormous costs that are exacerbated by propagation effects. Development and evaluation of advanced schedule planning approaches for mitigating propagated delays require primary delay distribution models with a long prediction horizon of several weeks to months. This paper presents a hybrid modeling approach combining logistic regression and quantile regression. Two large data sets, each consisting of approximately 6 million flights, were used as training and testing samples to identify types of factors affecting primary delay distributions. Several insights were obtained into the factors affecting delay distributions. Coefficient estimates were found to have a high statistical significance and intuitive interpretation of their signs and relative magnitudes. Results from model estimation, validation, and testing show that fit values are stable across data sets, avoiding overfitting. The relative explanatory power of various types of predictive factors—including distance factors, seasonality factors, time-of-day factors, airport factors, and airline factors—is quantified. A new method is provided for quantifying the fit of the joint model in the form of the log likelihood of the observed data, and the model provides a considerable improvement in log likelihood.