Revision with unchanged content. 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. This study aims to focus on the random and dynamic nature of flight departure delays to 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. Several models were proposed in this work based on the trends and patterns demonstrated by the delays. These models show reasonable goodness of fit, robustness to the choice of the model parameters, and good predictive capabilities. They could further advance the Enhanced Traffic Management System that is currently adopted by the Federal Aviation Administration. Mathematical algorithms used in this work can be adapted to similar problems in other fields. The book is addressed to professionals and researchers in Air Transportations and Statistics.