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Traffic flow management (TFM) allocates the various airport, airspace, and other resources to maintain an efficient traffic flow consistent with safety. TFM is a complex area of research involving the disciplines of operations research, guidance and control, human factors, and software engineering. Hundreds of human operators make TFM decisions that involve tens of thousands of aircraft, en route air traffic control centers, the Federal Aviation Administration's System Command Center, and many airline operation centers. This paper provides an overview of how TFM decisions are made today and challenges facing the system in the future, and reviews modeling and optimization approaches for facilitating system-wide modeling, performance assessments, and system-level optimization of the national airspace system in the presence of both en route and airport capacity constraints.