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Numerous factors influence the operational performance of the National Airspace System (NAS). In particular, the traffic efficiency is affected by uncertainties such as weather, navigation accuracy, aircraft performance and operational procedures, and air traffic management (ATM) actions. This study focuses on identifying various air traffic uncertainty sources and deriving the associated mathematical models of service time distributions. These models provide the distributions given air traffic uncertainties through analytical expressions without resorting to computationally expensive Monte-Carlo simulations.