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A Mathematical Analysis of Air Traffic Priority Rules

This paper analyzes priority rules, such as those in Part 91.113 of the Federal Aviation Regulations. Such rules determine which of two aircraft should maneuver in a given conflict scenario. While the rules in 91.113 are well accepted, other concepts of operation for Next Generation Air Transportation System (NextGen), such as self separation, may allow for different priority rules. A mathematical framework is presented that can be used to analyze a general set of priority rules and enables proofs of important properties. Specific properties considered in this paper include safety, effectiveness, and stability. A set of rules is said to be safe if it ensures that it is never the case that both aircraft have priority. They are effective if exactly one aircraft has priority in every situation. Finally, a set of rules is called stable if it produces compatible results even under small changes to input data.