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This paper considers the problem of intersecting aircraft flows under decentralized conflict avoidance rules. Using an Eulerian standpoint (aircraft flow through a fixed control volume), new air traffic control models and scenarios are defined that enable the study of long-term airspace stability problems. Considering a class of two intersecting aircraft flows, it is shown that airspace stability, defined both in terms of safety and performance is preserved under specific decentralized conflict resolution algorithms. A performance bound is derived and examples show that this bound is tight. A comparison is made with centralized approaches to conflict resolution.

Stability of intersecting aircraft flows under decentralized conflict avoidance rules