A class of problems in air traffic management (ATM) asks for a scheduling algorithm that supplies the air traffic services authority not only with a schedule of arrivals and departures but also with speed advisories. Since advisories must be finite, a scheduling algorithm must ultimately produce a finite data set, hence must either start with a purely discrete model or involve a discretization of a continuous one. The former choice, often preferred for intuitive clarity, naturally leads to mixed-integer programs (MIPs), hindering proofs of correctness and computational cost bounds (crucial for real-time operations). In this paper, a hybrid control system is used to model air traffic scheduling, capturing both the discrete and continuous aspects. This framework is applied to a class of problems, called the fully routed nominal problem. We prove a number of geometric results on feasible schedules and use these results to formulate an algorithm that attempts to compute a collective speed advisory, effectively piecewise linear with finitely many vertices, and has computational cost polynomial in the number of aircraft. This work is a first step toward optimization and models refined with more realistic detail.
An algorithm for detecting and analyzing potential enroute conflicts has been designed and implemented within the Center-TRACON Automation System (CTAS). The design uses the 4D trajectories provided by CTAS to produce a set of probable future conflicts, and assists the enroute sector controller in efficiently resolving these conflicts. Conflicts are detected via comparisons of trajectories at closely spaced time instants, with measures taken to limit the computations required to complete the search. Performance tests indicate more than 800 aircraft can be processed by the conflict detection and analysis algorithm within a search cycle of 10 seconds. This suggests that the search algorithm easily meets the performance requirements for an automated conflict detection and resolution tool in the current air traffic system.
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