Trajectory-based optimization for air traffic control in the terminal maneuvering area

We present a trajectory-based optimization framework for arrival sequencing and scheduling in the terminal maneuvering area (TMA). In contrast to node-link scheduling models that abstract trajectories into time-delay parameters, the proposed method computes implementable per-aircraft speed profiles and path extensions that realize the required landing separation through terminal air traffic control actions. The framework couples an analytic TMA path model, comprising a tangent leg, a radius-to-fix turn, and a final-approach segment, with a nonlinear program (NLP) that jointly optimizes path stretch and segment speeds under a weighted objective. Three landing-order policies are evaluated. First-Entry-First-Serve (FEFS), First-on-Final-First-Serve (FOFFS), and FOFFS with Constrained Position Shifting (CPS) up to k positions, realized by a two-phase scheme coupling mixed-integer linear programming (MILP) with NLP that selects an optimized landing order before trajectory optimization. The aircraft population is drawn from a weight class fleet mix with pair-specific wake-turbulence separation, and each scenario is perturbed by a Gaussian wind sample, projected per segment onto the aircraft heading to convert commanded airspeeds into ground speeds. Moreover, an online, rolling-horizon formulation commits each aircraft’s trajectory irrevocably upon entry, enabling real-time decision-making. Monte Carlo experiments on the simplified A80 TMA show that: (i) FOFFS consistently outperforms FEFS in delay, path stretch, and fuel burn by exploiting geometric asymmetries among arrival streams; (ii) CPS further reduces separation violations and path stretch, with diminishing returns and a fast-growing solver cost; (iii) fuel estimates from BADA 3 and OpenAP agree on the qualitative trends; and (iv) the per-entry optimization completes in near real-time, demonstrating real-time feasibility for practical deployment.