A Data-Driven Model Predictive Control Framework for Multi-Aircraft TMA Routing Under Travel Time Uncertainty

Conference: AAAI 2026 arXiv: 2511.19452
Area: Air Traffic Management / Terminal Maneuvering Area Route Planning Keywords: TMA operations, STAR route planning, travel time uncertainty, model predictive control, MILP

TL;DR

A closed-loop MPC framework is proposed for conflict-free multi-aircraft routing and scheduling within the 50 NM Terminal Maneuvering Area (TMA) of Changi Airport. The framework integrates XGBoost-based TMA boundary arrival time prediction, MILP optimization (incorporating route selection, speed adjustment, holding control, and separation constraints), and a receding-horizon simulator. Under peak congestion scenarios of 36 aircraft/hour, it achieves a 7× computational speedup while significantly outperforming the Dijkstra baseline in feasibility under Monte Carlo robustness validation.

Background & Motivation

Background: Flight delays impose substantial costs on passengers, airlines, and the environment. Air Traffic Flow Management (ATFM) is typically modeled as a dynamic multi-commodity network flow problem; however, optimization of the Terminal Maneuvering Area (TMA)—the high-density airspace surrounding airports—remains underexplored in the literature. Existing research focuses primarily on runway scheduling (Airport Scheduling Problem), with insufficient attention to holistic TMA airspace optimization.

Limitations of Prior Work: (1) Oversimplified TMA network models—existing methods employ simplified maps with limited waypoints, incapable of representing the complex structure of real-world STARs (Standard Terminal Arrival Routes); (2) Lack of closed-loop real-time control—most approaches rely on one-shot optimization and cannot adapt to dynamic changes in real-time systems; (3) Travel time uncertainty is ignored—holding patterns and radar vectoring occur frequently in the TMA, resulting in high flight time variance (TMA internal variance: 204s vs. en-route segment: 81s), yet existing methods disregard the impact of this uncertainty on scheduling.

Key Insight: This paper integrates prediction, optimization, and simulation into a closed-loop MPC framework—replacing unreliable runway ETA prediction with data-driven TMA boundary arrival time prediction, substituting simplified models with MILP optimization over a full STAR network, and employing a receding-horizon strategy to enable real-time computation and robust control.

Method

Overall Architecture

The system comprises four components: a historical database, an XGBoost traffic predictor, a MILP real-time MPC controller, and a custom traffic simulator. ADS-B radar data and meteorological METAR data serve as inputs; the predictor outputs TMA boundary arrival times; the MPC optimizes landing times, routes, and speeds within a receding horizon window; optimization commands are applied to the simulator to update system state; and the process iterates until simulation completes.

Key Designs

1. Data-Driven TMA Boundary Arrival Time Prediction

   • Function: Uses XGBoost to predict each aircraft's arrival time at the 50 NM TMA boundary: \(T_f^t = \mathcal{F}(X_f^t)\)
   • Input features: ADS-B real-time dynamics (latitude/longitude/ground speed/distance), runway direction, departure airport code, wake turbulence category, temporal attributes, and METAR meteorological information (wind speed/direction/visibility/cloud cover)
   • Design Motivation: Predicting TMA boundary arrival time is more reliable than directly predicting runway ETA—flight time variance within the TMA is extremely large due to holding and vectoring operations (2.5× that of en-route segments), whereas aircraft behavior prior to the TMA boundary is comparatively stable. Delegating uncertainty to the optimizer represents a more principled architectural choice.

2. Full STAR Network MILP Optimization Model

   • Function: Solves for conflict-free optimal routes for multiple aircraft over a real-world STAR network within a 50 NM radius
   • Core constraints:
     • Flow conservation (analogous to vehicle routing problem flow balance)
     • Arrival/departure time constraints (incorporating discrete speed level selection)
     • Separation constraints (arrival/departure interval at any shared waypoint between any two aircraft \(\geq t_{f,f'}\))
     • No-overtaking constraints (an aircraft departing first on a segment must arrive first)
     • Holding constraints (holding permitted only at designated waypoints)
   • Objective function: Minimize average landing time across all aircraft: \(J = \min \frac{1}{|F|}\sum_{f \in F, j \in E} AR_j^f\)
   • Design Motivation: A real STAR map constructed from complete AIP (Aeronautical Information Publication) data, rather than a simplified network, more accurately reflects operational constraints.

3. Receding-Horizon Closed-Loop Control

   • Function: Decomposes the full planning horizon into sub-problems, enabling real-time control through bidirectional interaction between the MPC and the simulator
   • Mechanism:
     • Look-ahead horizon = 10 min; control horizon = 5 min
     • At each step, only aircraft within the look-ahead horizon are optimized, but only commands within the control horizon are executed
     • The simulator updates system state per second, handling three aircraft position cases: en-route, arrived and holding, and departed
     • Under perturbation mode, arrival time deviation \(\xi_{arr}\) and state observation deviation \(\xi_{ob}\) are introduced
   • Design Motivation: One-shot MILP optimization is computationally intractable under high-congestion scenarios due to exponential growth in solve time; the receding-horizon approach decomposes the large problem into sub-problems solvable within seconds.

Key Experimental Results

Computational Complexity Comparison (10–27 Aircraft, 10-Minute Window)

Case	# Aircraft	MILP Time (s)	MILP Cost (s)	Dijkstra Time (s)	Dijkstra Cost (s)	Gap
1	10	2.38	1189.2	14.99	1191.5	0.19%
6	15	20.50	1084.7	21.97	1103.8	1.76%
8	25	173.51	1072.5	24.48	~1080.6	(2 infeasible)
9	27	2609.6	1083.9	24.82	~1085.3	(2 infeasible)

Receding Horizon vs. One-Shot Optimization (Historical Real Data, 1 Hour)

Case	# Aircraft	One-Shot Time (s)	One-Shot Cost (s)	Rolling Time (s)	Rolling Cost (s)
2	25	169.30	2298.1	42.41	2302.2
5	36	784.69	2736.3	102.75	2736.3

Monte Carlo Robustness Test (36 Aircraft, 100 Runs × 4 Perturbation Levels)

• Across random perturbation values in the range 0.05–0.2, the number of infeasible cases under MILP is substantially lower than under Dijkstra.
• At perturbation value = 0.2, Dijkstra yields only 1 feasible solution, whereas MILP maintains a significantly higher feasibility rate.
• MILP solve time remains stable within 30–40s and does not increase noticeably with perturbation intensity.

Key Findings

• Under peak congestion (36 aircraft/hour), the receding-horizon approach achieves over 7× computational speedup (784.69s → 102.75s) with no cost degradation.
• The greedy Dijkstra strategy cannot guarantee feasibility under high congestion (infeasible aircraft appear in large-scale cases), whereas MILP remains feasible throughout.
• MILP solve time grows exponentially with problem size (27 aircraft = 2609s), validating the necessity of the receding-horizon approach.
• Travel time variance within the TMA (204s) is 2.5× that of en-route segments (81s), supporting the design choice to predict TMA boundary arrival times rather than runway ETAs.

Highlights & Insights

1. System-level closed-loop framework: Seamlessly integrates prediction, optimization, and simulation, with genuine deployment potential.
2. Real AIP-based STAR network: More faithful to actual operations than simplified models, with comprehensive constraint coverage (route, speed, holding, separation, no-overtaking).
3. Pragmatic prediction design: Predicting TMA boundary arrival time (low uncertainty) rather than runway ETA (high uncertainty) delegates the hard-to-predict component to the optimizer.
4. Monte Carlo robustness validation: Systematic validation across 100 runs × 4 perturbation levels is convincing.

Limitations & Future Work

1. Only 2D route planning is considered; vertical layer strategies are not addressed.
2. Speed selection is restricted to preset discrete levels; continuous speed optimization is not supported.
3. Case 9 (27 aircraft/10 min) already requires 2609s; larger-scale instances require further acceleration (e.g., column generation, branch-and-price).
4. Multi-runway selection optimization and departure–arrival interaction are not considered.
5. The simulator is a custom-built simplified version; integration and validation with real ATC systems remain incomplete.

Related Work & Insights

• The closed-loop MPC + MILP framework is generalizable to other real-time scheduling problems (e.g., port scheduling, warehouse robot path planning).
• The architectural design of delegating prediction uncertainty to the online optimizer is worth adopting in related domains.
• The Monte Carlo robustness validation methodology is applicable to other safety-critical systems.

Rating

⭐⭐⭐⭐

• Novelty ⭐⭐⭐: Incremental innovation; individual components have precedents, but the system-level integration adds value.
• Experimental Thoroughness ⭐⭐⭐⭐⭐: Real ADS-B data, computational complexity analysis, receding-horizon comparison, and Monte Carlo robustness validation—extremely comprehensive.
• Writing Quality ⭐⭐⭐⭐: Mathematical modeling is clear and rigorous.
• Value ⭐⭐⭐⭐: Direct applicability to real-world ATC decision support.

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