🤖 machine learning

Graph-based Complexity Forecasts in UK En Route Airspace Using Relevant Aircraft Interactions

This study presents a graph-based probabilistic forecasting method that predicts Air Traffic Control Officer workload in the London Middle Sector by modeling the future number of relevant aircraft interactions, demonstrating significantly higher accuracy and correlation with actual complexity than standard traffic volume predictions.

Original authors: Edward Henderson, George De Ath, Nick Pepper

Published 2026-05-25

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Edward Henderson, George De Ath, Nick Pepper

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the sky above London as a giant, busy highway, but instead of cars, it's filled with airplanes. The people in charge of keeping everyone safe are Air Traffic Control Officers (ATCOs). Their job is like being a referee in a massive, high-speed game where the rules change every second. If there are too many planes getting too close to each other, the referee gets overwhelmed, and mistakes can happen.

This paper is about building a smarter "traffic jam detector" for these sky-high highways. Here is how the researchers did it, broken down into simple steps:

1. The Problem: Counting Cars Isn't Enough

Currently, the supervisors who manage the ATCOs look at how many planes are in a specific area to guess how busy the controllers will be. It's like trying to guess how stressful a highway is just by counting the number of cars.

But this is flawed. A highway with 20 cars driving in a straight line is easy. A highway with only 5 cars weaving in and out, changing lanes, and trying to merge is a nightmare. The paper argues that we shouldn't just count the planes; we need to count the potential trouble spots—the pairs of planes that might get too close and need a controller to step in and say, "Hey, you two, slow down or turn!"

2. The Solution: A "Relevant Pair" Filter

The researchers created a new digital tool to act like a super-observant co-pilot. Its only job is to look at two planes and ask: "Do these two need to be watched closely?"

The Old Way: They started with a standard computer program that guessed which planes were close.
The Human Touch: They didn't just trust the computer. They showed the results to real, licensed air traffic controllers and asked, "Is this right?" The controllers said, "No, that plane is actually fine because it's climbing away," or "Yes, watch that one, it's coming in fast."
The Result: The researchers tweaked the computer's rules based on this feedback. It's like teaching a new employee by showing them real-life examples until they get the hang of it. The new tool became much better at spotting the "trouble pairs," scoring an 84% accuracy rate compared to the old tool's 69%.

3. The Prediction: A Crystal Ball for the Sky

Once they had a good way to spot trouble pairs, they needed to predict them before they happened.

The Map: They turned the complex web of flight paths into a digital "graph" (a map made of dots and lines). To make it fair, they smoothed out the map so every little segment was the same size, like turning a jagged mountain path into a smooth, measured track.
The Uncertainty: Planes don't always arrive exactly on time. A plane might be 5 minutes early or 5 minutes late. The researchers built a system that accounts for this "fuzziness." Instead of saying, "Plane A will be at Point X at 10:00," they say, "There's a 70% chance Plane A is at Point X at 10:00."
The Forecast: By combining this fuzzy map with live data from the airport, the tool can look 45 minutes into the future and say, "In 45 minutes, there will likely be 8 pairs of planes that need close monitoring."

4. Why It's Better

The researchers tested their new crystal ball against the old method (which just counted total planes).

The Old Method: Predicted traffic volume with a correlation of 0.55.
The New Method: Predicted the actual "trouble pairs" with a correlation of 0.68.

Think of it this way: The old method told the supervisor, "It's going to be busy." The new method told them, "It's going to be busy specifically because these two planes are going to cross paths in a tricky way." This gives the supervisor a much clearer picture of why it will be hard, not just that it will be hard.

The Bottom Line

This tool is fast (it works in less than a second) and accurate. It helps the people in charge of the air traffic controllers decide how many controllers they need on duty and how to split up the sky sectors. Instead of guessing based on a simple headcount, they can now make decisions based on a detailed forecast of where the actual stress points will be in the sky.

Note: The paper specifically tested this on one busy sector above London (called the London Middle Sector). While it works great there, the authors note that it would need more testing and tweaking before it could be used everywhere else.

Technical Summary: Graph-based Complexity Forecasts in UK En Route Airspace Using Relevant Aircraft Interactions

Problem Statement
Effective management of Air Traffic Control Officer (ATCO) workload is critical for operational safety. Group supervisors currently rely on tools estimating traffic load to inform decisions regarding sector configuration and rostering. However, industry-standard complexity models often fail to capture the nuances of air traffic complexity. These models typically rely on deterministic trajectory predictions and heuristic measures (e.g., total aircraft count or climbing/descending aircraft) which lack the fidelity to model future traffic configurations accurately. They often overestimate complexity in low-traffic scenarios where specific route overlaps occur and fail to account for the inherent uncertainty in aircraft arrival times and the likelihood of aircraft being vectored off their filed routes. Furthermore, complexity is sector-specific and driven by "relevant" interactions rather than simple volume, making generalizable numerical measures difficult.

Methodology
The study proposes a probabilistic framework to forecast airspace complexity in the London Middle Sector (LMS), a complex area with multiple climbing and descending flows above major European airports. The methodology consists of three primary components:

Adaptation of a Relevant Aircraft Filter:
The authors adapted an existing flight filtering algorithm (originally by Vijay Kumbhar et al.) to serve as a proxy for ATCO workload. This filter identifies "relevant" aircraft pairs—those requiring monitoring or deconfliction—rather than just those in immediate conflict.
- Iterative Refinement: Through qualitative feedback from licensed ATCOs at the Swanwick Centre, the filter was tuned for LMS. This involved adjusting parameters (e.g., lateral distance thresholds, vertical distance spans) and incorporating new logic:
  - In-trail handling: Excluding aircraft with negligible relative velocity within a specific lateral cone.
  - Diverging routes: Excluding aircraft with sufficient lateral separation on diverging paths.
  - Data-driven vertical profiling: Replacing simple flight level span intersections with probabilistic trajectory predictions (using a 2σ credible interval) to model climb and descent cones, reducing false positives.
  - Operational trajectory prediction: Utilizing the last issued ATCO instruction (clearance) rather than just the filed flight plan or state-based assumptions to generate subject aircraft trajectories.
- Evaluation: The tuned filter was validated against 50 ATCO-labelled static traffic scenarios, achieving an F1-score of 0.84 compared to 0.69 for the original parameters.
Graph-based Route Representation:
To facilitate forecasting, the authors constructed a resampled graph representation of the LMS route network.
- Resampling: Historic flight plans (Jan–Dec 2024) were converted into a graph where edges were linearly subdivided and clustered to ensure consistent spatial fidelity (5–10 NM edges). This standardized the route legs, allowing for the collation of similar routes and finer spatial predictions.
- Lookup: A translation table was created to map original flight plan waypoints to the resampled graph structure.
Probabilistic Complexity Forecasting:
The forecasting method predicts the number of relevant aircraft pairs up to 45 minutes in advance by combining:
- Live Operational Data: Arrival time predictions from the NATS National Airspace System Flight Data Processor (NAS FDP).
- Occupancy Probability: A statistical model assuming aircraft arrival times at waypoints follow a normal distribution ( $N(\mu, \sigma^2)$ , with $\sigma=5$ mins). This calculates the probability of an aircraft occupying a specific route segment at a future query time.
- Historic Priors: An empirical expectation value ( $E[X | O_i, O_j]$ ) derived from historic data, representing the probability that two aircraft occupying specific route legs ( $O_i, O_j$ ) constitute a relevant pair.
- Prediction Formula: The total expected number of relevant pairs is calculated by summing the product of occupancy probabilities and the historic expectation of relevance for all pairs of route legs.

Key Results

Filter Performance: The updated filter demonstrated superior performance over the original algorithm, with a Precision, Recall, and F1-score of 0.84 (vs. 0.67, 0.72, and 0.69 respectively) on the ATCO-labelled test set.
Forecast Accuracy: When forecasting relevant pairs 30 and 45 minutes in advance, the proposed method achieved a Spearman's rank correlation coefficient ( $\rho$ ) of 0.68 with the actual number of relevant pairs identified by the filter.
Comparison to Baseline: This correlation was significantly stronger than a standard traffic volume prediction (counting aircraft in the sector), which yielded a $\rho$ of 0.55.
Statistical Significance: A moving block bootstrap analysis confirmed that the proposed method's correlation with actual workload was statistically significantly higher than the traffic volume baseline (mean difference 0.134, 95% CI [0.064, 0.211], $p=0.0004$ for the 45-minute lookahead).
Computational Efficiency: The tool generates predictions in less than one second on a standard laptop, making it feasible for real-time application within a single radar sweep (~6 seconds).

Significance and Claims
The paper claims that the proposed data-driven tool offers a more accurate proxy for ATCO workload than current industry standards by focusing on "relevant interactions" rather than raw traffic volume. By leveraging probabilistic modeling of arrival times and a graph-based representation of the airspace, the method accounts for uncertainty and operational realities (such as vectoring) that deterministic models miss.

The authors posit that this tool has the potential to support group supervisors in making informed decisions regarding sector configuration and ATCO rostering. The study emphasizes that the approach is specifically tuned to the geometric and operational characteristics of the LMS sector. While the results are promising, the authors note that the evaluation was limited to a single day and a single sector. Consequently, they claim the tool requires further calibration and evaluation across different seasons and sectors before it can be deployed more widely, particularly for sectors above the current altitude range of LMS.

1. The Problem: Counting Cars Isn't Enough

2. The Solution: A "Relevant Pair" Filter

3. The Prediction: A Crystal Ball for the Sky

4. Why It's Better

The Bottom Line

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