Power law model for subjective mental workload and validation through air traffic control human-in-the-loop simulation

Fürstenau, Norbert; Radüntz, Thea · 2021 · Crossref

DOI: 10.1007/s10111-021-00681-0

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Summary

This study addresses the quantification of mental workload (WL) in air traffic control (ATC) by establishing a theoretical power law relationship between subjective workload and objective task load. Motivated by the need for robust, real-time workload assessment in complex human-machine systems, the authors apply a psychophysics approach—specifically Stevens’ power law—to model the relationship between the subjective Instantaneous Self-Assessment (ISA) workload measure and radio communication task load. The research aims to validate this model using data from a human-in-the-loop simulation, expanding on previous findings that identified a logistic relationship between subjective WL and traffic flow. The methodology involved a simulation experiment conducted at the German Aerospace Center’s Air Traffic Management and Operations Simulator. Twenty-one participants, including experienced approach and tower controllers, completed eight scenarios varying in traffic flow (25 to 55 aircraft per hour) and the presence of a non-nominal priority event. Subjective workload was measured using the five-level ISA scale, reported every five minutes via touchscreen. Objective task load was quantified by the frequency of radio calls (RC-TL) between controllers and pseudo-pilots. The theoretical model was derived by combining two logistic functions: one describing the relationship between subjective ISA-WL and traffic flow, and another describing the relationship between radio communication task load and traffic flow. This combination yielded a power law equation linking subjective WL directly to objective communication load, with the exponent $\gamma$ representing the sensitivity of subjective response to task load. The results confirmed a power law relationship between ISA-WL and radio communication task load, with the characteristic exponent $\gamma$ approximating 1, consistent with classical psychophysical findings. The theoretically predicted parameters showed close agreement with regression-based estimates derived from the experimental data, despite significant inter-individual variance. The study also quantified the dissociation between task load and workload scaling parameters, revealing that workload sensitivity increased significantly for traffic flows exceeding a critical value, particularly during non-nominal events. Additionally, initial analysis suggested that the power law model is also applicable to a neurophysiological EEG-based workload index (Dual Frequency Headmaps), indicating broader validity across different measurement modalities. The significance of this work lies in providing a formal, theoretically grounded framework for linking subjective and objective workload measures in ATC. By validating the power law model, the study offers a method to predict subjective workload from easily measurable objective task variables like communication frequency. This approach supports the development of adaptive automation and interface design by enabling real-time workload monitoring. The findings reinforce the utility of psychophysical models in cognitive ergonomics and suggest that such models can be extended to other physiological measures, facilitating more comprehensive and robust workload assessment in high-stakes operational environments.

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• workload measurement
• mental demand
• time perception

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• Theoretical Contribution: theory or model