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

We provide evidence for a power law relationship between the subjective one-dimensional Instantaneous Self Assessment workload measure (five-level ISA-WL scale) and the radio communication of air traffic controllers (ATCOs) as an objective task load variable. It corresponds to Stevens’ classical psychophysics relationship between physical stimulus and subjective response, with characteristic power law exponent γ of the order of 1. The theoretical model was validated in a human-in-the loop air traffic control simulation experiment with traffic flow as environmental stimulus that correlates positively with ATCOs frequency and duration of radio calls (task load, RC-TL) and their reported ISA-WL. The theoretical predictions together with nonlinear regression-based model parameter estimates expand previously published results that quantified the formal logistic relationship between the subjective ISA measure and simulated air traffic flow (Fürstenau et al. in Theor Issues Ergon Sci 21(6): 684–708, 2020). The present analysis refers to a psychophysics approach to mental workload suggested by (Gopher and Braune in Hum Factors 26(5): 519–532, 1984) that was recently used by (Bachelder and Godfroy-Cooper in Pilot workload esimation: synthesis of spectral requirements analysis and Weber's law, SCL Tech, San Diego, 2019) for pilot workload estimation, with a corresponding power law exponent in the typical range of Stevens’ exponents. Based on the hypothesis of cognitive resource limitation, we derived the power law by combination of the two logistic models for ISA-WL and communication TL characteristics, respectively. Despite large inter-individual variance, the theoretically predicted logistic and power law parameter values exhibit surprisingly close agreement with the regression-based estimates (for averages across participants). Significant differences between logistic ISA-WL and RC-TL scaling parameters and the corresponding Stevens exponents as ratio of these parameters quantify the TL/WL dissociation with regard to traffic flow. The sensitivity with regard to work conditions of the logistic WL-scaling parameter as well as the power law exponent was revealed by traffic scenarios with a non-nominal event: WL sensitivity increased significantly for traffic flow larger than a critical value. Initial analysis of a simultaneously measured new neurophysiological (EEG) load index (dual frequency head maps, DFHM, (Radüntz in Front Physiol 8: 1–15, 2017)) provided eviden