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 evidence for the power law to be applicable to the DFHM load measure as well.

我们提供主观的一维瞬时自我评估工作量度量（五级ISA-WL等级）与作为目标任务负荷变量的空中交通管制员（ATCO）的无线电通信之间的幂律关系的证据。它对应于史蒂文斯在物理刺激和主观反应之间的经典心理物理学关系，特征幂律指数γ约为1。该理论模型在以交通流量为环境的环人空中空中交通管制模拟实验中得到了验证。刺激与ATCO的频率和无线电呼叫的持续时间（任务负载，RC-TL）及其报告的ISA-WL正相关。理论预测与基于非线性回归的模型参数估计一起，扩展了先前发表的结果，该结果量化了主观ISA度量与模拟的空中交通流量之间的形式逻辑关系（Fürstenau等人，Theor Issues Ergon Sci 21（6）：684–708） ，2020年）。本分析涉及（Gopher和Braune在Hum Factors 26（5）：519-532，1984年）中提出的一种针对心理工作量的心理物理学方法，该方法最近由（Bachelder和Godfroy-Cooper在飞行员工作量模拟：频谱合成中使用）需求分析和韦伯定律（SCL Tech，圣地亚哥，2019年）进行飞行员工作量估计，并具有典型史蒂文斯指数范围内的相应幂律指数。基于认知资源限制的假设，我们分别通过结合两种逻辑模型分别针对ISA-WL和通信TL特性得出幂定律。尽管个体间差异很大，但理论上预测的逻辑和幂律参数值与基于回归的估计值（参与者的平均值）惊人地接近。后勤ISA-WL和RC-TL缩放参数与相应的史蒂文斯指数之间的显着差异，因为这些参数的比率量化了TL / WL与交通流的分离。具有非标称事件的交通场景揭示了对逻辑WL缩放参数的工作条件以及幂定律指数的敏感性：对于大于临界值的交通流量，WL敏感性显着提高。