A Stochastic Delay Differential Equation Model of Multitasking While Driving

Models of human sensorimotor control have been developed from two perspectives. The human performance modelling perspective relies on mathematically complex models that cover a wide range of perceptual, decision and motor processes to understand human-machine interactions in complicated, realistic settings. The fundamental research perspective relies on mathematically tractable models to understand physical and statistical aspects of sensorimotor control in simple laboratory settings. In the present work we combine the two perspectives to develop a Stochastic Delay Differential Equation (SDDE) model of driving performance while multitasking. Our model comprises of three psychologically interpretable parameters that quantify cognitive sensitivity, delays, and noise. We apply our model to time-series data from a two-dimensional compensatory tracking task that simulates lateral and longitudinal control of a ground vehicle. Concurrently with the primary tracking task, participants performed secondary tasks that required mainly cognitive resources, or greater visual-manual resources. We show how our model can provide more fine-grained insight into the mechanisms underlying driver distraction than conventional one-dimensional behavioural measures.