A Mathematical Model of Driver Alertness

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Abstract
A ten parameter model is developed, relating to the experiences of a single driver in complex traffic. It is postulated that the driver observes the danger at time t imperfectly, and that his instants of observation form a non-homogeneous Poisson process. The mean value of the process is functionally dependent on the most recent observed value. The driver is assumed to exercise a measure of control over the process by means of a ‘ braking function ’ in which he chooses parameter values. After a ‘ reaction time ’ has expired, he may employ the braking function to modify the evolution of the process. The parameters chosen are also dependent on the most recent value of danger observed. A numerical example is given, as well as a discussion of possibilities for parameter calibration and estimation. The entire system is applicable to other control processes in which a subject attempts to choose parameters in a complex, imperfectly perceived, dynamic situation.

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