Variable Perception Time in Car Following and Its Effect on Model Stability

The functional variation of perception time T in car following is studied for the purpose of introducing a variable time delay into a previously proposed nonlinear model. The basic hypothesis is that the ratio of a just noticeable difference in visual angle (¿¿) to the visual angle (¿) is a constant. This hypothesis leads to a model in which perception time T is proportional to relative spacing and inversely proportional to relative speed. Experimental results agree very closely with the model for negative relative speeds between 3 and 18 ft/s. A second-order approximation is used to explain behavior for relative speeds of less than 3 ft/s in absolute value. This second-order approximation also agrees well with data taken previously with relative acceleration varying between 1 and 4.7 ft/s2 and initial relative speed between ¿ 1.9 and 2.9 ft/s. A brief discussion of "ideal" following distance b is presented to clarify the stability analysis. The introduction of a variable time delay and ideal following distance into the proposed car-following model changes the size of the minimum asymptotic stability region but not the basic properties of the model. The word "asymptotic" is used in the dynamic stability sense as in the classical control theory literature, not in the sense of platoon stability.