In this paper, a new statistic car-following regulation was described and car-following model was established by means of the time delay differential equation of chaos dynamics. Using a high precision GPS receiver we collected the time serial data that represented drivers' behaviors and vehicle status in real traffic flow. A complete course of car-following was divided up into three stages, acceleration, steady, and deceleration stage. Using the dynamic gathered measures, we analyzed the average acceleration as a compartmentalized index to reveal the relationship between the distance headway and the following vehicle velocity in an acceleration stage and deceleration stage, the regression relationship between the response time of the following driver and the following vehicle velocity in the deceleration stage and the regression relationship among expected distance headway, headway and following velocity by means of mathematical statistics. We made out the relationship between the following vehicle acceleration and the distance headway, and the relationship between the following vehicle acceleration and the following vehicle velocity in a steady stage. And we validated these relationships using simulation tests.
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