Understanding and Modeling Driver Behavior in Dense Traffic Flow

We present in this report a new car-following theory that can reproduce both the so-called capacity drop and traffic hysteresis, two prominent features of multi-phase vehicular traffic flow. This is achieved through the introduction of a single variable, driver response time, that depends on both vehicle spacing and traffic motion. By specifying different functional forms of response time, one can obtain not only brand new theories but also some of the well-known old car-following theories, which is demonstrated in this report through both theoretical analyses and numerical simulation.