A car-following theory for multiphase vehicular traffic flow

We present in this paper a new car-following theory that can produce both the so-called capacity drop and traffic hysteresis, two prominent features of multiphase vehicular traffic flow. This is achieved through the introduction of a single variable, driver response time, that depends on both vehicle spacing and traffic phase. 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 paper through both theoretical analyses and numerical simulation.