A car-following theory for multiphase vehicular traffic flow

We present in this paper a new car-following theory that can reproduce 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, gap-time, that depends on both vehicle gap-distance and traffic phase. By specifying different functional forms of gap-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 analysis and numerical simulation.