Hysteretic Cell Transmission Model

A new macroscopic model for traffic in freeways, the Hysteretic Cell Transmission Model (HCTM), is presented. The model is based on the Cell Transmission Model (CTM) and incorporates a feature to reproduce the capacity drop phenomenon observed in real traffic. An auxiliary dynamic state is included that induces hysteretic behavior on the density-flow relationship. The hysteresis is dependent on the time derivative of the density in a particular cell and allows to change the congested flow traffic wave velocity in the fundamental diagram and, with this, to produce a capacity drop. A Lyapunov stability analysis for a stretch of highway is presented that is compared with a similar analysis for the CTM. Simulation results show that the capacity of a congested stretch of highway is reduced when its vehicular density is decreasing.