Hysteresis and dynamical phases in a simple one-lane traffic model

A model for single-lane car-following is introduced and its equilibrium and non-equilibrium properties are studied. We modify the optimal velocity mod el in a way to include the mechanical response of each vehicle to its front car dynamics. Despite its simplicity, this model exhibits a rich phenomeno logy, like transitions between different dynamical regimes and hysteresis i n the fundamental flux-density diagram. We show that traffic jams can spont aneously appear in clustered-like structures. In the jammed phase, we obser ve a slow relaxation phenomenon ruled by the outgoing vehicle flux that det ermines the hysteretic dependence of the fundamental flux-density diagram. Coexisting phase regimes are also evidenced as propagating or stationary de nsity waves. The model can be easily calibrated to reproduce experimental o bservations.