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 model in a way to include the mechanical response of each vehicle to its front car dynamics. Despite its simplicity, this model exhibits a rich phenomenology, like transitions between different dynamical regimes and hysteresis in the fundamental flux-density diagram. We show that traffic jams can spontaneously appear in clustered-like structures. In the jammed phase, we observe a slow relaxation phenomenon ruled by the outgoing vehicle flux that determines the hysteretic dependence of the fundamental flux-density diagram. Coexisting phase regimes are also evidenced as propagating or stationary density waves. The model can be easily calibrated to reproduce experimental observations.