Dynamical phases and hysteresis in a simple one-lane traffic model

A two parameter model for single lane car-following is introduced and its equilibrium and non-equilibrium properties are studied. Despite its simplicity, this model exhibits a rich phenomenology, analogous to that observed in real traffic, 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 car flux that determines the hysteretic dependence of the fundamental flux-density diagram. Coexisting phase regimes are also evidenced so as propagating or stationary density waves. The model can be easily calibrated to reproduce experimental observations.