  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.
