  We show that all existing deterministic microscopic traffic models with
identical drivers (including both two-phase and three-phase models) can be
understood as special cases from a master model by expansion around
well-defined ground states. This allows two traffic models to be compared in a
well-defined way. The three-phase models are characterized by the vanishing of
leading orders of expansion within a certain density range, and as an example
the popular intelligent driver models (IDM) is shown to be equivalent to a
generalized optimal velocity (OV) model. We also explore the diverse solutions
of the generalized OV model that can be important both for understanding human
driving behaviors and algorithms for autonomous driverless vehicles.
