  Using the optimal velocity (OV) model as an example, we show that in the
non-linear regime there is an emergent quantity that gives the extremum
headways in the cluster formation, as well as the coexistence curve separating
the absolute stable phase from the metastable phase. This emergent quantity is
independent of the density of the traffic lane, and determines an intrinsic
scale that characterizes the dynamics of localized quasisoliton structures
given by the time derivative of the headways. The intrinsic scale is analogous
to the "charge" of quasisolitons that controls the strength of interaction
between multiple clusters, leading to non-trivial cluster statistics from
random perturbations to initial uniform traffic. The cluster statistics depend
both on the charge and the density of the traffic lane; the relationship is
qualitatively universal for general car-following models.
