Cluster statistics and quasisoliton dynamics in microscopic optimal-velocity models

Using the non-linear optimal velocity models as an example, we show that there exists an emergent intrinsic scale that characterizes the interaction strength between multiple clusters appearing in the solutions of such models. The interaction characterizes the dynamics of the localized quasisoliton structures given by the time derivative of the headways, and the intrinsic scale is analogous to the "charge" of the quasisolitons, leading to non-trivial cluster statistics from the random perturbations to the initial steady states of uniform headways. The cluster statistics depend both on the quasisoliton charge and the density of the traffic. The intrinsic scale is also related to 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. The relationship is qualitatively universal for general optimal velocity models.