We show that in the non-linear regime of the optimal velocity model, 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 the width of the transition region from the minimum headways (or clusters) to the maximum headways (or anti-clusters). The width also gives an intrinsic scale that controls the strength of interaction between multiple clusters. This leads to non-trivial cluster statistics from random initial perturbations, and the statistics also depends on the density of the traffic lane. We conjecture these aspects are universal features for various different car-following models.
Cluster Statistics and Universal Aspects of the Optimal Velocity Model in the Non-Linear Regime
B Yang, X Xu, Z.F. Pang, C Monterola