Power laws and phase transitions in heterogenous car following with reaction times

We study the effect of reaction times on kinetics relaxation to stationary states and congestion transitions in heterogeneous traffic using simulations Newell's model a ring. Heterogeneity is modeled as quenched disorders parameters time drivers. observed that at low densities, state from homogeneous initial governed by same power laws derived E. Ben-Naim et al., Kinetics clustering flow, Phys. Rev. E 50, 822 (1994). The state, single giant platoon vehicles with slowest vehicle being leader platoon. formation spontaneous jams inside which move upstream stop-go waves dissipate its tail. transition happens when head starts interacting tail, stable form, circulate ring without dissipating. system behaves differently point approached above than it does below. When density below, gap distribution behind has double peak fat-tailed but bounded support thus maximum variance tend size-independent values. above, becomes law and, consequently, gaps diverge law, thereby creating discontinuity transition. Thus, we observe phase unusual kind both are density. These features vanish absence time, i.e., react instantaneously perturbation ahead (e.g., automated driving). Overall, conclude nonzero drivers significantly change behavior free flow while doesn't alter state.