Continuously variable spreading exponents in the absorbing Nagel–Schreckenberg model

Abstract

I study the critical behavior of a traffic model with an absorbing state. The model is a variant of the Nagel–Schreckenberg (NS) model, in which drivers do not decelerate if their speed is smaller than their headway, the number of empty sites between them and the car ahead. This makes the free-flow state (i.e. all vehicles traveling at the maximum speed, vmax, and with all headways greater than vmax) absorbing; such states are possible for densities ρ smaller than a critical value . Drivers with nonzero velocity, and with headway equal to velocity, decelerate with probability p. This absorbing Nagel–Schreckenberg (ANS) model, introduced in Iannini and Dickman (2017 Phys. Rev. E 95 022106), exhibits a line of continuous absorbing-state phase transitions in the ρ-p plane. Here I study the propagation of activity from a localized seed, and find that the active cluster is compact, as is the active region at long times, starting from uniformly distributed activity. The critical exponents δ (governing the decay of the survival probability) and η (governing the growth of activity) vary continuously along the critical curve. The exponents satisfy a hyperscaling relation associated with compact growth.