A traffic model with an absorbing-state phase transition

TL;DR

This paper introduces a modified traffic flow model with an absorbing-state phase transition, revealing a reentrant phase diagram and a surprising link to stochastic sandpile models, enhancing understanding of traffic dynamics.

Contribution

The study proposes a new traffic model modification that clarifies the phase transition mechanism and uncovers a novel connection to stochastic sandpile models.

Findings

The free-flow state is absorbing below a critical density.

The phase diagram is reentrant in the density-probability plane.

A connection between traffic models and stochastic sandpiles is identified.

Abstract

We consider a modified Nagel-Schreckenberg (NS) model in which drivers do not decelerate if their speed is smaller than the headway (number of empty sites to the car ahead). (In the original NS model, such a reduction in speed occurs with probability $p$, independent of the headway, as long as the current speed is greater than zero.) In the modified model the free-flow state (with all vehicles traveling at the maximum speed, $v_{max}$) is {\it absorbing} for densities $\rho$ smaller than a critical value $\rho_c = 1/(v_{max} + 2)$. The phase diagram in the $\rho - p$ plane is reentrant: for densities in the range $\rho_{c,<} < \rho < \rho_c$, both small and large values of $p$ favor free flow, while for intermediate values, a nonzero fraction of vehicles have speeds $< v_{max}$. In addition to representing a more realistic description of driving behavior, this change leads to a better understanding of the phase transition in the original model. Our results suggest an unexpected connection between traffic models and stochastic sandpiles.