Evidence of Non-Equilibrium Critical Phenomena in a Simple Model of Traffic

TL;DR

This paper investigates traffic jams using a simple cellular automaton model, revealing non-equilibrium critical phenomena analogous to phase transitions, and introduces efficient algorithms and new observables for analysis.

Contribution

It develops a novel approach with specific observables and algorithms to characterize traffic flow and jams in a simple automaton model, linking to phase transition concepts.

Findings

Traffic jams exhibit features similar to continuous phase transitions.

The introduced 'elementary jams' enable efficient calculation of system observables.

Results suggest potential for a field-theoretic description of traffic phenomena.

Abstract

We present a novel approach to understand vehicular traffic jams by studying a simple model, Elementary Cellular Automaton Rule 184 (ECA 184). Using key traffic observables, such as the total delay and relaxation time, as well as microscopic measures like delays and lifetimes of individual jams, we show how these quantities can fully characterize the system's behavior, revealing features analogous to those of a continuous phase transition. We exploit specific properties of ECA 184 to develop an efficient algorithm for calculating these observables numerically and introduce an auxiliary quantity, termed ''elementary jams'', which allows us to determine these observables. We discuss the implications of our results, highlighting connections to a potential field-theoretic description of traffic and suggest future application of these methods to more complex models. Supporting code can be found on: https://github.com/Aryaman-Jha/ECA_184_Critical