Simple traffic model as a space-time clustering phenomenon.

Abstract

We propose a new framework for analyzing vehicular traffic jams based on the space-time geometry of congestion. Using the simple but instructive model elementary cellular automaton rule 184 (ECA 184), we identify jammed regions as connected clusters in space-time and show that their statistical properties follow scaling laws characteristic of a percolation transition. Key traffic observables-including total delay, relaxation time, and jam lifetimes-exhibit consistent scaling behavior. We introduce an auxiliary quantity, termed "elementary jams," that serves as the basis for computing these observables and interpreting jam propagation. The simplicity of ECA 184 allows for efficient analysis and reveals structure that we believe generalizes to more complex traffic models. We outline how this percolation-based approach can be applied to models such as the Nagel-Schreckenberg model.