The Biham-Middleton-Levine traffic model for a single junction

2007/03/07 by Itai Benjamini, Itaï Benjamini, Benjamini, Itai +4
Engineering · Mathematics · #60K35 #Advanced Optical Network Technologies #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR) #Traffic control and management #math.DS #math.PR #msc:60K35

paper · pdf · doi:10.48550/arxiv.math/0703201

21 pages, 9 figures

openalex publication_date 2007/03/07 · arxiv created 2007/09/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the Biham-Middleton-Levine traffic model cars are placed with some density p on a two dimensional torus, and move according to a (simple) set of predefined rules. Computer simulations show this system exhibits many interesting phenomena: for low densities the system self organizes such that cars flow freely while for densities higher than some critical density the system gets stuck in an endless traffic jam. However, apart from the simulation results very few properties of the system were proven rigorously to date. We introduce a simplified version of this model in which cars are placed in a single row and column (a junction) and show that similar phenomena of self-organization of the system and phase transition still occur.

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• Possible Self-Organised Criticality and Dynamical Clustering of Traffic flow in Open Systems
• Self-organization in BML Traffic Flow Model: Analytical Approaches