For what number of cars must self organization occur in the Biham-Middleton-Levine traffic model from any possible starting configuration?

2006/07/31 by Tim Austin, Tim D. Austin, Itai Benjamini +3 · 2 citations
Engineering · Mathematics · Physics and Astronomy · Social Sciences · #60C05 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Stochastic processes and statistical mechanics #Traffic control and management #Transportation Planning and Optimization #math-ph #math.CO #math.MP #msc:60C05

paper · pdf · doi:10.48550/arxiv.math/0607759

4 pages

openalex publication_date 2006/07/31 · arxiv created 2006/08/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any initial configuration of fewer than N/2 cars the BML model will self organize to attain speed one. On the other hand, there is a configuration of size m in which no car can move if and only if m is at least 2N.

Cited by

• Periodic states, local effects and coexistence in the BML traffic jam model
• Structure and dynamics in the low-density phase of a two-dimensional cellular automaton model of traffic flow

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