Work

The Jammed Phase of the Biham-Middleton-Levine Traffic Model

Year: 2005

Type: article

Abstract: Initially a car is placed with probability $p$ at each site of the two-dimensional integer lattice. Each car is equally likely to be East-facing or North-facing, and different sites receive independent assignments. At odd time steps, each North-facing car moves one unit North if there is a vacant site for it to move into. At even time steps, East-facing cars move East in the same way. We prove that when $p$ is sufficiently close to 1 traffic is jammed, in the sense that no car moves infinitely many times. The result extends to several variant settings, including a model with cars moving at random times, and higher dimensions.

Source: Electronic Communications in Probability

DOI: 10.1214/ecp.v10-1148

Authors: Omer Angel, Alexander Holroyd, James Martin

Institutions: University of British Columbia, Centre National de la Recherche Scientifique, Université Paris Diderot

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

SDG: Sustainable cities and communities

Open Access status: gold

Estimated APC paid: $675