Open Access
2005 The Jammed Phase of the Biham-Middleton-Levine Traffic Model
Omer Angel, Alexander Holroyd, James Martin
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Electron. Commun. Probab. 10: 167-178 (2005). DOI: 10.1214/ECP.v10-1148


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.


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Omer Angel. Alexander Holroyd. James Martin. "The Jammed Phase of the Biham-Middleton-Levine Traffic Model." Electron. Commun. Probab. 10 167 - 178, 2005.


Accepted: 12 August 2005; Published: 2005
First available in Project Euclid: 4 June 2016

zbMATH: 1111.60067
MathSciNet: MR2162816
Digital Object Identifier: 10.1214/ECP.v10-1148

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