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The Jammed Phase of the Biham-Middleton-Levine Traffic Model
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Omer Angel, University of British Columbia, Canada
Alexander E. Holroyd, University of British Columbia, Canada
James B. Martin, CNRS and Université Paris 7, France
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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.
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Full text: PDF
Pages: 167-178
Published on: August 12, 2005
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Electronic Communications in Probability. ISSN: 1083-589X |
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