## Electronic Communications in Probability

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

#### 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.

#### Article information

Source
Electron. Commun. Probab. Volume 10 (2005), paper no. 17, 167-178.

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

http://projecteuclid.org/euclid.ecp/1465058082

Digital Object Identifier
doi:10.1214/ECP.v10-1148

Mathematical Reviews number (MathSciNet)
MR2162816

Zentralblatt MATH identifier
1111.60067

Rights

#### Citation

Angel, Omer; Holroyd, Alexander; Martin, James. The Jammed Phase of the Biham-Middleton-Levine Traffic Model. Electron. Commun. Probab. 10 (2005), paper no. 17, 167--178. doi:10.1214/ECP.v10-1148. http://projecteuclid.org/euclid.ecp/1465058082.

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