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References (9)
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Tim Austin, I. Benjamini (2006)
For what number of cars must self organization occur in the Biham-Middleton-Levine traffic model from any possible starting configuration?arXiv: Combinatorics
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R. D’Souza (2004)
Geometric structure of coexisting phases found in the Biham-Middleton-Levine traffic modelarXiv: Statistical Mechanics
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O. Biham, A. Middleton, D. Levine (1992)
Self-organization and a dynamical transition in traffic-flow models.Physical review. A, Atomic, molecular, and optical physics, 46 10
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Starting at N −M −2 there is a sequence of K 1 ≥ min(s B , s R ) places for which R i = 1; B i = 0 -
Omer Angel, A. Holroyd, James Martin (2005)
The Jammed Phase of the Biham-Middleton-Levine Traffic ModelElectronic Communications in Probability, 10
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1 − 2 (i.e. right after the red sequence) there is a sequence of K 2 ≥ min(s B , s R ) places for which B i = 1 -
without the risk of getting lost in the indices. For the full proof, first get from lemma 3.7 that: 1. B i = 0 for i -
1 is empty -i.e. R i = B i = 0 -
There are no additional cars are at
- Publisher
- Birkhäuser Basel
- Copyright
- © Birkhäuser Basel 2008
- ISBN
- 978-3-7643-8785-3
- Pages
- 97 –116
- DOI
- 10.1007/978-3-7643-8786-0_5
- Publisher site
- See Chapter on Publisher Site
Abstract
[In the Biham-Middleton-Levine traffic model cars are placed in some density p on a two dimensional torus, and move according to a (simple) set of predefined rules. Computer simulations show this system exhibits many interesting phenomena: for low densities the system self organizes such that cars flow freely while for densities higher than some critical density the system gets stuck in an endless traffic jam. However, apart from the simulation results very few properties of the system were proven rigorously to date. We introduce a simplified version of this model in which cars are placed in a single row and column (a junction) and show that similar phenomena of self-organization of the system and phase transition still occur.]
Published: Jan 1, 2008
Keywords: Traffic; phase transition; cellular automata; 60K35