## 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.

Original language | English |
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Title of host publication | Progress in Probability |

Publisher | Birkhauser |

Pages | 97-116 |

Number of pages | 20 |

DOIs | |

State | Published - 2008 |

Externally published | Yes |

### Publication series

Name | Progress in Probability |
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Volume | 60 |

ISSN (Print) | 1050-6977 |

ISSN (Electronic) | 2297-0428 |

### Bibliographical note

Publisher Copyright:© 2008, Birkhäuser Verlag Basel/Switzerland.

## Keywords

- Traffic
- cellular automata
- phase transition