## Abstract

In this paper we investigate a cellular automaton model associated with traffic flow and of which the mathematical solution is unknown before. We classify all kinds of stationary states and show that every state finally evolves to a stationary state. The obtained flow-density relation shows multiple branches corresponding to the stationary states in congested phases, which are essentially due to the slow-to-start effect introduced into this model. The stability of these states is formulated by a series of lemmas, and an algorithm is given to calculate the stationary state that the current state finally evolves to. This algorithm has a computational requirement in proportion to the number of cars.

Original language | English |
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Pages (from-to) | 2904-2917 |

Number of pages | 14 |

Journal | Discrete Applied Mathematics |

Volume | 157 |

Issue number | 13 |

DOIs | |

Publication status | Published - 2009 Jul 6 |

## Keywords

- Cellular automaton
- Flow-density
- Metastable states
- Multiple branches
- Traffic flow

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics