### Abstract

We consider a general microscopic traffic model with a delay. An algebraic traffic function reduces the equation to the Aw-Rascle microscopic model while a sigmoid function gives the standard “follow the leader”. For zero delay we prove that the homogeneous solution is globally stable. For a positive delay, it becomes unstable and develops dispersive and dissipative shocks. These are followed by a finite time singularity for the algebraic traffic function and by kinks for the sigmoid function.

Original language | English |
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Title of host publication | Progress in Industrial Mathematics at ECMI 2016 |

Volume | 26 |

Publisher | Springer |

Publication date | 2018 |

Pages | 375-382 |

ISBN (Print) | 9783319630823 |

DOIs | |

Publication status | Published - 2018 |

Event | 19th European Conference on Mathematics for Industry - Rúa Lope Gómez de Marzoa, s/n, Campus Vida, Santiago de Compostela, Spain Duration: 13 Jun 2016 → 17 Jun 2016 |

### Conference

Conference | 19th European Conference on Mathematics for Industry |
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Location | Rúa Lope Gómez de Marzoa, s/n, Campus Vida |

Country | Spain |

City | Santiago de Compostela |

Period | 13/06/2016 → 17/06/2016 |

Series | Mathematics in Industry |
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Volume | 26 |

## Cite this

Gaididei, Y. B., Caputo, J. G., Christiansen, P. L., Rasmussen, J. J., & Sørensen, M. (2018). A General Microscopic Traffic Model Yielding Dissipative Shocks. In

*Progress in Industrial Mathematics at ECMI 2016*(Vol. 26, pp. 375-382). Springer. Mathematics in Industry, Vol.. 26 https://doi.org/10.1007/978-3-319-63082-3_59