### Abstract

Original language | English |
---|---|

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 |
---|---|

Volume | 26 |

### Cite this

*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

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*Progress in Industrial Mathematics at ECMI 2016.*vol. 26, Springer, Mathematics in Industry, vol. 26, pp. 375-382, 19th European Conference on Mathematics for Industry

, Santiago de Compostela, Spain, 13/06/2016. https://doi.org/10.1007/978-3-319-63082-3_59

**A General Microscopic Traffic Model Yielding Dissipative Shocks.** / Gaididei, Yuri Borisovich; Caputo, Jean Guy; Christiansen, Peter Leth; Rasmussen, Jens Juul; Sørensen, Mads.

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

TY - GEN

T1 - A General Microscopic Traffic Model Yielding Dissipative Shocks

AU - Gaididei, Yuri Borisovich

AU - Caputo, Jean Guy

AU - Christiansen, Peter Leth

AU - Rasmussen, Jens Juul

AU - Sørensen, Mads

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-319-63082-3_59

DO - 10.1007/978-3-319-63082-3_59

M3 - Article in proceedings

SN - 9783319630823

VL - 26

SP - 375

EP - 382

BT - Progress in Industrial Mathematics at ECMI 2016

PB - Springer

ER -