### Abstract

Macroscopic models of traffic flow on a network of roads can be formulated in terms of a scalar conservation law on each road, together with boundary conditions, determining the flow at junctions. Some of these intersection models are reviewed in this note, discussing the well posedness of the resulting initial value problems. From a practical point of view, one can also study traffic patterns as the outcome of many decision problems, where each driver chooses his departure time and route to destination, in order to minimize the sum of a departure and an arrival cost. For the new models including a buffer at each intersection, one can prove: (i) the existence of a globally optimal solution, minimizing the total cost to all drivers, and (ii) the existence of a Nash equilibrium solution, where no driver can lower his own cost by changing his departure time or the route taken to reach destination.

Original language | English (US) |
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Title of host publication | Theory, Numerics and Applications of Hyperbolic Problems I - Aachen, Germany, 2016 |

Editors | Michael Westdickenberg, Christian Klingenberg |

Publisher | Springer New York LLC |

Pages | 237-248 |

Number of pages | 12 |

ISBN (Print) | 9783319915449 |

DOIs | |

State | Published - Jan 1 2018 |

Event | 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016 - Aachen, Germany Duration: Aug 1 2016 → Aug 5 2016 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 236 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Other

Other | 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016 |
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Country | Germany |

City | Aachen |

Period | 8/1/16 → 8/5/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Theory, Numerics and Applications of Hyperbolic Problems I - Aachen, Germany, 2016*(pp. 237-248). (Springer Proceedings in Mathematics and Statistics; Vol. 236). Springer New York LLC. https://doi.org/10.1007/978-3-319-91545-6_19

}

*Theory, Numerics and Applications of Hyperbolic Problems I - Aachen, Germany, 2016.*Springer Proceedings in Mathematics and Statistics, vol. 236, Springer New York LLC, pp. 237-248, 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016, Aachen, Germany, 8/1/16. https://doi.org/10.1007/978-3-319-91545-6_19

**Traffic flow models on a network of roads.** / Bressan, Alberto.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Traffic flow models on a network of roads

AU - Bressan, Alberto

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Macroscopic models of traffic flow on a network of roads can be formulated in terms of a scalar conservation law on each road, together with boundary conditions, determining the flow at junctions. Some of these intersection models are reviewed in this note, discussing the well posedness of the resulting initial value problems. From a practical point of view, one can also study traffic patterns as the outcome of many decision problems, where each driver chooses his departure time and route to destination, in order to minimize the sum of a departure and an arrival cost. For the new models including a buffer at each intersection, one can prove: (i) the existence of a globally optimal solution, minimizing the total cost to all drivers, and (ii) the existence of a Nash equilibrium solution, where no driver can lower his own cost by changing his departure time or the route taken to reach destination.

AB - Macroscopic models of traffic flow on a network of roads can be formulated in terms of a scalar conservation law on each road, together with boundary conditions, determining the flow at junctions. Some of these intersection models are reviewed in this note, discussing the well posedness of the resulting initial value problems. From a practical point of view, one can also study traffic patterns as the outcome of many decision problems, where each driver chooses his departure time and route to destination, in order to minimize the sum of a departure and an arrival cost. For the new models including a buffer at each intersection, one can prove: (i) the existence of a globally optimal solution, minimizing the total cost to all drivers, and (ii) the existence of a Nash equilibrium solution, where no driver can lower his own cost by changing his departure time or the route taken to reach destination.

UR - http://www.scopus.com/inward/record.url?scp=85049362919&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049362919&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-91545-6_19

DO - 10.1007/978-3-319-91545-6_19

M3 - Conference contribution

SN - 9783319915449

T3 - Springer Proceedings in Mathematics and Statistics

SP - 237

EP - 248

BT - Theory, Numerics and Applications of Hyperbolic Problems I - Aachen, Germany, 2016

A2 - Westdickenberg, Michael

A2 - Klingenberg, Christian

PB - Springer New York LLC

ER -