TY - GEN

T1 - Traffic flow models on a network of roads

AU - Bressan, Alberto

N1 - Funding Information:
Acknowledgements This work was partially supported by NSF with grant DMS-1411786: “Hyperbolic Conservation Laws and Applications”.

PY - 2018

Y1 - 2018

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.

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

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

M3 - Conference contribution

AN - SCOPUS:85049362919

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

T2 - 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016

Y2 - 1 August 2016 through 5 August 2016

ER -