TY - GEN
T1 - Traffic flow models on a network of roads
AU - Bressan, Alberto
N1 - Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.
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 -