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**Circulation of car traffic in congested urban areas.**
*(English)*
Zbl 1158.35386

Summary: The aim of this work is to understand how urban traffic behavior, especially in cases of congestion, can be improved by an accurate choice of traffic coefficients. For this, we define three cost functionals that measure average velocity, average travelling time and total flux of cars. The global optimal control problem for a complex network is difficult to solve both from analytical and numerical points of view. Thus, we focus on a simple junction with one incoming road and two outgoing roads (junctions of \(1\times 2\) type), obtaining exact solutions to a simple optimization problem. Then, we use such results at each node of the network. The traffic evolution of some networks is then studied via simulations. In particular, it is shown that an appropriate choice of the traffic distributions can be useful in order to improve network conditions.

### MSC:

35L65 | Hyperbolic conservation laws |

49J20 | Existence theories for optimal control problems involving partial differential equations |

76N25 | Flow control and optimization for compressible fluids and gas dynamics |

90B20 | Traffic problems in operations research |

35B37 | PDE in connection with control problems (MSC2000) |