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arXiv · 1803.00953

A measure theoretic approach to traffic flow optimization on networks

Simone Cacace·Fabio Camilli·Raul De Maio·Andrea Tosin
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Abstract

We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective isto minimise/maximise macroscopic quantities, such as traffic volume or average speed,controlling few agents, for example smart traffic lights and automated cars. The measuretheoretic approach allows to study in a same setting local and nonlocal drivers interactionsand to consider the control variables as additional measures interacting with the driversdistribution. We also propose a gradient descent adjoint-based optimization method, ob-tained by deriving first-order optimality conditions for the control problem, and we providesome numerical experiments in the case of smart traffic lights for a 2-1 junction.

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Simone Cacace, Fabio Camilli, Raul De Maio, Andrea Tosin. 2018-03-02. A measure theoretic approach to traffic flow optimization on networks. https://doi.org/10.1017/s0956792518000621

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