We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective is to minimise/maximise macroscopic quantities, such as traffic volume or average speed, controlling few agents, e.g. smart traffic lights and automated cars. The measure theoretic approach allows to study in a same setting local and non-local drivers interactions and to consider the control variables as additional measures interacting with the drivers distribution. We also propose a gradient descent adjoint-based optimisation method, obtained by deriving first-order optimality conditions for the control problem, and we provide some numerical experiments in the case of smart traffic lights for a 2–1 junction.

A measure theoretic approach to traffic flow optimization on networks / Cacace, Simone; Camilli, Fabio; DE MAIO, Raul; Tosin, Andrea. - In: EUROPEAN JOURNAL OF APPLIED MATHEMATICS. - ISSN 0956-7925. - 30:6(2019), pp. 1187-1209. [10.1017/S0956792518000621]

A measure theoretic approach to traffic flow optimization on networks

Simone Cacace
;
Fabio Camilli
;
Raul De Maio
;
2019

Abstract

We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective is to minimise/maximise macroscopic quantities, such as traffic volume or average speed, controlling few agents, e.g. smart traffic lights and automated cars. The measure theoretic approach allows to study in a same setting local and non-local drivers interactions and to consider the control variables as additional measures interacting with the drivers distribution. We also propose a gradient descent adjoint-based optimisation method, obtained by deriving first-order optimality conditions for the control problem, and we provide some numerical experiments in the case of smart traffic lights for a 2–1 junction.
Network; transport equation; measure-valued solutions; transmission conditions; optimisation
01 Pubblicazione su rivista::01a Articolo in rivista
A measure theoretic approach to traffic flow optimization on networks / Cacace, Simone; Camilli, Fabio; DE MAIO, Raul; Tosin, Andrea. - In: EUROPEAN JOURNAL OF APPLIED MATHEMATICS. - ISSN 0956-7925. - 30:6(2019), pp. 1187-1209. [10.1017/S0956792518000621]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1173399
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