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A measure theoretic approach to traffic flow optimisation on networks

Part of: Existence theories Partial differential equations, initial value and time-dependent initial-boundary value problems Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  16 October 2018

SIMONE CACACE ,
FABIO CAMILLI ,
RAUL DE MAIO  and
ANDREA TOSIN Open the ORCID record for ANDREA TOSIN [Opens in a new window]
SIMONE CACACE
Affiliation:
Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, L. go S. Leonardo Murialdo 1, 00146 Roma, Italy email: cacace@mat.uniroma3.it
FABIO CAMILLI
Affiliation:
Dipartimento di Scienze di Base e Applicate per l’Ingegneria, “Sapienza” Università di Roma, Via Scarpa 16, 00161 Roma, Italy emails: camilli@sbai.uniroma1.it; raul.demaio@sbai.uniroma1.it
RAUL DE MAIO
Affiliation:
Dipartimento di Scienze di Base e Applicate per l’Ingegneria, “Sapienza” Università di Roma, Via Scarpa 16, 00161 Roma, Italy emails: camilli@sbai.uniroma1.it; raul.demaio@sbai.uniroma1.it
ANDREA TOSIN*
Affiliation:
Dipartimento di Scienze Matematiche “G. L. Lagrange”, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy email: andrea.tosin@polito.it
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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 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.

Keywords

Networktransport equationmeasure-valued solutionstransmission conditionsoptimisation

MSC classification

Primary: 49J20: Optimal control problems involving partial differential equations
Secondary: 35R02: Partial differential equations on graphs and networks (ramified or polygonal spaces) 65M99: None of the above, but in this section
Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Special Issue 6: Applied Optimal Transport , December 2019 , pp. 1187 - 1209
Copyright
© Cambridge University Press 2018 

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