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Minimax Theory and its Applications 06 (2021), No. 2, 205--226
Copyright Heldermann Verlag 2021

On Optimization of Traffic Flow Performance for Conservation Laws on Networks

Fabio Ancona
Dip. di Matematica "Tullio Levi-Civita", UniversitÓ di Padova, 35121 Padova, Italy

Annalisa Cesaroni
Dipartimento di Scienze Statistiche, UniversitÓ di Padova, 35121 Padova, Italy

Giuseppe M. Coclite
Dip. di Meccanica, Matematica e Management, Politecnico di Bari, 70125 Bari, Italy

Mauro Garavello
Dip. di Matematica e Applicazioni, UniversitÓ di Milano Bicocca, 20125 Milano, Italy

We investigate several optimization problems related to different traffic performance indexes considered in the literature: to diminuish mean travel time or queue lengths, to minimise stop-and-go waves, or to get a fuel consumption reduction. We analyze these problems within the general control setup for conservation law models on networks recently proposed by the authors [On the optimization of conservation law models at a junction with inflow and flow distribution controls, SIAM J. Control Optimization 56 (2018) 3370--3403]. The existence of optimal solutions for the above mentioned problems is obtained in the context of distribution and inflow controls acting at a single junction. A variational formulation of such optimization problems is also provided and some numerical simulations of optimal solutions are discussed.

Keywords: Conservation laws, traffic models, networks, weak solutions.

MSC: 35F25, 35L65, 90B20.

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