Optimal regions for congested transport

Buttazzo, Giuseppe; Carlier, Guillaume; Lo Bianco, Serena Guarino

doi:10.1051/m2an/2015022

Buttazzo, Giuseppe ¹ ; Carlier, Guillaume ² ; Lo Bianco, Serena Guarino ¹

¹ Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56126 Pisa, Italy.
² CEREMADE UMR CNRS 7534, Université de Paris Dauphine, Pl. de Lattre de Tassigny, 75775 Paris cedex 16, France.

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 6, pp. 1607-1619.

Résumé

We consider a given region $Ω$ where the traffic flows according to two regimes: in a region $C$ we have a low congestion, where in the remaining part $Ω ∖ C$ the congestion is higher. The two congestion functions $H_{1}$ and $H_{2}$ are given, but the region $C$ has to be determined in an optimal way in order to minimize the total transportation cost. Various penalization terms on $C$ are considered and some numerical computations are shown.

Reçu le : 2015-03-20

MR Zbl

DOI : 10.1051/m2an/2015022

Classification : 49Q20, 49Q10, 90B20
Mots clés : Shape optimization, transport problems, congestion effects, optimal networks

Affiliations des auteurs :

Buttazzo, Giuseppe ¹ ; Carlier, Guillaume ² ; Lo Bianco, Serena Guarino ¹

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     publisher = {EDP-Sciences},
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     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2015022/}
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Buttazzo, Giuseppe; Carlier, Guillaume; Lo Bianco, Serena Guarino. Optimal regions for congested transport. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 6, pp. 1607-1619. doi : 10.1051/m2an/2015022. http://www.numdam.org/articles/10.1051/m2an/2015022/

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