Optimal regions for congested transport

Guillaume Carlier (1, 2) , Giuseppe Buttazzo (3) , Serena Guarino Lo Bianco (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
3 Dipartimento di Matematica [Pisa]

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 H1 and H2 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.

Mots clés: Shape optimization; transport problems; congestion e ects; optimal networks

Domaines: Equations aux dérivées partielles [math.AP]

Guillaume Carlier, Giuseppe Buttazzo, Serena Guarino Lo Bianco. Optimal regions for congested transport. 2015. ⟨hal-01112233⟩