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Synchronized traffic plans and stability of optima

Marc Bernot;  Alessio Figalli — 2008

ESAIM: Control, Optimisation and Calculus of Variations

The irrigation problem is the problem of finding an efficient way to transport a measure μ onto a measure μ. By efficient, we mean that a structure that achieves the transport (which, following [Bernot, Caselles and Morel, (2005) 417–451], we call traffic plan) is better if it carries the mass in a grouped way rather than in a separate way. This is formalized by considering costs functionals that favorize this property. The aim of this paper is to introduce a dynamical cost functional...

Traffic plans.

Marc Bernot;  Vicent Caselles;  Jean-Michel Morel — 2005

Publicacions Matemàtiques

In recent research in the optimization of transportation networks, the problem was formalized as finding the optimal paths to transport a measure y+ onto a measure y- with the same mass. This approach is realistic for simple good distribution networks (water, electric power,. ..) but it is no more realistic when we want to specify who goes where, like in the mailing problem or the optimal urban traffic network problem. In this paper, we present a new framework generalizing the former approathes...

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