TRAFFIC PLANS

In recent research in the optimization of transportation networks, the problem was formalized as finding the optimal paths to transport a measure μ⁺ onto a measure μ⁻ 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 approaches and permitting to solve the optimal transport problem under the "who goes where" constraint. This constraint is formalized as a transference plan from μ⁺ to μ⁻ which we handle as a boundary condition for the "optimal traffic problem".