Resumen de Configurations of wardrop’s equilibrium and application to traffic analysis
Farhad Hatami
This thesis consists of two parts, and the connection between them is the so-called Wardrop’s equilibrium. In the first part of this thesis, which is the theoretical part, we study the congested transport dynamics arising from a non-autonomous traffic optimization problem. In this setting, we prove one can find an optimal traffic strategy with support on the trajectories of a DiPerna-Lions flow. The proof follows the scheme introduced by Brasco, Carlier, and Santambrogio in the autonomous setting, applied to the case of supercritical Sobolev dependence in the spatial variable. This requires both Lipschitz and weighted Sobolev apriori bounds for the minimizers of a class of integral functionals whose ellipticity bounds are satisfied only away from a ball of the gradient variable. We are then able to find the configuration of Wardrop’s equilibrium.
In the second part of this thesis, which is the practical part, we use the established Wardrop’s equilibrium in the theoretical section, in order to optimize the traffic problem in the real-life application. New OD demand problem formulation is explored which allows the modeller to define structural similarity between the historical and estimated OD matrix while ensuring computationally fast and tractable solution. Shrinkage regression methods, such as Ridge and Lasso regression, are proposed to define distance function between historical and estimated OD matrix, in order to minimize estimation variance, and ensure the estimated OD matrix is close to true value. The presented OD estimation models reduce the dimensionality of the OD demand vector, which is crucial when the dimensionality of OD matrix is high, due to a high level of the zoning system. A new solution approach based on the well-known gradient descent algorithm is applied to solve the proposed models. Finally, results are tested out on a real life-size network.
