Dissertation/ Thesis
Configurations of Wardrop's equilibrium and application to traffic analysis
| العنوان: | Configurations of Wardrop's equilibrium and application to traffic analysis |
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| المؤلفون: | Hatami, Farhad |
| المساهمون: | University/Department: Universitat Autònoma de Barcelona. Departament de Matemàtiques |
| Thesis Advisors: | Clop, Albert, Ruiz de Villa Robert, Aleix |
| المصدر: | TDX (Tesis Doctorals en Xarxa) |
| بيانات النشر: | Universitat Autònoma de Barcelona, 2018. |
| سنة النشر: | 2018 |
| وصف مادي: | 99 p. |
| مصطلحات موضوعية: | Transpor òptim amb congestió, Transporte óptimo con congestión, Optimal transport with congestion, Modelatge de trànsit, Modelado de tráfico, Traffic modelling, PDE degenerat, PDE degenerado, Degenerat PDEs, Ciències Experimentals |
| الوصف: | This thesis consists of two parts, and the connection between them is the so-called Wardrop's equilibrium. In the rst part of this thesis, which is the theoretical part, we study the congested transport dynamics arising from a non-autonomous tra c optimization problem. In this setting, we prove one can nd an optimal tra c strategy with support on the trajectories of a DiPerna-Lions ow. 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 satis ed only away from a ball of the gradient variable. We are then able to nd the con guration of Wardrop's equilibrium. In the second part of this thesis, which is the practical part, we use the established Wardrop's equi- librium in the theoretical section, in order to optimize the tra c problem in rel-life application. New OD demand problem formulation is explored which allows the modeler to de ne 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 de ne distance function between historical and estimated OD matrix, in order to minimize estimation vari- ance, and ensure the estimated OD matrix is close to true value. The presented OD estimation models reduce dimensionality of the OD demand vector, which is crucial when the dimensionality of OD ma- trix is high, due to high level of 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. |
| نوع الوثيقة: | Dissertation/Thesis |
| وصف الملف: | application/pdf |
| اللغة: | English |
| ردمك: | 978-84-490-7948-1 84-490-7948-9 |
| URL الوصول: | http://hdl.handle.net/10803/565891 |
| Rights: | L'accés als continguts d'aquesta tesi queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| رقم الانضمام: | edstdx.10803.565891 |
| قاعدة البيانات: | TDX |
| ردمك: | 9788449079481 8449079489 |
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