Configurations of Wardrop's equilibrium and application to traffic analysis

dc.contributor
Universitat Autònoma de Barcelona. Departament de Matemàtiques
dc.contributor.author
Hatami, Farhad
dc.date.accessioned
2018-06-04T11:13:32Z
dc.date.available
2018-06-04T11:13:32Z
dc.date.issued
2018-05-07
dc.identifier.isbn
9788449079481
en_US
dc.identifier.uri
http://hdl.handle.net/10803/565891
dc.description.abstract
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.
en_US
dc.format.extent
99 p.
en_US
dc.format.mimetype
application/pdf
dc.language.iso
eng
en_US
dc.publisher
Universitat Autònoma de Barcelona
dc.rights.license
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/
dc.rights.uri
http://creativecommons.org/licenses/by-nc-nd/4.0/
*
dc.source
TDX (Tesis Doctorals en Xarxa)
dc.subject
Transpor òptim amb congestió
en_US
dc.subject
Transporte óptimo con congestión
en_US
dc.subject
Optimal transport with congestion
en_US
dc.subject
Modelatge de trànsit
en_US
dc.subject
Modelado de tráfico
en_US
dc.subject
Traffic modelling
en_US
dc.subject
PDE degenerat
en_US
dc.subject
PDE degenerado
en_US
dc.subject
Degenerat PDEs
en_US
dc.subject.other
Ciències Experimentals
en_US
dc.title
Configurations of Wardrop's equilibrium and application to traffic analysis
en_US
dc.type
info:eu-repo/semantics/doctoralThesis
dc.type
info:eu-repo/semantics/publishedVersion
dc.subject.udc
51
en_US
dc.contributor.authoremail
fhatami@mat.uab.cat
en_US
dc.contributor.director
Clop, Albert
dc.contributor.director
Ruiz de Villa Robert, Aleix
dc.embargo.terms
cap
en_US
dc.rights.accessLevel
info:eu-repo/semantics/openAccess


Documents

faha1de1.pdf

1.835Mb PDF

Aquest element apareix en la col·lecció o col·leccions següent(s)