An Infinite-Dimensional Variational Inequality Formulation and Existence Result for Dynamic User Equilibrium with Elastic Demands

This paper is concerned with dynamic user equilibrium (DUE) with elastic travel demand (E-DUE). We present and prove a variational inequality (VI) formulation of E-DUE using measure-theoretic argument. Moreover, existence of the E-DUE is formally established with a version of Brouwer's fixed po...

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Bibliographic Details
Published inarXiv.org
Main Authors Han, Ke, Friesz, Terry L, Yao, Tao
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 28.04.2013
Subjects
Existence theorems
Fixed points (mathematics)
Hilbert space
Travel demand
Upper bounds
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Summary:This paper is concerned with dynamic user equilibrium (DUE) with elastic travel demand (E-DUE). We present and prove a variational inequality (VI) formulation of E-DUE using measure-theoretic argument. Moreover, existence of the E-DUE is formally established with a version of Brouwer's fixed point theorem in a properly defined Hilbert space. The existence proof requires the effective delay operator to be continuous, a regularity condition also needed to ensure the existence of DUE with fixed demand (Han et al., 2013c). Our proof does not invoke the a priori upper bound of the departure rates (path flows).
ISSN:2331-8422