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This paper is concerned with dynamic user equilibrium (DUE) with elastictravel demand (E-DUE). We present and prove a variational inequality (VI)formulation of E-DUE using measure-theoretic argument. Moreover, existence ofthe E-DUE is formally established with a version of Brouwer's fixed pointtheorem in a properly defined Hilbert space. The existence proof requires theeffective delay operator to be continuous, a regularity condition also neededto ensure the existence of DUE with fixed demand (Han et al., 2013c). Our proofdoes not invoke the a priori upper bound of the departure rates (path flows).

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