2013/04/28 by Ke Han, Han, Ke, Terry L. Friesz +3
Engineering · Mathematics · Social Sciences · #90B10 #90B20 #91A10 #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC) #Traffic control and management #Transportation Planning and Optimization #Urban Transport and Accessibility #math.DS #math.OC #msc:90B10 #msc:90B20 #msc:91A10
paper · pdf · doi:10.48550/arxiv.1305.1276
19 pages. arXiv admin note: text overlap with arXiv:1211.4614, arXiv:1304.5286
arxiv created 2013/04/28 · openalex publication_date 2013/04/28 · arxiv updated 2019/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).