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

TL;DR

This paper develops a measure-theoretic variational inequality formulation for dynamic user equilibrium with elastic demands and proves its existence using fixed point theory, without requiring upper bounds on departure rates.

Contribution

It introduces a novel VI formulation for E-DUE and establishes its existence under mild regularity conditions, extending prior fixed-demand results.

Findings

VI formulation for E-DUE established

Existence proof using Brouwer's fixed point theorem

No need for upper bounds on departure rates

Abstract

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).