Network User Equilibrium with Elastic Demand: Formulation, Qualitative Analysis and Computation∗

This paper presents an elastic demand extension of the fixed-demand simultaneous routeand-departure choice dynamic user equilibrium model originally presented in Friesz et al. (1993). Although Friesz et al. (2011) show that analysis and computation of dynamic user equilibrium with constant travel demand is tremendously simplified by stating it as a a differential variational inequality (DVI), they do not discuss how elastic demand may be accommodated within a DVI framework. The DVI formulation of elastic demand DUE (E-DUE) is not straightforward. In this paper, we advance knowledge of E-DUE in its mathematical formulation, existence, and computation. We first present an infinite-dimensional variational inequality formulation in a Hilbert space using measure-theoretic argument. Existence result for such variational inequality is show by invoking a version of Brouwer’s fixed point theorem (Browder, 1968). Finally, we employ the mathematical paradigm of differential variational inequality to formally establish a fixed point formulation of E-DUE in an extended Hilbert ∗The complete work is reported in two papers available at http://arxiv.org/abs/1304.5286 and http://arxiv.org/abs/1305.1276