Existence of simultaneous route and departure choice dynamic user equilibrium

TL;DR

This paper proves the existence of a dynamic user equilibrium in transportation networks considering simultaneous route and departure choices, using advanced mathematical models and the generalized Vickrey model.

Contribution

It establishes the existence of SRDC-DUE in continuous time without requiring a priori bounds on path flows, extending previous theoretical results.

Findings

Proves existence of SRDC-DUE in continuous time.

Uses generalized Vickrey model for network loading.

No need for a priori bounds on path flows.

Abstract

This paper is concerned with the existence of the simultaneous route-and-departure choice dynamic user equilibrium (SRDC-DUE) in continuous time, first formulated as an infinite-dimensional variational inequality in Friesz et al. (1993). In deriving our existence result, we employ the generalized Vickrey model (GVM) introduced in and to formulate the underlying network loading problem. As we explain, the GVM corresponds to a path delay operator that is provably strongly continuous on the Hilbert space of interest. Finally, we provide the desired SRDC-DUE existence result for general constraints relating path flows to a table of fixed trip volumes without invocation of a priori bounds on the path flows.