Existence of simultaneous route and departure choice dynamic user equilibrium

•The existence of continuous-time simultaneous route-and-departure choice DUE is shown.•The proof does not invoke any a priori boundedness of the path flows.•Difficulty arising from the non-compact nature of the set of feasible flows is overcome.•The network loading subproblem employs the generalized Vickrey model.•The delay operator is shown to be continuous without a priori bounds on path flows.

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 Han et al., 2013a and Han et al., 2013b 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.