  This paper analyzes simultaneous route-and-departure-time (SRDT) dynamic user
equilibrium (DUE) that incorporates the notion of boundedly rational (BR) user
behavior in the selection of departure time and route choices. Intrinsically,
the boundedly rational dynamic user equilibrium (BR-DUE) model we present
assumes that travelers do not always seek the least costly
route-and-departure-time choice. Rather, their perception of travel cost is
affected by an indifference band describing travelers' tolerance of the
difference between their experienced travel costs and the minimum travel cost.
An extension of the BR-DUE problem is the so-called variable tolerance dynamic
user equilibrium (VT-BR-DUE) wherein endogenously determined tolerances may
depend not only on paths, but also on the established path departure rates.
This paper presents a unified approach for modeling both BR-DUE and VT-BR-DUE,
which makes significant contributions to model formulation, analysis of
existence, solution characterization, and heuristic numerical computation of
such problems. The VT-BR-DUE problem, together with the BR-DUE problem as a
special case, is formulated as a variational inequality. We provide a very
general existence result for VT-BR-DUE and BR-DUE that relies on assumptions
weaker than those required for mere DUE models. Moreover, a characterization of
the solution set is provided based on rigorous topological analysis. Finally,
three computational algorithms are proposed based on the VI and DVI
formulations. Numerical studies are conducted to assess the proposed algorithms
in terms of solution quality, convergence, and computational efficiency.
