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This paper analyzes simultaneous route-and-departure-time (SRDT) dynamic userequilibrium (DUE) that incorporates the notion of boundedly rational (BR) userbehavior in the selection of departure time and route choices. Intrinsically,the boundedly rational dynamic user equilibrium (BR-DUE) model we presentassumes that travelers do not always seek the least costlyroute-and-departure-time choice. Rather, their perception of travel cost isaffected by an indifference band describing travelers' tolerance of thedifference between their experienced travel costs and the minimum travel cost.An extension of the BR-DUE problem is the so-called variable tolerance dynamicuser equilibrium (VT-BR-DUE) wherein endogenously determined tolerances maydepend 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 ofexistence, solution characterization, and heuristic numerical computation ofsuch problems. The VT-BR-DUE problem, together with the BR-DUE problem as aspecial case, is formulated as a variational inequality. We provide a verygeneral existence result for VT-BR-DUE and BR-DUE that relies on assumptionsweaker than those required for mere DUE models. Moreover, a characterization ofthe solution set is provided based on rigorous topological analysis. Finally,three computational algorithms are proposed based on the VI and DVIformulations. Numerical studies are conducted to assess the proposed algorithmsin terms of solution quality, convergence, and computational efficiency.

Formulation, existence, and computation of boundedly rational dynamic user equilibrium with fixed or endogenous user tolerance