Formulation, existence, and computation of boundedly rational dynamic   user equilibrium with fixed or endogenous user tolerance
  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. 
Ke Han, W. Y. Szeto, Terry L. Friesz
math.OC