A Variational Inequality Formulation for Inferring Dynamic Origin-Destination Travel Demands

In this paper we extend the relaxation strategy for the static O-D estimation (SODE) problem [1] to its dynamic counterpart. The dynamic O-D estimation problem (DODE) is formulated as a variational inequality (VI), which endogenizes the determination of the dynamic path-link incidence relationship (i.e., the dynamic assignment matrix) and takes users' response to traffic congestion into account. Different from numerous previous studies, our formulation avoids the bi-level structure that poses analytical and numerical difficulties. This is achieved by balancing the path cost and the path deviation (the latter measures the difference between estimated and measured traffic conditions), weighed by a dispersion parameter which determines the extent to which users' behavior is respected. We proved the equivalence between the VI problem and the derived dynamic DODE optimality conditions, and established the conditions under which a solution to the VI problem exists.

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