Simultaneous estimation of the origin–destination matrices and travel-cost coefficient for congested networks in a stochastic user equilibrium

This article proposes an optimization model for simultaneous estimation of an origin–destination (O–D) matrix and a travel-cost coefficient for congested networks in a logit-based stochastic user equilibrium (SUE). The model is formulated in the form of a standard differentiable, nonlinear optimization problem with analytical stochastic user equilibrium constraints. Explicit expressions of the derivatives of the stochastic user equilibrium constraints with respect to origin–destination demand, link flow, and travel-cost coefficient are derived and computed efficiently through a stochastic network-loading approach. A successive quadratic-programming algorithm using the derivative information is applied to solve the simultaneous estimation model. This algorithm converges to a Karusch–Kuhn–Tucker point of the problem under certain conditions. The proposed model and algorithm are illustrated with a numerical example.