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.