A single-level joint formulation for travel demand estimation under stochastic user equilibrium

The Origin-Destination (OD) travel demand is an essential component of transportation analysis, particularly for simulation models, such as static or dynamic traffic assignment that assess the impact of various strategic transportation plans. The conventional formulation of the OD estimation from traffic measurements is a bi-level optimization problem with equilibrium constraints. However, tackling bi-level problems for large-scale networks is computationally challenging, preventing the scalability of OD estimation. This paper presents a single-level join formulation of the travel demand estimation problem under Stochastic User Equilibrium (SUE) as a non-linear equation system. This single level formulation uses an extension of the SUE assignment fixed point formulation, making it transparent to the congestion and route choice model. A Jacobian free version of the Gauss-Newton algorithm is used to solve the model, which gave the freedom to incorporate multiple sources of traffic measurements in the estimation process. Numerical results on two networks illustrate the effectiveness and efficiency of the proposed methodology. In addition, estimation results indicate that the new formulation is robust with respect to count location coverage, measurement errors, and historical OD demand.