A Generalized Single-Level Formulation for Origin–Destination Estimation under Stochastic User Equilibrium

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Origin–destination (OD) demand is an indispensable component for modeling transportation networks, and the prevailing approach to estimating OD demand using traffic data is through bi-level optimization. A bi-level optimization approach considering equilibrium constraints is computationally challenging for large-scale networks, which prevents the OD estimation (ODE) being scalable. To solve for ODE in large-scale networks, this paper develops a generalized single-level formulation for ODE incorporating stochastic user equilibrium (SUE) constraints. Two single-level ODE models are specifically discussed and tested. One employs a SUE based on the satisfaction function, and the other is based on the Logit model. Analytical properties of the new formulation are analyzed. The estimation methods are proven to be unbiased. Gradient-based algorithms are proposed to solve for this formulation. Numerical experiments are conducted on a small network and a large network, along with sensitivity analysis on sensor locations, historical OD information and measurement error. Results indicate that the new single-level formulation, in conjunction with the proposed solution algorithms, can achieve accuracy comparable with the bi-level formulation, while being much more computationally efficient for large networks.