A new one‐level convex optimization approach for estimating origin–destination demand

Accurately estimating Origin–Destination (OD) trip tables based on traffic data has become crucial in many real‐time traffic applications. The problem of OD estimation is traditionally modeled as a bilevel network design problem (NDP), which is challenging to solve in large‐scale networks. In this paper, we propose a new one‐level convex optimization formulation to reasonably approximate the bilevel structure, thus allowing the development of more efficient solution algorithms. This one‐level approach is consistent with user equilibrium conditions, and improves previous one‐level relaxed OD estimation formulations in the literature by ‘equilibrating’ path flows using external path cost parameters. Our new formulation can, in fact, be viewed as a special case of the user equilibrium assignment problem with elastic demand, and hence can be solved efficiently by standard path‐based traffic assignment algorithms with an iterative parameter updating scheme. Numerical experiments indicate that this new one‐level approach performs very well. Estimation results are robust to network topology, sensor coverage, and observation error, and can achieve further improvements when additional data sources are included.