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.