A New Model for Updating Origin-Destination Matrices and Path Choice Probabilities in Public Transportation Networks

Abstract: The inverse problem of estimating an actual origin-destination (OD) matrix is one of the most important public transit planning steps. Most of the time, the route choice probabilities by which a user transits along the network are rst calculated, and then the OD matrix is updated. In this article, these two steps are solved simultaneously by an integer linear programming model based on partial knowledge of the transit segment ow along the network. A novelty in our methodology to avoid a quadratic objective function is to measure the dierence between the reference and the estimated OD matrices by dening demand decits and excesses for the estimated OD matrix. To test our methodology, we build an instance generator based on small-world graphs to mimic real transit networks. The results are compared with an augmented Lagrangian model solved by the dual ascent and multipliers method. Our integer linear model yields high-quality estimators of the actual OD matrices, the exact ow volume segment counts, and an adequate interval for the route choice probabilities. Additionally, we test our methodology in a real-world case from the city of Monterrey, Mexico.