Updating origin–destination matrices and link probabilities in public transportation networks

To update a public transportation origin–destination (OD) matrix, the link choice probabilities by which a user transits along the transit network are usually calculated beforehand. In this work, we reformulate the problem of updating OD matrices and simultaneously update the link proportions as an integer linear programming model based on partial knowledge of the transit segment flow along the network. We propose measuring the difference between the reference and the estimated OD matrices with linear demand deficits and excesses and simultaneously having slight deviations from the link probabilities to adjust to the observed flows in the network. In this manner, our integer linear programming model is more efficient in solving problems and is more accurate than quadratic or bilevel programming models. To validate our approach, we build an instance generator based on graphs that exhibit a property known as a “small-world phenomenon" and mimic real transit networks. We experimentally show the efficiency of our model by comparing it with an Augmented Lagrangian approach solved by a dual ascent and multipliers method. In addition, we compare our methodology with other instances in the literature.