Optimisation models for estimating public transport OD matrices using different data types

Efficient public transport systems rely on origin–destination matrices (ODMs) estimation to accurately capture passenger travel patterns, enabling adjustments to frequencies and lines as needed. In this study, we address the ODM estimation problem by employing multiple bi-level programs that consider an outdated ODM and observed passenger flows on specific transit line arcs. Additionally, we consider various optional data types, including boarding and alighting data, as well as the structure of the outdated ODM and passenger flows, either all, separately, in combination, or none. In our study, we reformulate these bi-level programs into single-level models, and we use a commercial solver to address the problem in benchmark instances. In our analysis, we focus on the impact of incorporating different types of information into the estimation process, leading to valuable insights. We find that considering all the data types leads to a higher accuracy than only a subset of these data types. In particular, focussing only on boarding and alighting data leads to improvements in the estimation process, whereas considering only the structure of the outdated ODM and passenger flows leads to reduced accuracy compared to not incorporating either. The latter highlights the significance of data selection in ODM estimations.