Transportation Origin-Destination Demand Estimation with Quasi-Sparsity

Origin-destination (OD) demands for a city or a region are essential input to many transportation applications. For a real-world transportation network, the OD demand matrix may present certain quasi-sparsity property, that is, most OD pairs have small demands, whereas only a small portion of OD pairs have large demands. In this paper, we formally define quasi-sparsity and propose a quasi-sparsity–based OD (QSOD) estimation framework to explore such a property for OD demand estimation. We study two QSOD models, that is, the fixed-mapping QSOD model and the bilevel QSOD model, by applying the compressed sensing technique. We theoretically and numerically show that under certain conditions the estimated OD matrix shares the same quasi-sparsity feature with the prior OD matrix, and the estimated demands of most OD pairs (of a large-size network) will be equal to either their prior values or zeros (or a very small value). Results show that the QSOD framework has the capability in keeping OD quasi-sparsity consistency and is computationally less demanding compared with existing methods. The practical implications of the QSOD framework are also discussed.