From Physical Properties of Transportation Flows to Demand Estimation: An Optimization Approach

Efficient management of transportation systems requires accurate trip demand data. It is sometimes possible to track anonymized users through their commutes, accomplished through previous studies on smart cards, license plates, and mobile phones. However, frequently the main public transit data sources are in aggregated forms such as entry and exit counts, and one must recover the original demand from these aggregated counts. Such problems are generally underspecified. To address this, we present an optimization framework to recover origin–destination matrices under minimal assumptions, incorporating reasonable physical constraints such as flow conservation, smoothness, and symmetry. The proposed method is evaluated and shows strong (∼5%–10%) improvement in R2 over the maximum entropy method on a variety of real-world data sets from Boston, New York City, and San Francisco, comprising tens to hundreds of stations.