A Bi-Level Model to Estimate the US Air Travel Demand

A single-level optimization model (i.e., a Route Flow Estimator (RFE)) has been proposed to estimate the historical air travel demand. However, the RFE may require a significant amount of additional data collection effort when applied to estimate travel demand in small or medium-sized networks. We propose a novel bi-level model as an alternative to the RFE to handle demand estimation for small or medium-sized networks. The upper-level model is designed as a constrained least square (LS) model. The lower-level model is designed based on the RFE. The bi-level model estimates travel demand by considering travelers' choice behaviors and some observed data. It requires less data collection effort yet it produces estimation results consistent with those from the RFE. A Gauss-Seidel type (GST) algorithm is proposed to solve the bi-level model. To solve the upper-level model, we propose a heuristic algorithm, which is designed to solve the dual of the upper-level model. The estimation results from the two models are compared using two numerical examples: a small-sized example with one OD pair and a medium-sized example with 400 OD pairs.