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

Abstract

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.

A Demand Estimator Based on a Nested Logit Model

“…Many other bi-level formulations have been developed ever since. In most cases, the upper-level model estimates demand matrix and is usually formulated as a least squares model (Spiess 1990;Yang, Meng, and Bell 2001;Doblas and Benitez 2005;Li 2015a), a generalized least squares model (Yang et al 1992;Chen 1992, 1995;Yang 1995;Maher, Zhang, and Vliet 2001;Codina and Barcel 2004;Lundgren and Peterson 2008), or a maximum likelihood/entropy model (Fisk 1988;Shihsien and Fricker 1996). The lower-level model estimates travelers' responses to congestion in terms of route-choice proportion or link usage proportion using an equilibrium model.…”

A Least-Square Model to Estimate Historical Percentages of Itinerant General Aviation Operations by Aircraft Types and Flight Rules at an Airport

“…These methods could produce relatively accurate and cost-beneficial estimates [10,23]. It is worthwhile to point out that models that utilize posterior observations have also been developed to estimate the historical demand in commercial air transportation (see, e.g., Li et al [24]; Li and Baik [25]; Li [26]; Li et al [27]; and Li [28]) and ground transportation (see, e.g., Maher [29]; Cascetta [30]; Bell [31]; Yang et al [32]; Codina and Barceló [33]; Chootinan et al [34]; Doblas and Benitez [35]; Nie et al [36]; Lundgren and Peterson [37]; Chen et al [38]). …”

Heuristics to Improve Efficiency of Solution Algorithm of Path Flow Estimator

“…The estimator could also have a bilevel structure because of the possible coupling between the derivative of path choice proportion and travel demand. Recently, Li proposed a bilevel formulation for estimating the air travel demand in small or medium-sized networks (26). In contrast to the bilevel models developed to capture congestion effects, his bilevel model was designed to handle situations in which a significant portion (unknown) of link traffic counts are not generated by the travel demand within the study areas.…”