Modeling the sparsity and density of measurement errors for origin–destination demand estimation

Conventional studies on origin–destination (OD) demand estimation (ODDE) problems often overlook the inherent characteristics of different input data sources, namely the currently observed data and historical/empirical data. These data sources contain varying information on OD demand with differing levels of accuracy. Herein, this study introduces a model that incorporates these two different data sources and considers the different measurement criteria arising in ODDE problems. In the introduced model, most of the estimated link flows are expected to exactly match the observed ones. To achieve this, we use the ℓ1-norm as a measurement criterion to obtain a sparsity error between estimated and observed link flows, with the goal of aligning some of the estimated link flows to match the observed values exactly. For the historical/empirical data (the prior OD demand), the model aims for the estimated demands of all OD pairs to be as close as possible to the historical/empirical values, without requiring any estimated demands to match them exactly. We apply the ℓ2-norm as the measurement criterion to capture the density error between the estimated and historical OD demands. The introduced model, termed the ℓ1-ℓ2 ODDE model, explicitly accounts for the sparsity and density of measurement errors using ℓ1- and ℓ2-norms. Considering the travelers’ path choice behavior in congested transportation networks, we formulate a bilevel ODDE model, wherein the upper-level problem balances measurement errors from different input data sources, and the lower-level problem is based on user equilibrium principle. Furthermore, we use a heuristic algorithm based on upper–lower alternating iteration to solve the introduced model. Numerical experiments, conducted on two real transportation networks, show the applicability and effectiveness of the introduced model and algorithm.