L∞-Norm path flow estimator for handling traffic count inconsistencies: Formulation and solution algorithm

Path flow estimator (PFE) is a single-level network observer proposed to estimate path flows and origin-destination flows from traffic counts in a transportation network. The PFE model handles the traffic count inconsistency problem by allowing user to specify appropriate error bounds (or confidence interval) on the traffic counts. This approach, although flexible, introduces a systematic bias in underestimating the total demand when improper error bounds are specified. This paper presents an L∞-norm PFE model that minimizes the systematic bias of the total demand estimate encountered in the PFE model by determining the least maximum absolute error needed to accommodate measurement errors and traffic count inconsistencies within the estimation process. A solution algorithm based on the dual formulation combined with a column generation procedure is developed for solving the proposed L∞-norm PFE model. Numerical results are presented to illustrate the features and applicability of the proposed L∞-norm PFE model and solution algorithm.