Trip matrix and path flow reconstruction and estimation based on plate scanning and link observations

This paper deals with the problem of trip matrix and path flow reconstruction and estimation based on plate scanning and link flow observations. To solve the problem, the following steps are used. First, the class FF of feasible subsets of scanned links for single users is identified. Second, the conservation laws are stated in terms of flows associated with the class FF and path flows. Finally, the path flows are reconstructed based on minimizing a quadratic (weighted) function of the errors with respect to a given set of prior path flows, subject to the conservation law constraints, stated for each of the possible subsets in FF, and to the observed information. Once the path flows have been reconstructed, the trip matrix and other link flow estimates become immediately available. In addition, an algorithm for selecting optimal sets of links to be scanned for predicting path flows is provided. Finally, the methods are illustrated by their application to the Nguyen–Dupuis network, showing the important gain obtained, in estimating path and OD-pair flows, if one uses the extra information contained in the scanned data, which is shown to be much more informative than the traditional link count information. This has important practical implications on an efficient estimation of traffic flows.