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This article deals with the problem of estimating and updating the origin-destination matrix and link flows from traffic counts and its optimal location. A combination (bi-level) of an OD-pair matrix estimation model based on Bayesian networks, and a Wardrop-minimumvariance model, which identifies origins and destinations of link flows, is used to estimate OD-pair and unobserved link flows based on some observations of links and/or OD-pair flows. The Bayesian network model is also used to select the optimal number and locations of the links counters based on maximum correlation. Finally, the proposed methods are illustrated by their application to the Nguyen-Dupuis and the Ciudad Real networks.

This article deals with the problem of observability of traffic networks, understanding as such the problem of identifying which is the subset of OD-pair and link flows that can be calculated based on a subset of observed OD-pair and link flows and related problems. Two algebraic methods for solving the observability problems are given, one global approach based on nullspaces and a step by step procedure allowing updating the information once each item of information (OD-pair or link flow) becomes available. In particular, seven different observability problems are stated and solved using the proposed methods, which are illustrated by their application to the Nguyen-Dupuis network problem. The results show that the proposed methods provide useful information on which OD-pair or link flows are informative on other OD-pair and link flows, and that the methods are applicable to large networks.