The Observability Problem in Traffic Models: Algebraic and Topological Methods

This paper deals with the problem of observability of traffic networks, understanding as such the problem of identifying which is the subset of the origin-destination (OD)-pair and link flows that can be calculated based on a subset of observed OD-pair and link flows, and related problems. A modified topological version of an existing algebraic method for solving observability problems is given. The method is based on a step-by-step procedure, allowing us to update the information once each item of information (OD-pair or link flow) becomes available. In particular, three different observability problems are stated and solved using the proposed methodology, which is illustrated by its application to the Nguyen-Dupuis network and compared with the algebraic version. The topological version is much faster, uses much less memory, and presents no rounding errors or zero test problems but identifies fewer observable flows.