Matrix Tools for General Observability Analysis in Traffic Networks

We deal with the problem of observability of a given subset V1 of flows in terms of another subset V2, no matter which type of flows [link, origin-destination (OD), route, node, plate scanned, etc.] they contain or whether they are mixed types. Two problems are stated: The first consists of determining which subsets of flows in V1 can be calculated in terms of the observed flows V2. The second consists of determining which subset of flows V2 needs to be observed to calculate a given subset V1. A theorem providing necessary and sufficient conditions for observability is provided and used in the proposed methods to solve the two problems. Two theorems, one lemma, and one corollary provide the bases for optimizing the numerical procedures to solve these problems. Some examples of applications are used to illustrate the proposed methods.

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