Dynamic analysis of the sizes of relations

We present a dynamic modelization of a database when submitted to a sequence of queries and updates, that allows us to study the evolution of the sizes of relations. While the problem of estimating the sizes of derived relations at a given time (“static” case) has been the subject of several studies, to the best of our knowledge the evolution of the relation sizes under queries and updates (“dynamic” cases) has not been studied so far. We consider the size of a relation as a random variable, and we study its probability distribution when the database is submitted to a sequence of insertions, deletions and queries. We show that it behaves asymptotically as a Gaussian process, whose expectation and covariance are proportional to the time. This approach also allows us to analyze the maximum of the size of the derived relation.SCOPUS: cp.k