Dynamic analysis of some relational databases parameters

AbstractWe present a dynamic modelization of a relational database, when submitted to a sequence of queries and updates, that allows us to study the evolution of the sizes of relations. These sizes, either present in the database or computed by application of a relational operator (derived relation), have long been recognized as important parameters in query optimization. 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” case) 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 the relation sizes behave asymptotically as Gaussian processes, whose expectation and covariance are proportional to the time. This approach also allows us to analyse the maximum of the size of the derived relation