Distribution of Time Interval between the Modifications of Result Sets Cardinalities in Random Databases

In this paper, we propose a method to estimate the probability distribution of the time interval which ellapses between the modifications of the cardinality in a random database query’s result set. This type of database is important either in modeling uncertainty or storing data whose values follow a probability distribution. The result that we introduce is important from the point of view of the database optimization, providing a useful method for an integrated module. In previous research on random databases the sizes of some relational operations results were investigated. This kind of information is rather useful in an analytical database which provides decision-making support. The result we particularly aim to present in this paper concerns the transactional random databases, addressing its specific functionality. It will be proven that the interval of time between the cardinalities changes is exponentially distributed. The proof is based on the technique of the Markovian Jelinski-Moranda model, which is used in the reliability of software programs.