Mathematical models of database degradation

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Abstract
As data are updated, the initial physical structure of a database is changed and retrieval of specific pieces of data becomes more time consuming. This phenomenon is called database degradation. In this paper two models of database degradation are described. Each model refers to a different aspect of the problem. It is assumed that transactions are statistically independent and either add, delete, or update data. The first model examines the time during which a block of data is filling up. The second model examines the overflows from a block of data, which essentially describes the buildup of disorganization. Analytical results are obtained for both models. In addition, several numerical examples are presented which show that the mean number of overflows grows approximately linearly with time. This approximation is used to devise a simple formula for the optimal time to reorganize a stochastically growing database.

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