Unsafe operations in B-trees

Summary

A simple mathematical model for analyzing the dynamics of a B-tree node is presented. From the solution of the model, it is shown that the simple technique of allowing a B-tree node to be slightly less than half full can significantly reduce the rate of split, merge and borrow operations. We call split, merge, borrow and balance operations unsafe operations in this paper. In a multi-user environment, a lower unsafe operation rate implies less blocking and higher throughput, even when tailored concurrency control algorithms (e.g., that proposed by Lehman and Yao [10]) are used. A lower unsafe operation rate also means a longer life time of an optimally initialized B-tree (e.g., compact B-tree). It is in general useful to have an analytical model which can predict the rate of unsafe operations in a dynamic data structure, not only for comparing the behavior of variations of B-trees, but also for characterizing workload for performance evaluation of different concurrency control algorithms for such data structures. The model presented in this paper represents a starting point in this direction.