What are the reasons of bucket overflow? Explain any two methods for solving this problem.

Ans:  It is general for file structures to be divided into equal-length partitions, known as buckets, into which records arrive for insertion and to which records are physically deleted. We provide a simple algorithm that allows calculation of the average time until overflow for a bucket of capacity n records, supposing that record insertions and deletions can be modelled as a stochastic process in the common way of queuing theory. We offer some numerical instances, from which we make some general observations about the relationships among insertion and deletion rates, bucket capacity, initial fill, and average time till overflow. Particularly, we observe that it makes sense to describe the stable point as the product of the arrival rate and the average residence time of the records; after that a bucket tends to fill up to its stable point quickly, in an amount of time approximately independent of the stable point, but the average time until overflow increases quickly with the difference among the bucket capacity and the stable point.