The average time until bucket overflow

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Abstract
It is common for file structures to be divided into equal-length partitions, called buckets, into which records arrive for insertion and from which records are physically deleted. We give a simple algorithm which permits calculation of the average time until overflow for a bucket of capacity n records, assuming that record insertions and deletions can be modeled as a stochastic process in the usual manner of queueing theory. We present some numerical examples, from which we make some general observations about the relationships among insertion and deletion rates, bucket capacity, initial fill, and average time until overflow. In particular, we observe that it makes sense to define the stable point as the product of the arrival rate and the average residence time of the records; then a bucket tends to fill up to its stable point quickly, in an amount of time almost independent of the stable point, but the average time until overflow increases rapidly with the difference between the bucket capacity and the stable point.

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