Derivation of Miss Ratios for Merged Access Streams

An access stream is the sequence of storage accesses made by an executing program; a merged stream results from the multi-programming of a number of individual access streams. Assuming that LRU (least recently used) miss ratio functions for individual streams are known, we consider the problem of predicting the LRU miss ratio function for merged streams. Each access stream is modeled as a sequence of independent, identically distributed LRU stack distances which evolves in time as a Poisson process and the merged stream is taken to be the superposition of these processes. For an arbitrary number of such streams, a closed form expression for the expected miss ratio function is obtained.