Extension of the working set for modeling spatial locality in program behavior

The paper extends the definition of the working set for modeling spatial locality in program behavior, and it presents theoretical results. One of the theoretical results is that the working set based hit ratio can be given by the time or ensemble averages of the distributions of the interreference interval. We also present, as a theorem, that the average number of unique blocks in the extended working set can be given by the sum of the miss ratios. We derive a mathematical formula to calculate the hit ratio for Markov Chains. A kind of random walk is examined as an example of program behavior. The average number of unique blocks of a given block size in the extended working set is used for comparison with other empirical observations. The comparison had good agreement with our random walk model of program behavior and the empirical observations