Extension of the working set for modeling spatial locality inprogram behavior

摘要

The paper extends the definition of the working set for modelingnspatial locality in program behavior, and it presents theoreticalnresults. One of the theoretical results is that the working set basednhit ratio can be given by the time or ensemble averages of thendistributions of the interreference interval. We also present, as antheorem, that the average number of unique blocks in the extendednworking set can be given by the sum of the miss ratios. We derive anmathematical formula to calculate the hit ratio for Markov Chains. Ankind of random walk is examined as an example of program behavior. Thenaverage number of unique blocks of a given block size in the extendednworking set is used for comparison with other empirical observations.nThe comparison had good agreement with our random walk model of programnbehavior and the empirical observations