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A particularly simple Markov chain model for a reference string is described. The model, which is only slightly more complicated than the independent reference model, generates strings that have a locality property and that have a specified probability distribution of references over pages. Expressions are obtained for expected working-set size and expected working-set miss ratio. The model is used in an examination of the effect of grouping pages into blocks and in a discussion of the problem of evaluating the effect of changes in the size of the data base. Predictions of the model are shown to agree closely with observations of a string of data base references generated by an interactive data base system having a large number of concurrent users.
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