TAILIEUCHUNG - THE FRACTAL STRUCTURE OF DATA REFERENCE- P7

THE FRACTAL STRUCTURE OF DATA REFERENCE- P7:For purposes of understanding its performance, a computer system is traditionally viewed as a processor coupled to one or more disk storage devices, and driven by externally generated requests (typically called transactions). Over the past several decades, very powerful techniques have become available to the performance analyst attempting to understand, at a high level, the operational behavior of such systems. | 16 THE FRACTAL STRUCTURE OF DATA REFERENCE But assuming that the placement of interval boundaries falls at random the average number of interval boundaries crossed by front ends and by back ends must be in proportion to their durations. Therefore for each touched interval containing a back end i o there must be on average At t touched intervals that do not. We may therefore conclude that the probability that a touched interval contains a back end i o and the probability that a touched interval contains a miss are both equal to 1-0 where the expression on the right follows from . To apply the conclusion just stated as a method oftrace analysis we count the total number of i o s nreq and touches ntch. We may then estimate z zi z n ch m t s 1 - 0 ------- rea Note that if 6 is in the general ballpark of the guestimate then the estimate is not highly sensitive to the exact value of 0 being assumed. For example suppose that in some interval we count a total of 100 000 references to 20 000 distinct tracks. Then the guestimate would yield an estimated hit ratio of 1 - .2 x 1 85 percent. By comparison the alternative assumptions 0 .2 and 0 .3 would yield estimated hit ratios of 84 percent and 86 percent respectively. REQUIREMENTS FOR MEMORY We havejust devoted several pages to a detailed discussionofthe key closely related results 1 and which describe the time spent by a track during a visit to memory. We now derive what is by far the most important consequence ofthis visit time the resulting cache memory requirements. We relate these requirements both to the cache miss ratio as well as to the level of service being provided to applications as reflected in the average or single-reference residency time . our starting point for calculating the requirements for cache memory is Little s law as applied previously in the result . The same result can be stated equivalently as j zrmT By and we also have m bT e where

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