tailieunhanh - THE FRACTAL STRUCTURE OF DATA REFERENCE- P27

THE FRACTAL STRUCTURE OF DATA REFERENCE- P27: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. | 120 THE FRACTAL STRUCTURE OF DATA REFERENCE In addition the access density A and storage intensity q are in effect inverses of each other Gva G a Qa This relationship applies not just to individual applications but also to aggregates of applications since the average access density per unit of storage is given by Gv 2a S G q We can therefore conclude from that In words this says that as the cost of disk storage falls the access density of applications should also be expected to fall but at a slower rate. Note however that the deployable applications model does not predict how much of a time lag should be expected between these events. Equation provides a convenient method of model calibration. As Figure illustrates both storage cost and access density declined steadily throughout the 1980 s and early 1990 s. From 1980 to 1993 storage costs fell at a compound annual rate of approximately 15 percent from about 39 to about 5 dollars per megabyte while access densities fell at a compound annual rate of approximately 11 percent from about 9 to about i o s per second per gigabyte . Due to the reasonably steady nature of the process during this extended period oftime we can therefore conclude even without knowing the specific time lag between cause and effect that or - ln T -----------1 - 1 l A ln Here we have added slightly to the exact calculation so as to express 3 as a round number. The upward direction ofround-offis the conservative direction it corresponds in the subsequent section to adopting a slightly more demanding objective for disk performance than would have been the case ifwe had carried forward additional digits. Disk Applications A Statistical View 121 Figure . Approximate trends in access density and storage cost. 3. DISK PERFORMANCE REQUIREMENTS The results just obtained apply directly to the assessment of disk performance for new generations of disks. For concreteness consider the case in which