As disk arrays become widely used, tools for understanding and analyzing their performance become increasingly important. In particular, performance models can be invaluable in both configuring and designing disk arrays. Accurate analytic performance models are desirable over other types of models because they can be quickly evaluated, are applicable under a wide range of system and workload parameters, and can be manipulated by a range of mathematical techniques. Unfortunately, analytic performance models of disk arrays are difficult to formulate due to the presence of queuing and fork-join synchronization; a disk array request is broken up into independent disk requests which must all complete to satisfy the original request. In this paper, we develop, validate and apply an analytic performance model for disk arrays. We derive simple equations for approximating their utilization, response time and throughput. We then validate the analytic model via simulation and investigate the accuracy of each approximation used in deriving the analytic model. Finally, we apply the analytic model to derive an equation for the optimal unit of data striping in disk arrays.




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