Modelling andValidation ofResponse TimesinZonedRAID

vious measures canbeeasily derived. Analytical queueing network models ofRAIDperformance [4,9, 12,18,19]deWepresent andvalidate anenhanced analytical queueing veloped prior to[10] approximate onlythemeanresponse network model ofzoned RAID.Themodelfocuses onRAID timeofthesystem. Wenotethat RAIDperformance can levels 01and5,andyields thedistribution ofI/Orequest also bemodelled using other techniques including simularesponse time. Whereas ourprevious workcould only sup- tion [4,12], table-based [2]andblack-box modelling [13]. portarrival streams ofI/Orequests ofthesametype, the OurRAIDmodelisdeveloped inabottom-up hierarchimodelpresented here supports heterogeneous streams with calfashion. Webegin bymodelling eachdisk drive inthe amixture ofread andwrite requests. This improved realism array asasingle M/G/1queue. Wethenabstract theRAID ismadepossible through multiclass extensions toourex- asafork-join queueing network [3]inwhicheachdisk in isting model. Whencombined with priority queueing, this thearray isrepresented byanM/G/1queue. InanN-queue development alsoenables moreaccurate modelling ofthe fork-join network (see Fig.1)eachincoming jobissplit waysubtasks ofRAID5write requests arescheduled. In into N subtasks attheforkpoint. Eachofthese subtasks allcases wederive analytical results forcalculating not queues forservice ataparallel service nodebefore joining onlythemeanbutalso higher moments andthefull distri-aqueueforthejoin point. Whenall N subtasks inthejob bution ofI/Orequest response time. Wevalidate ourmodel areattheheadoftheir respective join queues, theyrejoin against measurements fromareal RAIDsystem. (synchronise) atthejoin point.