Towards Petascale Computing

Tarek Abdelzaher, University of IllinoisYixin Diao, IBM ResearchJoseph L. Hellerstein, Microsoft Developer DivisionChenyang Lu, Washington UniversityXioayun Zhu, Hewlett Packard Laboratories

June 2, 2008

Introduction to Control Theory and Its Application to Computing Systems Presentation subtitle:20pt Arial Regular,teal R045 | G182 | B179

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Maximum length: 1 lineCopyright: 10pt ArialRegular, whiteTemplate release: Oct 02For the latest, go to http://w3.ibm.com/ibm/presentationsOptional slide number: 10pt Arial Bold, whiteIndications in green = Live content Indications in white = Edit in masterIndications in blue = Locked elementsIndications in black = Optional elements5So far, we have been talking about closed loop systems. That is, the measured output is used to determine the next input. This means that the closed loop controller can be quite simple since it is just adjusting to the previous output of the target system. It also means that the closed loop system can adapt to changes, such as the execution of administrative tasks.There is an alternative to closed loop systems called open loop systems. The latter do not employ feedback. As a result, they avoid problems with stability since the inputs to the open loop controller do not depend on past values of the measured output. Open loop systems also settle quickly, which has appeal. The big disadvantage of open loop systems is that the open loop controller is much more complicated than the closed loop controller and it often requires much more data (e.g., arrival rates, service times). For these reasons, we focus on closed loop systems.Regulatory ControlManage to a reference valueEx: Service differentiation, resource management, constrained optimizationTypes of ControlMeasuredRISControllerServerMaxUsersReferenceRISSensorTarget System-+Eliminate effect of a disturbanceEx: Service level management, resource management, constrained optimizationDisturbance RejectionMeasuredRISControllerServerMaxUsersReferenceRISSensorTarget SystemAdministrative Tasks-+Achieve the best value of outputsEx: Minimize Apache response timesOptimizationMeasuredRISControllerServerMaxUsersSensorTarget SystemAdministrative TasksSIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Yu, and Zhu.IBM logo must not be moved, added to, or altered inany way.

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Unstable SystemStabilityAccuracyShort SettlingSmall OvershootThe SASO Properties of Control Systems

SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Yu, and Zhu.IBM logo must not be moved, added to, or altered inany way.

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ControllerAdminBlock DiagramControllerServerMaxUsersDesiredRISActualRIS-+r(k)e(k)u(k)y(k)

Good

BadSIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Yu, and Zhu.IBM logo must not be moved, added to, or altered inany way.

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Server

Transfer Function (TF)Z-TransformPole:Fast systems have small polesGain:Ratio of steady state outputto steady state inputOutput at time k is proportional to ak, for pole a.Oscillations result if neg or im polesSIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Yu, and Zhu.IBM logo must not be moved, added to, or altered inany way.

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KI=0.1ControllerG(z)ServerN(z)-+ Closed Loop Transfer FunctionExample: Control Law

KI=1

KI=5

KI=0.1Control Designr(k)y(k)e(k)u(k)

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Key Results From Linear Systems

Steady state gain of G(z):Stable if |a|70%!!SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Yu, and Zhu.IBM logo must not be moved, added to, or altered inany way.

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Control Architecture

R: Impact LimitE: ErrorU: Sleep %Y: Pageometer (pages/sec): Model parametersY*: Baseline perfyu1Assume linear effect of throttling on YOnline modeling provides a transducer that translates from Pages/sec (Y) to % Impact (M)% Impact% ImpactPages/secSIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Yu, and Zhu.IBM logo must not be moved, added to, or altered inany way.

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15ControllerThreadPoolQueueUserWorkItem()Completion Rate (throughput)ConcurrencyLevelSIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Yu, and Zhu.IBM logo must not be moved, added to, or altered inany way.

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(50 work items:100ms with 10%CPU, 90% wait. 2.2GHz dual core X86.)Discrete DerivativeCurrentConcurrencyLevelCurrentHistoryNewConcurrencyLevel for small ControlGainLarge ControlGainNewConcourrencyLevel for large ControlGainLastConcurrencyLevel= History meanLastHistorySmall ControlGainWant large gain so move quickly, but not overshoot.Making good moves depends onthroughput varianceshape of curveHybrid Control State DiagramState 1 - Initializing LastHistory.LastHistory.Add(data)

State 2 Looking for move.CurrentHistory.Add(data)CompletedInitializingIsStableHistory(LastHistory): LastControlSetting = CurrentControlSetting CurrentControlSetting = ExploreMove()ChangePointWhileInitializingIsChangePoint(LastHistory): LastHistory = data CurrentControlSetting = ExploreMove()ReverseBadMoveCurrentHistory.Count > MinimumHistory& LastHistory.Mean() > CurrentHistory.Mean(): Swap(CurrentControlSetting, LastControlSetting)DirectedMoveIsSignificantDifference(CurrentHistory, LastHistory): LastControlSetting = CurrentControlSetting CurrentControlSetting = DirectedMove() LastHistory = CurrentHistory CurrentHistory = nullChangePointWhileLookingForMoveSame as ChangePointWhileInitializingStuckInStateIsStableHistory(CurrentHistory) & CurrentHistory.Count > SufficientlyLargeHistory: LastControlSetting = CurrentControlSetting CurrentControlSetting = ExploreMove() LastHistory = CurrentHistory CurrentHistory = nullState 1a InTransition.WaitForSteadyStateIsInTransition()ChangePointInQueueWaitingIsChangePoint(QueueOfWaiting)State 2a InTransitionCurrentHistory.Add(data)SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Yu, and Zhu.text

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