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TRANSCRIPT
ENERGYEFFICIENTCONTROLOFVIRTUAL
MACHINE
CONSOLIDATIONUNDERUNCERTAIN
INPUTPARAMETERSFORGREENCLOUDS
§ Assumesmalldatacenter,1064Servers
– Outofthe588KWforCompute/Network
• 44%areforprocessor,serverpowersupplyandotherservercomponents(in
total258kW),àThisiswhatwetrytoopWmize
• 4%forstorage
• 4%forcommunicaWonequipment
– Saving1WforprocessingsavesaddiWonal1.84Wforothercomponents
ENERGYSAVINGINVIRTUALIZEDDATACENTERS
10
7228
588
LighWng
UPS
Cooling
Compute
§ Forexample,save20%energyforthisdatacenterresultsin:
– TotalCO2footprintavoidedperyear
• 846tCalifornia
• 690tSweden
• 1387tChina
• 1407tAustralia
– Monetarysavingsperyear
• 167.000USDforCalifornia
• 1.335.000SEKforSweden
• 872.000YuanforChina
• 141.000$forAustralia
ENERGYSAVINGINVIRTUALIZEDDATACENTERS
VMWorkload
§ VariesoverWmeduetounpredictableworkload
§ Mayrequire– VMresizing,VMcreaWon,VMterminaWon
§ Resultinthephysicalserverstobe– UnderuWlized
– OveruWlized
§ ConsequencesforCloudOperators– SLAViolaWonsversusMinimumEnergyConsumpWon
§ CaseStudy– EvaluatedWorkloadof6VMsinKAUComputeServiceDepartment
VMCONSOLIDATION:MOTIVATION
EXAMPLE:KAUDatacenterworkloadtraces
VMCONSOLIDATION:KAUWORKLOADTRACES
VMDemandVariesover/me
VMCONSOLIDATION:KAUWORKLOADTRACES
VMDemandVarieswithinbounds
VMCONSOLIDATION-REVISITIED
VM1 VM2 VM3 VM4
VM1
VM3
80% 90%
60% 40% 20% 50%
VMdemandsvaryoverWme…
SLAmaybeviolated!!!
105%
VM2
VM4
GOAL:ProvideasoluWonthatis
robustagainstinputvariability
VMCONSOLIDATION-REVISITED
GOAL:ProvideasoluWonthatis
robustagainstinputvariability
DeterminisWcOpWmizaWon:Too
conservaWve
ApplyrobustopWmizaWontheory
40%
VM1 VM2 VM3 VM4
VM1
VM3
80%
60% 40% 20% 50%
VMdemandsvaryoverWme…
SLAmaybeviolated!!!
VM4
50%
VM2
HigherenergyconsumpWonand
moreunusedresources
LessprobabilityofSLAviola/on
§ AlmostallmodelsforCloud(any?)OpWmisaWon(e.g.VM
ConsolidaWon)assumeperfectknowledge!
– MINcT(x)s.t.Ax<=b
– Oncex*calculated,itisused
§ BUT:Manyfactorsnotknownprecisely,e.g.
– VMResourceDemands
– EnergyModelofServers
– WecanonlyassumeincompleteknowledgeinA,b,c
§ Consequence(BenTal+Nemirovski,2000):Smallerrorsin
parameterscanmakex*highlyunfeasible
CLASSICALOPTIMIZATIONFRAMEWORKS
§ Assumeuncertaintymodelfordataisknown(e.g.bounds)
§ DefineasoluWonisrobustfeasibleasonethatisguaranteedto
remainfeasibleforalladmissibledatavalues(outof
uncertaintysetU)
§ OpWmizeobjecWveoversetof
robustlyfeasiblesoluWons
§ Robustcounterpart
– ai’i-throwofuncertainmatrix
ROBUSTOPTIMIZATIONPARADIGM
approximate
nominalrobust
objecWve
Nominalboundary
x*à
becomesinfeasible
§ ROBUSTMixedIntegerLinearProblem
– SoluWonx*isrobustfeasibleifitsaWsfies
alluncertainconstraints
– Robustcounterpart
• Typicallyhasinfinitenumberofconstraints
• DependsonuncertaintysetU
• SoluWontypicallyhasworseobjecWvevalue
• TriestomiWgateadverseeffectsofuncertainty
– Specialcase:cardinalityconstraintuncertaintyset(Bertsimas,Sim)
• Polyhedraluncertaintyset,budgetofuncertaintyintermsofcardinalityconstraints
• Eachcoefficientinmatrixiswithin ,maxΓicoefficientsdeviate
• Robustcounterpartbecomesaqerduality
ROBUSTVMCONSOLIDATIONMODEL
§ PowerofservercanbemodeledaslinearfuncWonofresource
uWlizaWon(e.g.CPUload,etc)
– Buterrorsupto10-14%duetoprocessoropWmizaWons,etc
– PowerconsumpWonisrandomvariable
fromuncertaintysetsymmetrically
distributedbetween
withzeromean
– Decisionvariable
– Constraints
dependonVMuWlizaWon,
seenextslide
UNCERTAINTYONSERVERPOWERMODEL
§ PowerconsumpWondependsonresourcedemandsofVMs,
whichareuncertain
– Resourcedemandisrandomvariable
symmetricallydistributed
withzeromeanplusfixeddemand
– UWlizaWon
– Budgetconstraint
UNCERTAINTYONVMRESOURCEDEMANDS
ResourcedemandsofOldassignmentVMsmigraWngtowardsserver
VMsmigraWngaway
OverprovisioningFactor
§ Uncertaintysetforcardinalityconstraint
– DefinesdeviaWonsfromnominalvalues,i.e.meanvaluesplusdeviaWon
bounds
– ProtecWonfromdeviaWonbyintroducinghardconstraintsthatcut-off
feasiblesoluWonsthatmaybecomeunfeasibleonesforsomedeviaWons
§ Priceofrobustness
– CloudOperatorcantradeoffbymodifyingΓ
– HigherriskaversionàconsidermoreunlikelydeviaWonsàhigher
protecWonàhigherenergyconsumpWon
– OpportunisWcsoluWonàlessprotecWonàlessenergyconsumpWon
UNCERTAINTYMODEL–PRICEOFROBUSTNESS
§ ProbabilityofconstraintviolaWon
– ωcoefficientsmaydeviate
– Upperboundcanbecomputedaccordingto(Bertsimas,Sim)
– Forsmallω needtoensurefullprotecWon(sesngΓ tomax)toensure
smallviolaWonprobability
HOWMUCHRISKTOTAKE?TUNINGOFΓ
§ ImplementaWoninMatlabwith
IBMCPLEX
§ Notsuitableforonline
opWmizaWon
§ BenchmarkforheurisWcs
§ Smallexampletodemonstrate
modelcapabiliWes
– 0.1CPU=1core
– 0.1RAM=512MB
EVALUATION
CPUDEMANDSUNCERTAIN(Δ=5%)
PROTECTIONAGAINSTUNCERTAINTYOF50UNITS
HIGHER ENERGY = PRICE OF ROBUSTNESS
CONSERVATIVESOLUTION=TOTALPROTECTIONLEVEL(MAXΓ)=HIGHESTENERGY
Γ=0
Pr(viol)=52%Γ=50
Pr(viol)<1%
OPPORTUNISTICSOLUTION(NOPROTECTION)=LESSENERGYCONSUMPTION
CloudOperatorcan
tradeoffbymodifyingΓ
CPUDEMANDSUNCERTAIN
CPUDEMANDSUNCERTAIN–LARGEINSTANCE
(100/14)ADDITIONALPOWER,NOOVERBOOKING RELATIVEPOWER,40%UNCERTAINTYONDEMAND
EXPECTEDPOWER,50%DEMANDUNCERTAINTY SLAVIOLATION,50%DEMANDUNCERTAINTY
§ Conclusions
– AppliedRobustOpWmizaWonFrameworktocopewithunknownand
impreciseinputdatatoVMConsolidaWonproblem
– UncertaintyonVMresourcedemandsandPowermodelofservers
– ΓuncertaintyandconstraintviolaWonprobabilitygivesCloudoperators
atooltotradeoffrobustnessversusenergyefficiency
– Manymoreresultswithenhancedmodelwithe.g.resource
overbooking
§ Futurework
– ComparisonwithrobustheurisWcs
– IntegraWonofnetworkmodelandNFVconcept(servicechain)
– ApplyRobustOpWmizaWonto5GNetworkOpWmizaWon
CONCLUSIONSANDFUTUREWORK
§ ThankyouforyouraxenWon!
THANKYOUFORYOURATTENTION!
ACROSSWORKSHOP,11THSEPTEMBER2015,GHENT,BELGIUMANDREASKASSLER