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A robust optimization for proactive energy management in virtualized data centers

A robust optimization for proactive energy management in virtualized data centers
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  A Robust Optimization for Proactive Energy Managementin Virtualized Data Centers Ibrahim Takouna ∗ Wesam Dawoud ∗ Kai Sachs ± Christoph Meinel ∗∗ Hasso Plattner InstituteUniversity of PotsdamPotsdam, Germany ± SAP AGWalldorf, Germany ABSTRACT Energy management has become a significant concern indata centers to reduce operational costs and maintain sys-tems’ reliability. Using virtualization allows servers consoli-dation, which increases server utilization and reduces energyconsumption by turning off unused servers. However, serversconsolidation and turning off servers can cause also conse-quences if they are not exploited efficiently. For instance,many researchers consider a deterministic demand for capac-ity planning, but the demand is always subject to uncertain.This uncertainty is an outcome of the workload predictionand the workload fluctuation. This paper presents a robustoptimization for proactive capacity planning. We do notpresume that the demand of VMs is deterministic. Thus, weimplement a range prediction approach instead of a singlepoint prediction. Then, we implement a robust optimizationmodel exploiting the range-based prediction to determinethe number of active servers for each capacity planning pe-riod. The results of the simulation show that our approachcan mitigate undesirable changes in the power-state of theservers. Additionally, the results indicate an increase inthe servers’ availability for hosting new VMs and reliabilityagainst a system failure during power-state changes. Asfuture work, we intend to apply our approach to dynamicworkload such as a web application. We plan to investigateapplying our approach to other resources, where we justconsider only the CPU demand of VMs. Finally, we com-pare our approach against the approaches using stochasticoptimization. Categories and Subject Descriptors k.6 [ Management of computing and information sys-tems ]: General; k.6.2 [ Installation Management ]: Per-formance and Usage Measurement General Terms Management, Performance, Experimentation Permission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies arenot made or distributed for profit or commercial advantage and that copiesbear this notice and the full citation on the first page. To copy otherwise, torepublish, to post on servers or to redistribute to lists, requires prior specificpermission and/or a fee.  ICPE’13,  April 21–24, 2013, Prague, Czech Republic.Copyright 2013 ACM 978-1-4503-1636-1/13/04 ...$15.00. Keywords Energy-aware; Robust Optimization; Prediction; Virtualiza-tion 1. INTRODUCTION Energy efficient resource management has become a sig-nificant concern in virtualized data centers to reduce op-erational costs. As an idle server consumes approximately70% of the power consumed by the server running at fullcapacity [1], turning off idle servers for reducing energy con-sumption has been widely proposed by many researchers[1][2][3]. However, these approaches considered the num-ber of VMs and their capacity demands are deterministic.Hence, they built deterministic models that did not takeinto account the uncertainty of the demand. Furthermore,a typical server has multiple power states including on, off,sleep, and hibernated. Some related work has ignored theenergy consumption during the change of the server’s power-state, which we consider as a wasted energy. During a power-state change, a server consumes energy without performingany useful work. For instance, a normal PC takes around25 seconds to switch from one state to off state and viceversa [4]. Furthermore, we found that a server with 1TBmemory requires 5 minutes for a clean boot, which includesthe hardware check stage. On the other hand, Mao et al. [5]have observed that the start-up time of a VM is proportionalto its image size. The start-up time of a VM is very cru-cial for online applications such as web applications. Thus,implementing a proactive optimization solution can assistto avoid SLA’s violations. By predicting the number of therequired VMs in the next planning period, we can preparethese VMs images and the physical server in advance. Manyresearchers consider a deterministic demand for capacityplanning, but the demand is always subject to uncertain.This uncertainty is an outcome of the workload predictionand the workload fluctuation. Ignoring the uncertainty inreal world applications can make the usual optimal solutioninfeasible [7]. Unlike deterministic models, Dance et al.[8] have used the stochastic optimization for consideringuncertainty. However, the stochastic optimization requiresto know the probability distributions of the demand. Inour approach, we used the robust optimization that ad-dresses data uncertainty. The robust optimization modelassumes that uncertain parameters belong to a boundedrange. Importantly, the robust optimization can outperformthe stochastic optimization when selecting an appropriaterobustness level, and it is less computationally intensive  Figure 1: The stages of the range-based prediction approachwhen the distribution of uncertain parameters is compli-cated [9]. To build the robust optimization model for proac-tive capacity planning, we implement an adaptive range-based workload prediction instead single point prediction forpredicting the number of the requested VMs. The results of the simulation show that our approach can mitigate undesir-able changes in the power-state of the servers. Additionally,the results indicate an increase in the servers’ availabilityfor hosting new VMs and reliability against a system failureduring power-state changes. 2. RANGE-BASED PREDICTION Typically, point value prediction approaches might notcover the workload fluctuation. The approaches solve theproblem as a deterministic optimization, which assume theprecise knowledge of the workload demand. Furthermore,optimization based on the mean-value or the max-value of the workload can produce low provision or high provision,respectively. This is costly in both cases. In this section, wepresent a range-based prediction approach with an adaptivewindow-size algorithm to predict the number of demandingVMs in a data center. Our approach consists of three stagesas shown in Figure 1: (1) selecting the historical window sizebased on the statistical test (F/T-test); (2) smoothing thevalues of the selected historical window; and (3) predictingthe next number of active VMs and its minimum and max-imum range. Most of the related work in the context havebeen done for grid computing [10][11]. For example, Wuet al. [10] have proposed an adaptive prediction of gridperformance with a confidence window for the historicalvalues. They used an auto-regression to find a model forthe historical interval by which predicts the future work-load. However, we consider the historical data variation toenhance the prediction accuracy and bound the predictedrange. As shown in Figure 2, the number of VMs shows arandom behavior, but it also depicts a certain pattern. Forinstance, it starts low at morning then increases reachingthe peak at around the midday. At evening, it starts to godown again. Our approach uses an adaptive window-size of historical values to provide a high accurate prediction range.In Figure 1, the measured workload values are shown by aseries of line-dots up to time t. On the other hand, the graydot represents the predicted workload value. •  Window selection: our interest is to predict the num-ber of VMs for the next 5 minutes from the historicalwindow hw. The historical window-size is determinedbased on the P-value of both F-test and T-test to filterout the values that are very unlikely to be in the samewindow. We used F-test and T-test to probe the sig-nificance of the change in variance and mean betweentwo samples of populations, respectively. Using theP-value of F-test and T-test, we can decide whetherthe two samples have almost the same variance andthe same mean. For example, after performing F-test,if we find out that the P-value is less than  α  = 0 . 05,we reject the null hypothesis. This means that thesevalues do not belong to the same historical window.Thus, the algorithm stops going back to take morehistorical values and moves to the next stage, which iswindow smoothing. •  Window smoothing: using prediction algorithms withthe historical values causes errors. Thus, we used asmoothing filter to remove noise and prevent its in-fluence on the prediction algorithm. There are manysmoothing filters, but we selected Savitzky-Golay filterdue its effectiveness in keeping the peak values andremoving the spikes, which can be considered as noise.The filter has two significant parameters that guidethe smoothing process: the frame size and polynomialdegree. In our approach, the frame size is not constant,and it equals to the selected historical window-size. Incontrast, Wu et al. [10] fixed the frame size. •  Range prediction: we used Holt-Winter implementedin the R-tool, because it dynamically optimizes anddetermines the level and the trend of the time series.Importantly, we determine the predicted range basedon the single predicted point value pv and the standarddeviation of the selected window  σ hw . The predicatedrange pr  { r l  ,  r h }  where  r l  and  r h  equal (  pv  −  σ hw )and (  pv  +  σ hw .) 2.1 Planet-lab Workload Traces The monitoring infrastructure project of Planet-lab [6]provides traces of historical data for CPU utilization, whichmeasured every 5 minutes. These traces are for more thana thousand machines running in more than 500 locationsaround the world. Here, we present data for two days thathave different workload fluctuations. We assume that thesemachines are hosted as VMs.To simulate the on-demand concept of the cloud com-puting environment (i.e., the open system behavior), weterminate the VMs with less than 5% CPU utilization. Inother words, we considered it as being destroyed and exitedthe system. Then, when the trace shows a VM with a CPU  440 460 480 500 520 540 560 580 0 50 100 150 200 250    N  u  m   b  e  r  o   f   V   M  s Time index (5 min.) (a) Day03  320 340 360 380 400 420 440 460 480 500 0 50 100 150 200 250    N  u  m   b  e  r  o   f   V   M  s Time index (5 min.) (b) Day06Figure 2: Planet-lab workload traces  utilization higher than 5%, we consider a new request forprovisioning a VM. 2.2 Implementation and Evaluation We implemented the proposed approach using Java withintegration of the R-tool, which consists of many statisticalfunctions and the required filters. Here, we present theresults of our approach. Figure 3 shows the predicted rangefor each value of workload (i.e., number of VMs). Thelow predicted  r l  is shown by a red dashed-line meanwhilethe high predicted  r h  is represented by a blue dashed-line.The purple sold-line represents the single point predictedvalue. The predicted range is propositional to the workloadfluctuation. For instance, due to the low fluctuation of theworkload around the time index 58, the predicted range issmall. Contrarily, a large range is predicted around the timeindex 225.Figure 3: The results of the range-based prediction approach 3. ROBUST OPTIMIZATION As we implemented the prediction approach based on arange not a single value, we will study the implementationof robust optimization for capacity planning. Robust op-timization deals with optimization problems whereas therobustness is sought against uncertainty or deterministicvariability in the value of a parameter of the problem (i.e.,the workload). The principle of robust optimization con-siders point prediction meaningless and it is replaced byrange prediction. Thus, robust optimization addresses datauncertainty by assuming that uncertain parameters belongto a bounded range. In our approach, we avoid the as-sumption that considers the precise knowledge of the work-load demand in the planning horizon where many proposedsolutions have solved the problem as a deterministic op-timization [1][2][3]. We have a predicted range, centeredat the nominal prediction ¯ d , for the demand at each timeperiod. The robust optimization approach replaces eachdeterministic demand ¯ d  by an uncertain parameter ˜ d  = ¯ d + ˆ d *z, where  | z  | ≤  1. Furthermore, it guarantees that theconstraints hold for a given uncertainty set. cient of itsconstraint matrix. to solve this problem 3.1 Robust Problem Formulation In this section, we present a robust formulation of thecapacity planning problem. We use the following notation: e idle  is the energy consumption of a server during idle state(i.e.,  p idle * t idle  ). The parameter  e swt  is the energy con-sumption of a server to change from power-state to another,which consumes  p swt  and takes  t swt  seconds. So,  e swt  thepower-state change energy wastage equals  p swt * t swt . Thebinary variables n and b represent currently active serversand previously active servers, respectively. The parameters˜ nv , ¯ nv , and ˆ nv  represent the uncertain number of VMs, themean of the predicted number of VMs, and the standarddeviation of the predicted number of VMs, respectively. Theparameters ˜ vc , ¯ vc , and ˆ vc  represent the uncertain utilizationof a VM, the mean of the VM’s utilization, and the standarddeviation of the VM’s utilization, respectively. Finally, theparameter ˜ d  is the total uncertain demand of the numberof VMs and their utilization. The objective function inEquation 1 is to minimize the wastage energy that mightresult from keeping the server idle and switching the power-state of a server. Equation 2 guarantees that the constraintshold for a given uncertainty set of the demand in Equa-tion 3. Equation 4 and Equation 5 represent uncertaindemand of a number of VMs and uncertain utilization of VMs, receptively. We formulate this problem based on thefollowing assumption. When a VM is requested, it occupiesa certain portion of a server capacity. For instance, a small-instance with 1 vCPU might take 1/4 of a server has 4logical cores. Then, after running the VM for while the realresource consumption of this VM can be revealed and will betaken into consideration for the next planning period. Theconstant parameters  t swt ,  t idle ,  p swt  and  p idle  are 150s, 300s,120watts, 100watts, respectively. Observably, the switchingpower is slightly greater than the idle power due to theCPU utilization. The power constants were set based onSPECpower [12] results of HP ProLiant ML110 G3 server[13]. A scalar variable z models the demand uncertainty. Wedo not presume exact knowledge of the actual distribution of demand, but instead we assume that the distribution is char-acterized by the mean of the number of VMs ¯ nv  and theircapacity ¯ vc  and standard deviation of the demand of thenumber of VMs ˆ nv  and their capacity ˆ vc . Moreover, we havean accurate estimations of the most optimistic uncertainty z  min  and the most pessimistic uncertainty  z  max . Theseparameters form lower and upper bounds of z, respectively.Minimize: ns  i =1 e idle  + ns  i =1 e swt  ∗  ( n  ∗  (1  −  b ) +  b (1  −  n )) (1)Subject to:˜ d  ≤ ns  i =1 ˜ sc i  ∗  n  (2)˜ d  = nv  i =1 ˜ vc i  (3)˜ nv  = ¯ nv  + ˆ nv  ∗  z  nv  (4)˜ vc  = ¯ vc  + ˆ vuz  vc  (5) | z  | ≤  1 , z   = [ z  min ,z  max ] , and n,b  ∈ { 0 , 1 } 3.2 Implementation and Evaluation To solve a robust optimization problem, we used RobustOptimization Made Easy (ROME), which is an algebraicmodeling tool implemented in the MATLAB environment  [14]. ROME operates as an intermediate layer between themodeler and optimization solver engines. It helps convertingthe srcinal uncertain optimization problem into its robustcounterparts. Its core functionality consists of translatingmodeling code into an internal structure in ROME. Then,it translated into a solver-specific input format for solvingby linear optimization solvers. This can be done manually,but it is tedious and error-prone [14]. We used IBM ILOGCPLEX as optimization solver.Figure 4 depicts simulation results of a deterministic op-timization and different values of uncertainty scalar z. Thelift axis represents the amount of energy and the right axisrepresents the percentage of the energy consumption by thepower-state switching and the idle state. The deterministicresult means that prediction of the VMs demand is 100%accurate. So, we used the real traces to perform capacityplanning using deterministic optimization. Then, we com-pared the results with the range-based prediction taking intoaccount uncertainty of demand. This shows the results withdifferent range of uncertainty scalar z. Figure 4 depicts thefollowing observations. In deterministic, there is no idleenergy consumption, because we assumed that the demandis known, and the total wastage energy results from changinga server’s power-state. On the other hand, the robust opti-mization considering the uncertainty of the demand, we haddifferent results by changing the uncertainty scalar z. First,the range of uncertainty is very wide, z { -1,1 } . The totalof the objective function and the total of idle energy arethe highest, and the total of switching energy is the lowestcompared to the other results. Second, when changing theuncertainty scalar z from z { -1,1 }  to z { -0.5,0.5 } , we decreasedthe uncertainty range. Thus, we could save energy by reduc-ing an unbeneficial power-state switching and keeping someserver idle. This also can increase the system availabilityand reliability. Finally, when z was set  { -0.25,0.25 } , wecould achieve more energy savings from both power-stateswitching and idle servers. However, this can cause someunder provisioning of capacity and violation of allocationsome VMs. The calculated mean and standard deviation of under provisioning VMs are 3VMs and 5VMs, respectively.Importantly, the execution time of our proposed approachis less than 1 second while using a computer with Pentium2.6GHz processor. 0 20 40 60 80 100 120 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Deterministic base-line Robust z{-1,1} Robust z{-0.5,0.5} Robust z{-0.25,0.25}    P   e   r   c   e   n   t   a   g   e   E   n   e   r   g   y    (   K   W .   H    ) Approach Sum of Obj. Fun. Sum of Energy by SWT Sum of Energy by IdlePe r c. Energy by SWT Pe r c. Energy by Idle Figure 4: The result of the proposed robust optimizationapproach 4. CONCLUSIONS AND FUTURE WORK In this paper, we presented a proactive robust optimiza-tion approach for capacity planning in virtualized data cen-ters. To achieve this, we implemented a range-based pre-diction algorithm, which allows formulating the problemusing the robust optimization. The robust optimizationmodel takes into account the prediction uncertainty. Wecompared the results of deterministic and robust of capacityplanning, and we found that the robust optimization morerealistic to be used in data centers where VMs demandand their utilization are uncertain. Importantly, by usingour approach, we could achieve energy saving and providehigh availability and reliability for the system. As futurework, we will consider heterogeneous servers and VMs size.Furthermore, we intend to extend our approach for a dy-namic provision of web applications. Thus, we intend tocompare our approach against the other approaches thatuse stochastic and deterministic optimization for dynamicprovision of web applications. Furthermore, we intend toinvestigate applying our approach to other resources, wherewe just consider only the CPU demand of VMs. 5. 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