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Adaptive Data Center Activation with UserRequest Prediction

Min Sang Yoon, Student Member, IEEE, Ahmed E. Kamal, Fellow, IEEE and Zhengyuan Zhu

Abstract—The problem of energy saving in data centers has recently attracted significant interest within the research community, andthe adaptive data center activation model has emerged as a promising technique to save energy. However, this model has notintegrated adaptive activation of switches and hosts in data centers because of its complexity. This paper proposes an adaptive datacenter activation model that consolidates adaptive activation of switches and hosts simultaneously integrated with a statistical requestprediction algorithm. The learning algorithm predicts user requests in a predetermined interval by using a cyclic window learningalgorithm. Then the data center activates an optimal number of switches and hosts in order to minimize power consumption that isbased on prediction. We designed an adaptive data center activation model by using a cognitive cycle composed of three steps: datacollection, prediction, and activation. In the request prediction step, the prediction algorithm forecasts a Poisson distribution parameterλ in every predetermined interval by using Maximum Likelihood Estimation (MLE) and Local Linear Regression (LLR) methods. Then,adaptive activation of the data center is implemented with the predicted parameter in every interval. The adaptive activation model isformulated as a Mixed Integer Linear Programming (MILP) model. Switches and hosts are modeled as M/M/1 and M/M/c queues. Inorder to minimize power consumption of data centers, the model minimizes the number of activated switches, hosts, and memorymodules while guaranteeing Quality of Service (QoS). Since the problem is NP-hard, we use the Simulated Annealing algorithm tosolve the model. We employ Google cluster trace data to simulate our prediction model. Then, the predicted data is employed to testthe adaptive activation model and observe energy saving rate in every interval. In the experiment, we could observe that the adaptiveactivation model saves 30 to 50% of energy compared to the full operation state of data centers in practical operating conditions of datacenters.

Index Terms—Data center, operational power minimization, Fat-tree data center, traffic prediction, machine learning, queuing theory,Mixed Integer Linear Programming.

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1 INTRODUCTION

Increase in data traffic with mobile devices and expansionof cloud computing environment will demand continuousgrowth in data center utilization and energy consumption.Data centers consumed 91 billion kilowatt-hours of electric-ity in 2013, which is equivalent to energy from 34 large coalfire power plants. This huge amount of energy consumptionin data centers has attracted interest from many researchers,and many energy saving models are proposed. Amongmany proposals, the adaptive data center activation modelhas emerged as the most promising energy-saving strategiesthat controls the activation of hosts and network switches tosave energy. However, the complexity of the problem hasprevented researchers from developing cooperative activa-tion strategy of switches and servers simultaneously. As aresult, only a few studies have considered the joint adaptiveoperation of data center network and server layers [1][2].However, the latency and service quality constraints are notconsidered in the previous study of [1].

With the goal of standardizing energy-aware networkmanagement, the European Telecommunications StandardsInstitute (ETSI) published ETSI Standard (ES) 203 237, ’theGreen Abstraction Layer (GAL)’, which is a framework tomanage energy efficient networks of the future [3], [4], [5].The GAL is an architecture interface that provides informa-tion exchange between the power managed data plane andthe control plane. The GAL supports discovery, provision-ing, and monitoring of functionalities in the networks, andregulates QoS of the network. The overall network powerconsumption through adaptation of Network-wide ControlPolicies (NCP) and Local Control Policy (LCP). We followthe GAL scheme in this paper. The NCP is applied by the

controller in the data center and the LCP controls eachserver and switch state, such as ports, memory, and nodestates, according to the control policy of controller.

In this paper, we propose an advanced interactive adap-tive data center activation model that controls switch andhost layers’ activation simultaneously while satisfying Qual-ity of Services (QoS) requirements. This model will beimplemented as an adaptive data center activation modelwith a three step cognitive cycle: data collection, requestsprediction, and data center activation. An accurate predic-tion of user requests should support the implementation ofthe adaptive activation model properly. According to [6], in2013 50% of the energy is wasted in data centers due to lackof awareness of the traffic. This data shows how the accurateprediction of the requests will be increasingly important inthe future with an indisputable increase in energy consump-tion. Also, the accurate request prediction has an effect onthe performance of data centers. Excessive deactivation ofcomputing or network devices for energy saving will causea bottleneck and delay in handling requests.

For the prediction step, we collect the history of requestsarriving at the data center and observe the histogram. Basedon the histogram analysis, we decide on a probability distri-bution model to fit to the collected data. Then, parametersof the probability distribution model are inferred usingthe Maximum Likelihood Estimation (MLE) method andsaved for the prediction. After enough data is collectedfor prediction, the prediction model estimates parametersof the probability distribution with Local Linear Regression(LLR) by using a cyclic window approach. Parameters of theprobability distribution are time-dependent on data, whichmeans the parameters change with time. Therefore, the

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parameters have different patterns during every interval,but they exhibit the same pattern during the same period inevery day or every week.

Arriving traffic is not constant. The traffic usually in-creases during daytime and decreases during night. There-fore, powering all components of data center will wasteunnecessary energy when there is low traffic. Deciding onthe number of activated switches and hosts is important anddepends on arriving job rates. If a data center is runninginsufficient hosts compared to requests, it will not be ableto serve all requests from users. Even if there are enoughhosts, if the data center is not operating enough switchesin order to save energy, it will cause latency in transferringdata. Most of data centers architectures are constructed witha tree architecture, so if the data center does not activatenecessary switches for connecting core switches to hosts, itwill fail to transfer requests to hosts.

We develop an optimal energy consumption model forthe Fat-tree based data center depending on the incomingrate λ while guaranteeing QoS and connectivity.

For optimal energy consumption of data centers, we con-trol the activation of switches, server nodes, switch ports,and memory modules. The server power consumption isestimated as 40 to 55% and switch layer power consumptionis estimated as 10 to 20% from the total data center energyconsumption [1]. Thus, deactivating unneeded hosts andswitches is expected to save a significant portion of energy.Turning off unneeded switch ports will result additionalenergy savings. Since we deactivate servers and switches,it is possible to turn off ports connected to inactive nodes.We also dynamically activate memory of switches and hostsbecause the memory also consumes a significant portionof energy. According to [7], DRAM consumes 25% of totalpower in data centers.

Scalability of data centers is an important issue. As trafficrequests to data centers increase, many data center operatorsface the need for increasing data centers sizes. Most of datacenters are designed homogeneously, which means that itis not easy to increase the capacity of data center resources.Our model employs a heterogeneous Fat-tree architectureof data centers that is controlled with a Software DefinedNetwork (SDN) controller.

We model an optimal SDN controlled data center usinga Mixed Integer Linear Program (MILP). Switches are mod-eled as M/M/1 queue and servers are modeled as M/M/cqueue. This model will minimize the operational powerby deciding active switches, hosts, and operating memory.The problem is NP-hard. Therefore, Simulated Annealing isused to find a near optimal solution of the problem withinreasonable computation time.

Google cluster-trace data, which is real measurements ofusage requests in Google cluster, is employed to test ourprediction model and predict λ for the adaptive activationmodel.

To summarize, the contributions of this paper are: i)A request prediction algorithm is developed by using acyclic window learning approach. The algorithm predictsthe probability distribution parameters of requests duringevery predetermined period. ii) An optimal adaptive datacenter activation model is modeled as MILP. The data centeroperates the minimum number of switches and hosts whileguaranteeing the QoS requests submitted to the data center.

iii) We designed an adaptive data center activation modelwhich activates the data center in every predeterminedperiod based on predicted traffic.

The rest of the paper is organized as follows. Previ-ous work is reviewed in Section II. The system model foradaptive activation model is introduced in Section III. Weintroduce the requests prediction algorithm in Section IVand adaptive data center activation model in Section V. InSection VI, the Simulated Annealing algorithm is presentedto solve the NP-hard optimization problem. Simulation re-sults of the prediction model and adaptive activation modelare presented in Section VII and we end this paper withconclusions in Section VIII.

2 RELATED WORK

2.1 Traffic prediction in cloud systems

Request prediction in cloud and data center has been stud-ied by many researchers for the adaptive scaling of systems.

Akindele A. Bankole et al. employ the machine learningfor predictive resource provisioning in the clouds [8]. Theirprediction model is achieved with machine learning tech-niques including: Neural Network, Linear Regression, andSupport Vector Machine. They predict the CPU utilization,response time, and throughput based on collected data fromvirtual machines web servers and database servers. Theprediction model generates prediction values in every givenminute with machine learning techniques and measure errorrate with Mean Absolute Percentage Error (MAPE) andRoot Mean Squared Error (RMSE). However, the predictionmodel did not show a high prediction accuracy, and theirresults show 24% prediction error in predicting the CPUutilization at a certain point of time and a 21% error in theresponse time prediction.

Sedeka Islam et al. present more advanced machinelearning techniques for predicting resource usage in [9].Error Correction Neural Network (ECNN) and the LinearRegression techniques are employed for the prediction.Then they included a sliding window method to reflect thecurrent state of the system. They generated prediction val-ues based on window sizes and evaluated them with MAPE,PRED(25), RMSE, and R2prediction accuracy. The CPUutilization data is collected from the Amazon EC2 cloudthrough the TPC-W benchmark and prediction values aregenerated with the ECNN and Linear Regression method.The prediction values of CPU utilization have around 19%error rate without the sliding window and have a minimum18.6% error rate when they employ the sliding window.

Many statistical approaches are also applied to trafficprediction in clouds. Bruno Lopes Dalmazo et al. proposea traffic prediction approach based on a statistical modelwhere observations are weighted with Poisson distributioninside a moving window [10]. They consider the past in-formation by means of a sliding window of size λ andthis window is applied by weighting the past observationsaccording to the Poisson distribution with parameter λ.Dropbox trace data is employed for testing their predic-tion model and Normalized Mean Square Error (NMSE)evaluation method is utilized for error measurement. Theprediction model could achieve NMSE values between 0.044and 0.112. The prediction is ideal when NMSE value is equal

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to zero and worse when it is greater than one. This approachachieves a reasonably accurate prediction.

They also propose a traffic prediction model with adynamic window approach [11]. The sliding window sizeis changed based on variance of the previous window size.A small variance indicates the predicted data is close to theactual data while a high variance means the predicted datais spread out from the mean. Therefore, they update thewindow size in every prediction interval by consideringthe size of the variance in the previous prediction. Theprediction accuracy is improved from 7.28% to 495.51%compared to the previous statistical model.

2.2 Cloud system modeling using queuing theoryJordi Vilaplana et al studied the computer service QoSin cloud computing based on queuing theory [12]. Cloudplatforms are modeled by an open Jackson network whichconsists of multiple nodes, where each node correspondsto a queue in which the service rates are node dependent.They modeled multi-server system with Entering Server(ES) and Processing Server (PS). ESs are modeled by M/M/1queues, which works for the load balancer, PSs are modeledas M/M/m queues. However, all queues are assumed tohave the same service rate so heterogeneity of systems isnot considered. By using the queuing system analysis, theyanalyzed the response time of the global cloud architecturewith different parameters.

Wei-Hua Bai et al investigated heterogeneous moderndata centers and the service process in data centers byusing queuing theory [13]. They built a complex queuingmodel composed of the master server and computing nodes.The master node works as the main scheduler to allocateresources for tasks to dispatch a node to execute tasks,which is modeled as M/M/1/K queue. Computing nodeswhich are a multi-core server are modeled as an M/M/cqueue because each multicore execution server can parallel-process multiple tasks. By using queuing theory analysis,they investigate system metrics such as the mean responsetime, the mean waiting time, and other important perfor-mance indicators. Although they investigated the systemperformance of heterogeneous data centers efficiently, theydid not include the switch node in their consideration.Since the switch architecture and connections with serverssignificantly affect data centers performance, switches arealso required to be considered when we analyze the datacenter performance.

Junwei Cao et al studied the problem of optimal multi-server configuration for profit maximization in cloud com-puting environments [14]. They included the amount ofservice, the workload of an application environment, theconfiguration of multiserver system, the service level agree-ment, the satisfaction of a consumer, the quality of service,the penalty of a low-quality service, the cost of renting,the cost of energy consumption, and the service provider’sprofit margin in their profit modeling and maximizedtheir profit through optimal multiserver configuration. Theymodeled a multiserver system as an M/M/m queuingmodel so that the optimization problem can be formulatedand solved analytically. For more general analysis, theyderived the density function of the waiting time of a newlyarriving service request and the expected service charge toa service request is also calculated.

2.3 Power saving in cloud systems

Energy saving in data centers is considered in many aspectsbecause of its importance. Junwei Cao et al. propose optimalpower allocation and load distribution in a heterogeneousdata center environment [15]. They model a multicore serverprocessor as a queuing system with multiple servers andprove optimal server setting for two different core speedmodels, idle speed model and the constant speed model.

Kuangyu Zheng et al. propose joint power optimizationof data center network and servers with correlation analysis[1]. They propose a power optimization strategy that lever-ages workload correlation analysis to jointly minimize totalpower consumption of servers and data center network.After they analyze the correlation between Virtual Machines(VMs), they consolidate VMs that are not correlated witheach other onto the same physical servers to save serverpower consumption and consolidate network traffic to savedata center network power. Through this approach, theycould achieve up to 51.6% of energy saving in their testbed.This paper has a similarity with our proposal in termsof joint optimization of data center networks and servers.However, the authors consolidate VMs based on correlationanalysis between VMs, and then activates traffic flow be-tween VMS that are correlated, which means the activationof servers and switches are not jointly considered. Also, thetraffic flow is consolidated between correlated VMs. Thus,this strategy cannot guarantee connectivity between physi-cal servers due to data center network layer deactivation.

This paper has differences from all previous works in thefollowing aspects: Our prediction model predicts the prob-ability distribution parameter in a certain period insteadof predicting quantified value of requests. Therefore, weachieve a more flexible prediction by deciding the desiredprobability of the predicted distribution.

The dynamic data center activation model integrates thedynamic operation of switch layer and server layer whileguaranteeing the performance of the data center network.Since we jointly decide activated switches and hosts, wecould save more energy compared to other dynamic activa-tion models which determine operating hosts and switchesindependently.

3 SYSTEM MODEL

3.1 Distribution parameter adaptive data center activa-tion model

The cognitive cycle of the adaptive data center activation,which is shown in Fig. 1, is composed of three phases: datacollection, request prediction, and data center activation.For the first phase, the control plane collects the numberof incoming tasks and refines collected data to utilize it forthe prediction. The collected data is saved in the predictiondata set and the prediction model employs it to forecast thefuture requests of users by using a cyclic window learningalgorithm. According to the predicted requests, the controlplane solves the adaptive activation problem and activatesthe optimal set of switches and hosts, and keeps unneces-sary components in the idle state. This cycle is repeatedperiodically in every predetermined period. For example,if we set the duration to 30 minutes, the system repeats onecycle every 30 minutes. Thus, the system can reconfigure the

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data center every 30 minutes in order to reduce the waste ofresources.

In adaptive data center activation, the system setup timeis not a negligible factor of system performance. The inactivedevices are kept in standby or low power idle states asdescribed in [3], [4]. If the devices are put in the low poweridle state for power saving purpose, a longer wake up timewill be required when the device is activated. By using thecognitive cycle of the system, the wake up delay of devicescan be minimized through the predictive system activation.The prediction process is executed in advance of the systemactivation. Based on the prediction result, the controller canput newly activated devices in the standby state. So thesystem wake up time will be minimized according to theprediction and activation schemes.

Figure 1: Cognitive cycle of system

3.2 Fat-Tree Data CenterThere are many data center architectures: Fat-tree, VL2,Bcube, and so on. In this paper, we adopt the Fat-treearchitecture, the most widely used data center architectureby many cloud service providers [16], [17].

Fat-tree is composed of three switch layers (core, aggre-gation, and Top of Rack (ToR) layer) and a host layer asshown in Fig. 2. All switches have the same number of ports.If we assume the number of ports in each switch is k, wehave k core switches and k Points of Delivery (POD). Coreswitches are grouped into k/2 groups. Since a core switchhas k ports, each core switch is connected to all PODs. Forexample, in Fig. 2, the first core switch in each group isconnected to the first aggregation switch in each POD andthe second core switch in each group is connected to thesecond aggregation switch in each POD. Each POD has k/2aggregation switches and k/2 ToR switches. Aggregation,ToR switches, and their interconnection network forms acomplete bipartite graph. Since a ToR switch uses k/2 portsfor connecting aggregation switches, they can serve k/2hosts each. Therefore, the data center has a total of k3/4hosts.

The Fat-tree architecture is widely used because of itsscalability and interconnection capability [16]. Due to thescalable characteristic of Fat-tree data center, it is able toconfigure large size data center with lower Capital Expendi-ture (CAPEX). Also, interconnections between hosts in thesame data centers are easy with full bandwidth.

In the Fat-tree architecture, we cannot deactivate nec-essary switches to operate required hosts because of itsconnectivity. For example, the first ToR switch cannot beturned off when we want to allocate jobs to the first host inthe first POD. In our model, the core switch should be ableto reach any host using three links and a host should be ableto reach a core switch using three links as well. Therefore,we will turn on and off switches without violation of thisrule to guarantee connectivity.

3.3 SDN based data center

For comprehensive management of network management,we employ an SDN based data center model. The SDNbased data center is composed of the control plane and thedata plane. The control plane plays the role of managingthe network and deciding routing paths. The data planejust forwards data according to the values in the forwardingtable.

The control plane should have access to data planeswitches and needs to receive system status informationfrom all data plane switches. All switches implement thedata plane functionality since they have to forward data. Inaddition, the core switch layer implements the control plane.

Since the workload distribution and resource allocationare determined by the control plane switches, the data centercan activate only a limited number of switches and hosts byallocating workloads optimally.

Figure 2: SDN fat-tree data center model (k=4)

4 REQUEST PREDICTION ALGORITHM

The prediction model estimates parameters of the proba-bility distribution of future user requests in every prede-termined period. For the traffic analysis, one week trafficdata is selected from Google Cluster trace data in [18].Since the data is selected starting from a random point ofthe whole data, we do not know the exact data and timeof the traffic measurement. However, we could find thatuser requests have obvious patterns and the patterns arerepeated periodically, as shown in the Fig. 3.

The hourly pattern shows high peaks for the first 4 hoursand the last 10 hours. So, we can assume daytime startsaround the 10th hour from the measurement and end at the4th hour in Fig. 3. If we observe the daily pattern, the firsttwo days and the last two days show higher requests. In thesame way, we can assume weekdays start on the 4th dayof the measurement by assuming requests increases during

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weekdays rather than the weekend. The daily pattern analy-sis of task arrivals presents obvious patterns of the incomingrequests. Therefore, the cyclic data collection should be aneffective approach for the prediction. Based on our analysis,the prediction model adopts periodic history data at thesame time point in order to make predictions about futuredata center loads.

Figure 3: Prediction data set

We introduce three time scales for the prediction periods:Pattern Period (PP ), Target Period (TP ) and UtilizationPeriod (UP ). The PP is a cyclic interval that exhibits patternrepetition. The TP is a unit duration for which we wantto make a prediction. The UP is a cyclic window that weuse for predicting the activities in TP . In the example, wepredict the request distribution during a certain Monday byassuming the same pattern is repeated every week. Then,we can set the TP to a day and the PP to a week becausewe assume the pattern of a day is repeated every week. Ifwe only use the past Mondays′ data for the prediction, theUP becomes one day.

Since patterns are repeated on every PP , any timeduration for the prediction corresponds to a certain TP onthe PP . Therefore, we can predict the request distributionduring any time interval by correlating them to a certain TPon the PP . For precise prediction, data is accumulated forseveral PP s. Although patterns of the traffic distributionswill be similar at the same time point in every PP , thetraffic amount will be different. In other words, we cansay the distribution of the traffic shows similar pattern inevery Monday, but we cannot ensure that the amounts oftraffic will be the same. Therefore, the prediction model canachieve higher prediction accuracy by accumulating dataduring several PP s.

To implement prediction, the data set saves the past datain an m× l matrix. m represents the number of TP s on thePP and l denotes the number of PP s we accumulate. In Fig.4, each vertical block corresponds to saved parameters of theprobability distribution in each TP during a PP . We startto stack the data from the first block of the first iteration.If the data set is filled until the TPm’s block, which is thelast TP, we move to the second iteration and stack the datafrom the first block of the second iteration, which meanswe have saved data during a PP . When the matrix is full,the data set goes back to the first block of the first iteration

Figure 4: Prediction data set

and replaces the old data to reflect the tendency of recentrequests.

Any time duration that we want to predict the trafficdistribution can be related to a certain TP on the matrix.In order to make a prediction, the UP data is employed.In Fig. 4, we can see that distribution parameters of TPmcan be predicted by using UPm. We can set the size of UPdepending on how many previous TP s will affect the stateof the current TP . For example, UP is set to two days andTP is one day, e.g., previous Sunday and Monday′s historyparameters are utilized to predict next Monday’s requestdistribution.

In this paper, the prediction model forecasts the numberof task arrivals during each target period. In the first step ofprediction, the prediction model constructs a histogram ofuser requests in every target period to observe distributionsof requests. Then, it fits a probability distribution to the dis-tribution of requests. When the probability distribution ker-nel is decided for fitting, we adopt MLE in order to obtainparameters of the probability distribution in every observedperiod and the parameters are saved on the data set. Afterthe data set accumulates enough data for prediction, it isable to predict parameters of a following TP . LLR will beemployed to predict parameters of the future requests. LLRis one of the kernel smoother techniques for estimating areal valued function, when no parametric model for thisfunction is known. Since the data set is updated and solvedin every predetermined period, the prediction model is adynamical operation problem. The detailed process of thealgorithm is included in [18].

5 ADAPTIVE DATA CENTER ACTIVATION MODEL

We formulate an adaptive data center activation problemas an MILP. Our objective is to minimize the activationpower, port power, and memory power consumption in thedata center while guaranteeing QoS. This model decides theactive state of switches and hosts by using binary variablesand determines load distribution over switches and hostswith continuous variables. Based on allocated workload inswitches and servers, controllers can determine how manymemory modules need to be on. We assume that jobs arriveat the data center according to a Poisson distribution withrate λ. We define the following variables:• Cij : working state of ith group jth core switch; binary variable.•Aij : working state of ith POD jth aggregation switch; binary variable.• Tij : working state of ith POD jth ToR switch; binary variable.• Hij ToRmn : working state of ith POD jth host connected to ToRmn

ToR switch; binary variable.•MCij , MAij , MTij , MHij ToRmn

: The number of operating memory

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modules in core, aggregate, ToR switches, and hosts; integer variables.• λCij , λAij , λTij , λHij ToRmn : Job arrival rate to core, aggregate, ToRswitches and hosts; continuous variable.• λCij l : Job arrival rate to ith POD jth core switch lth port; continuousvariable.• λAij l : Job arrival rate to ith POD jth aggregation switch lth port;continuous variable.• λTij l : Job arrival rate to ith POD jth ToR switch lth port; continuousvariable.• P static

Cij, P static

Aij, P static

Tij, P static

Hij ToRmn: Static power consumption of

core, aggregate, ToR switches and hosts during a unit time; constant.• P dynamic

Cij, P dynamic

Aij, P dynamic

Tij, P dynamic

Hij ToRmn: Dynamic power con-

sumption of core, aggregate, ToR switches and hosts on the full utiliza-tion state during a unit time; constants.• P port

Cij, P port

Aij, P port

Tij: Power consumption of each port in core,

aggregate, and ToR switche per job; constants.• Pmemory

Cij, Pmemory

Aij, Pmemory

Tij, Pmemory

Hij ToRmn: Memory power con-

sumption of core, aggregate, ToR switches and hosts during a unit time;constants.• µCij , µAij , µTij , µHij ToRmn : service rate of core switch; constants.• λ: Job arrival rate to data center; constant.

5.1 Objective Function

Minimizepactivation + pport + pmemory (1)

The objective function includes activation power, portpower, and memory power consumption during a unittime. Activation power is the power consumption necessaryfor operating switches or hosts. Port power is the powerconsumption for transmitting a job through the port. Weassume that ports are in the idle state when they do nottransmit jobs and do not consume power in the idle state. Soport power is calculated depending on the number of jobsthey transmit. Memory power is determined depending onhow many memory modules are powered. If we turn onmore memory modules than those required in a switch or ahost, this will waste energy. Therefore, we propose to turnon the appropriate number of required memory modulesbased on statistical estimation.

5.1.1 Activation Power

pactivation =

k/2∑i=1

k/2∑j=1

Cij(PstaticCij + P dynamicCij

λCijµCij

)

+

k∑i=1

k/2∑j=1

Aij(PstaticAij + P dynamicAij

λAijµAij

)

+

k∑i=1

k/2∑j=1

Tij(PstaticTij + P dynamicTij

λTijµTij

)

+

k∑i=1,m=1

k/2∑j=1

k/2∑n=1

Hij ToRmn(PstaticHij ToRmn

+ P dynamicHij ToRmn

λHij ToRmnµHij ToRmn

)

(2)

We can calculate the activation power by considering thestatic and dynamic power of switches and hosts. The staticpower is a constant power required for activating switches

and hosts. The static power can be calculated by multiplyingthe binary variables that represent the state of each switchand host by the static power consumption constant of eachswitch and host. The dynamic power increases proportion-ally to the utilization rate of switch and host. Thus, thedynamic power can be computed by multiplying the utiliza-tion, λµ , and dynamic power consumption constant of eachswitch and host. The dynamic power expression includesa non-linear term, corresponding to the multiplication ofthe binary variable and continuous variable. This non-linearterm can be linearized by using a simple transformationintroduced in Section 5.2.1.

5.1.2 Port Power

pport =

k/2∑i=1

k/2∑j=1

k∑l=1

λCij lPportCij

+

k∑i=1

k/2∑j=1

k/2∑l=1

λAij lPportAij

+

k∑i=1

k/2∑j=1

k/2∑l=1

λTij lPportTij

(3)

Port power should only be considered in switches. Theproblem decides how each switch will distribute arrivingjobs through which port. Therefore, we can measure theport power consumption by multiplying the amount of jobspassing through each port and the power consumption perjob of each port.

5.1.3 Memory Power

pmemory =

k/2∑i=1

k/2∑j=1

MCijPmemoryCij

+

k∑i=1

k/2∑j=1

MAijPmemoryAij

+

k∑i=1

k/2∑j=1

MTijPmemoryTij

+

k∑i=1,m=1

k/2∑j=1

k/2∑n=1

MHij TmnPmemoryHij ToRmn

(4)

We will estimate the number of jobs in each switch andhost memory by using a queuing model. Then we candecide how many memory modules we need to operatebased on the estimated number of jobs in each switchand host by queuing theory. After we decide the numberof working memory modules, we can evaluate memorypower consumption by multiplying the number of memorymodules and memory power consumption of each memorymodule in each switch and host.

5.2 Load Distribution Constraints

Workload should be distributed rationally in the data center.Since we are proposing to turn off parts of the switches andhosts, we have to decide exactly which port will transferjobs to the lower layers in order to prevent job losses. Forexample, if the core switch transfers jobs to an inactiveaggregation switch, we will not be able to allocate thosejobs to hosts. Thus, load distribution constraints decide howwe distribute the workload to low layer switches throughwhich ports.

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5.2.1 Load Distribution in Each Layer

The summation of workload in each layer should be equiv-alent to λ, the total arriving workload to the data center.The inter-POD traffic does not need to go through the coreswitch layer in traditional data centers. However, all trafficgoes through the core switch layer in SDN data centerarchitecture. Therefore, the summation of traffic in eachlayer will be the same. The purpose of this constraint is toallocate the workload to working switches and hosts whileguaranteeing that we forward all requests to hosts.

k/2∑i=1

k/2∑j=1

CijλCij = λ (5)

k∑i=1

k/2∑j=1

AijλAij = λ (6)

k∑i=1

k/2∑j=1

TijλTij = λ (7)

k∑i=1,m=1

k/2∑j=1

k/2∑n=1

Hij ToRmnλHij ToRmn = λ (8)

Equations (5)-(8) are multiplications of binary variablesand continuous variables, so they are non-linear equation.Therefore we linearize those non-linear constraints. Whenx is a binary variable and y is a continuous variable thatis greater than or equal to zero, we can linearize theirproduct by replacing it by a continuous variable t with theconstraints shown below.

0 ≤ t ≤ max(y) · x (9)

y − (1− x) ·max(y) ≤ t ≤ y (10)

The maximum of continuous variables, λCij , λAij , λTij ,and λHij Tmn is λ because it is the maximum workloadthat can be allocated to each switch and host, and is thesummation of all workloads in the same layer. Therefore,we can linearize non-linear constraints (5), (6), (7), and (8)with this linearization technique.

5.2.2 Link Distribution

As mentioned before, it is important to determine whichport to use for transferring jobs. If we use a port connectedto an inactive switch or host for transmitting that job, wewill lose the request.

λCij =

k∑l=1

λCij l ,∀i, j (11)

λAij =

k∑l=1

λClj i ,∀i, j (12)

λAij =

k/2∑l=1

λAij l ,∀i, j (13)

λTij =

k/2∑l=1

λAil j ,∀i, j (14)

λTij =

k/2∑l=1

λTij l ,∀i, j (15)

λTij l = λHil ToRij ,∀i, j, ToRij (16)

Equations (11), (13), and (15) regulate the distribution fromeach switch to lower layers. Arriving job requests to eachswitch should be equivalent to the summation of workloadsto go out through their ports.

Equations (12), (14), and (16) decide how arriving jobsare handled by each switch. Summation of the number ofjobs going into switches should be equal to the summationof arriving jobs from upper layer through connected port.

Through this constraint, we can decide which port willtransfer how many jobs in each link. We can obtain an opti-mal workload distribution strategy with these constraints.

5.2.3 Distribution RestrictionJobs cannot be distributed to inactive switches and hosts.Constraints (5)-(8) regulate the summation of jobs in eachlayer but it can allocate jobs to deactivated switches becausethe summation of workload is still the same if the switchis turned off. Therefore, we need constraints that prohibitworkloads from being allocated to inactive switches andhosts, and these are as follows:

λCij ≤ λ · Cij ,∀i, j (17)

λAij ≤ λ ·Aij ,∀i, j (18)

λTij ≤ λ · Tij ,∀i, j (19)

λHij ToRmn ≤ λ ·Hij ToRmn ,∀i, j,m, n (20)

These constraints force the workload allocated to a switchor a host to zero if the binary variable corresponding to theswitch or host is zero.

5.3 Performance Constraints

In order to guarantee the QoS of data centers, latencyconstraints will be applied to each switch and host. Switchesare assumed to be M/M/1 queues and hosts are M/M/cqueues, where c is equivalent to the number of cores ofthe host using the queuing model, we can obtain the dis-tribution of residual time in the queue. Residual time of ajob in queue corresponds to how long each job will stayin switches and hosts. Thus, we will use the residual timedistribution to obtain the latency constraint.

5.3.1 Latency in a SwitchSwitches are modeled as M/M/1 queues. Using the Cu-mulative Density Function (CDF) of the residual time inM/M/1 queue to obtain the residual time equation inM/M/1 queue, we have

FR(tresidual) = 1− e−(µ−λswitch)tresidual (21)

Equation (21) represents the probability that the residualtime in the queue will be less than tresidual. Therefore, wecan obtain the maximum residual time in the queue byletting FR(tresidual) = α, where α is close to 1 and tresidualsatisfies.

1− e−(µ−λswitch)tresidual = α (22)

8

Slightly manipulating (22) we have the upper bound on theresidual time in the queue as,

tresidual = −ln(1− α)

(µ− λswitch)(23)

Since the residual time cannot exceed the latency constraint,Latency, we have the following constraint.

− ln(1− α)(µ− λswitch)

≤ Latency (24)

which can be expressed in the following linear form, where

− ln(1− α) ≤ Latency · (µ− λswitch) (25)

By using (25), we can obtain the latency constraint for allswitches.

5.3.2 Latency in a Host

We use a strategy similar to the above to obtain the delay inhosts. A host is modeled as an M/M/c queue, and the CDFof the residual time in an M/M/c queue is [19]:

FR(tresidual) = 1− c

c− ρ· pc · e−(cµ−λ)tresidual (26)

pc is the probability that there are c jobs in a queue,c represents the number of cores in our model, which isusually a small number and ρ represents λ

µ . For the mostcases of practical interest, all cores will be active and we canassume pc to be equal to 1 for the purpose of simplifyingthe problem. Therefore,

FR(tresidual) = 1− c

c− ρ· e−(cµ−λ)tresidual (27)

Again, if the residual time satisfies (27) with probabilityα, with α ≈ 1, then

1− c

c− ρ· e−(cµ−λ)tresidual = α (28)

After simple manipulations of (28) we obtain

tresidual =ln (1−α)(1−ρ)

c

−(cµ− λ)(29)

Since the residual time in the queue should be less than thelatency constraint, we can get constraint below

ln (1−α)(1−ρ)c

−(cµ− λ)≤ Latency (30)

Which can also be written as

− ln(1− α)− ln(1− ρ) + ln c ≤ Latency(cµ− λ) (31)

Equation (31) is non-linear because it includes the non-linear term, −ln(1 − ρ). We will linearize (31) by using thepiecewise approximation technique used in [24]. Since ρ hasa limited domain between 0 to 1, then we can linearize−ln(1 − ρ) by calculating a linear function which lowerbounds −ln(1 − ρ) in each of a number of sub-domainsof ρ. We divide ρ to three sub-domains: [0, 0.75], [0.75, 0.95],and [0.95, 1]. Then, we obtain a linear function that fits eachsub-domain, f1(ρ), f2(ρ),and f3(ρ), which lower bounds−ln(1− ρ).

Through approximation, we could achieve three linearfunctions in each sub-domain, f1(ρ) = 1.72ρ, f2(ρ) =

7.1679ρ− 4.1698, f3(ρ) = 40.2359ρ− 35.6308. By replacing− ln(1 − ρ) in (31) by maxy fy(ρ), y represents a linearfunction in the y sub-domain, and we obtain the linearconstraint below.

maxy

fy(ρ)− ln(1− α) + ln c

≤ Latency · (cµHij ToRmn − λHij ToRmn),∀i, j,m, n, y(32)

5.3.3 Service RateFor the stability of the system, the summation of servicerates of each layer should be greater than the total arrivalrates jobs. That is,

k/2∑i=1

k/2∑j=1

µCijCij ≥ λ (33)

k∑i=1

k/2∑j=1

µAijAij ≥ λ (34)

k∑i=1

k/2∑j=1

µTijTij ≥ λ (35)

k∑i=1,m=1

k/2∑j=1

k/2∑n=1

µHij ToRmnHij ToRmn ≥ λ (36)

5.4 Memory ConstraintsMain memory consumes almost 25% of total energy con-sumption in the data center. Therefore, minimizing the num-ber of working memory modules will contribute to savingenergy consumption in data centers. We decide the numberof working memory modules based on the probability thatan arriving job is rejected. We assume the job is rejected onlywhen there is not enough memory in the queue.

5.4.1 Memory in SwitchSwitches are modeled as M/M/1 queue. If we assume thenq + 1 job is rejected in the queue, the probability of losinga job is equal to probability of nq jobs in the queue. So wecan calculate the probability of loss like below:

p(loss) = pnq (37)

We set the probability that an arriving job is successfullyqueued to α ≈ 1.

p(queuing) = α (38)

Then we can get the equation below:

p(loss) = 1− p(queuing) = 1− α (39)

p(loss) is when there are nq jobs in queue. So we cancalculate the probability of loss like below:

p(loss) = 1−nq−1∑i=0

pi (40)

If we substitute p(loss) in (39) with (40) to obtain pi = ρi(1−ρ) in the M/M/1 queue.

nq−1∑i=0

pi = α (41)

9

So from (41) we can obtain,

1− ρnq−1 = α (42)

If we take the log on both sides, we can achieve:

nswitch =ln(1− α)ln(ρ)

+ 1 (43)

Equation (43) represents the number of existing jobs in aswitch with very high probability α. Based on the numberof jobs in the queue, we can obtain the number of memorymodules we need. If we assume the expected size of a jobis J and memory module size is MS, we can establish thefollowing memory constraint.

nswitch · J ≤Mswitch ·MS (44)

Since all switches are modeled as M/M/1 queues, we canapply this constraint to all switches and decide the numberof working memory modules depending on their allocatedworkloads.

5.4.2 Memory in HostHosts are modeled as M/M/c queues. We can use the sameapproach used with the switch, but instead using the steadystate probability of the M/M/c queue. As mentioned before,we assume hosts are always busy when they are turnedon. Since c represents the number of cores in a host, wecan consider there will be always more than c jobs in thehost. Therefore we can use the following equation to obtainsteady state probability:

∞∑i=c

pi ≈ 1 (45)

The steady state of probability in M/M/c queue is given fori ≥ c,

pi =ccρn

c!p0 (46)

where ρ = λhostcµ .

The initial state probability p0 can be found by substitut-ing pi in (45) by (46).

∞∑i=c

ccρn

c!p0 ≈ 1 (47)

ccρc

c!(1− ρ)p0 ≈ 1

So, the initial probability p0 is given by,

p0 ≈c!(1− ρ)ccρc

(48)

By using (48), we can use steady state probabilities bysubstituting p0 in (46).

If we substitute (46) in (41), we can obtain the number ofjobs in hosts in terms of utilization.

nhost =ln(1− α)ln(ρ)

+ c (49)

By using (49), we can achieve the required number ofmemory modules that can accommodate jobs in hosts withthe following constraint.

nhost · J ≤Mhost ·MS (50)

However, (44) and (50) are non-linear. Similar to theabove piecewise linear approximation, we will divide theminto three sub-domains: [0, ρ∗1], [ρ∗1, ρ∗2], and [ρ∗2, 1]. Then wecould get a linear function in each sub-domain. The approx-imation function is different depending on the service rateof switches and hosts. So, if we define the functions thatobtain the number of jobs in each switch and host,nswitchand nhost as fn(ρ), we can calculate sub-linear functions as:

fn1(ρ) =fn(ρ

∗1)

ρ∗1ρ (51)

fn2(ρ) =fn(ρ

∗2)− fn(ρ∗1)ρ∗2 − ρ∗1

(ρ− ρ∗2) + fn(ρ∗2)

fn3(ρ) =µ− fn(ρ∗2)1− ρ∗2

ρ+fn(ρ

∗2)

1− ρ∗2µ is the service rate of each switch and host. Since weapproximate the number of jobs by a linear function, wecan linearize the constraints (44) and (50) like below in eachswitch and host:

maxy

(fny(ρCij )) ≤Mhost ·MS

J(52)

y represents the number of approximation functions and Mis the number of memory module that are powered, whichis an integer variable.

5.5 Connectivity ConstraintsThe connectivity constraints are applied to the problem toprotect the connectivity of the data center. If we deactivatenecessary switches for connecting to working hosts, it willcause the disconnection between the core layer and hosts.Therefore, we define the connectivity constraints that main-tain the architecture of data centers.∑k/2

j=1 Tij

k≤

k/2∑j=1

Aij ,∀i (53)

ToR switches and aggregation switches in the same PODhave a complete bipartite connection. Therefore, ToR switchcan be connected to the core switch layer even if there isonly one working aggregation switch in the same POD. (53)activates at least one aggregation switch if ToR switches areactivated in the same POD.

k

2

k/2∑j=1

Hij ToRmn ≤ Tmn,∀i (54)

If a host is turned on and is connected to Tmn ToR switch,Tmn should be turned on as well. Since Tmn is a binaryvariable, the right hand side should not exceed 1. So, wedivide the number of turned on hosts by 2/k in order tomake the upper bound of summation equal to 1.

6 SIMULATED ANNEALING ALGORITHM

The optimization problem includes binary variables andinteger variables in the objective function and constraints.The binary variables decide the state of switches and hostsand the integer variables decide the number of workingmemory modules in each switch and host. As we includeinteger variables in the problem, this optimization becomes

10

NP-hard. When we consider a small size data center, theoptimization problem can be solved in a reasonable time.However, data centers usually include a large number ofservers and switches. In such cases, it will take a long timeto solve. Therefore, we will use the Simulated Annealing al-gorithm which, is a popular randomized heuristic algorithmthat can find a near optimal solution in a reasonable time.

Algorithm 1 Simulated Annealing AlgorithmRequire: SHij ToRmn

, STij , SAij , SCij , λ, β, iterationEnsure: Pminimum, λHij ToRmn , λTij , λAij , λCij1: We generate initial allocation to hosts λHij ToRmn depends on

service rate of hosts2: Decide ToR, aggregation and core switches based on allocation into

hosts.3: λTij , λAij , λCij=Switch(λhij ToRmn )4: Pminimum=Cal power(λhij ToRmn , λTij , λAij , λCij )5: while t≤ iteration do6: Search neighbor allocation λ

′hij ToRmn

7: λ′Tij

, λ′Aij

, λ′Cij

=Switch(λ′Hij ToRmn

)

8: Pcandidate = Cal power(λ′Hij ToRmn

, λ′Tij

, λ′Aij

, λ′Cij

)

9: r←rand()

10: if Pcandidate < Pminimum or epminimum−pcandidate

β > r then11: λHij ToRmn ← λ

′Hij ToRmn

12: λTij ← λ′Tij

13: λAij ← λ′Aij

14: λCij ← λ′Cij

15: Pminimum ← Pcandidate

16: t++, β ← β · α17: else18: t++, β ← β · α19: end if20: end while21: OUTPUT: Pminimum, λHij ToRmn , λTij , λAij , λCij

The algorithm requires input parameters: theservice rates (jobs/sec) of hosts and switches(SHij ToRmn , STij , SAij , SCij ), total incoming jobs intothe data center (λ), parameter β that has a value between0 to 1, and the maximum number of iterations, iteration.We generate the initial allocation of λ into hosts whileguaranteeing the latency constraint and capacity (line 1).The latency goes to infinity when the allocation to hosts isclose to service rates. Therefore, we decide the allocationrates that do not violate the latency constraint and let theallocation of jobs not exceed that ratio. After we decidethe initial allocation to hosts, we can determine whichswitches will be needed to operate the data center properly.So then the Switch() function finds which switches arerequired and how many jobs can be allocated to switchesbased on the assignment result of hosts (line 3). After wedecide the allocation of jobs over the entire data center,we calculate the power consumption of the data centerbased on the result of allocations (line 4). Then we set thatsolution and the power as a candidate solution. We startfinding neighbor solutions in lines 5 to 20. We find theneighbor solution of job allocation into hosts (line 6). Inthe same method, we can find which switches are requiredto be activated to reach working hosts. So, we turn on therequired switches by using Switch() function (line 7). Then,we can calculate the power consumption of a neighborsolution in line 8. If the power consumption of the neighborsolution is less than the power consumption of candidatesolution, we replace the candidate solution with the

neighbor solution. We also replace candidate solutions withneighbor solutions with some probability to avoid isolationof solution. A random number r is generated between 0 and1. If epminimum−pcandidate/β is greater than random numberr, we replace candidate solution with the neighbor solutioneven if power consumption of neighbor solution is greaterthan power consumption of candidate solution (line 10 -line 15). In every iteration, β is multiplied by α, which hasa value less than 1, to decrease the β in every iteration (line16 and line 18). The algorithm repeatedly finds neighborsolutions for t iterations. Then, the candidate solution willbecome a near optimal solution of the problem.

7 EXPERIMENTS

7.1 Google Cluster DataThe experiments reported in this section are implementedusing Google cluster-usage traces data [20]. Google clusteris a set of computing resources composed of thousands ofmachines. A job is composed of several tasks which can beprocessed separately. So each task will be a unit processing.We consider the number of task arrivals. Each task has atime-stamp which represents when the task arrives at thecluster. Therefore, the distribution of the number of task ar-rivals can be observed by using the time-stamp. The clusterstarts measurement 600 seconds after the system is operatedand has accumulated data for one month approximately.We select a random point to collect data for the predictionmodel. One week data is sampled as a training data setfor the prediction modeling and the following week datais employed to test the accuracy of the prediction model.

7.2 Request Prediction7.2.1 Time Dependent Parameter PredictionPredicted parameters are obtained from the accumulateddata within blocks of 30 minutes each. Based on our ob-servation of Google cluster data, the data is fitted to aPoisson distribution with parameter λ which is evaluatedusing the data in every predetermined period, values of λare then saved in prediction the data set. Parameter valuesare stacked in data set for the several periods. Therefore, it ispossible to estimate the parameter values in future periodsmore accurately as we accumulate more data. Followingparameter values are achieved by implementing LLR overcorresponding UP . For example, if we implement LLR overUP including the 1st to the 10th TP s, the last point value ofLLR function becomes the prediction value of the eleventhTP . The prediction values change depending on the UP weset or bandwidth value that we use for LLR.

Fig. 5 represents the prediction of Poisson distributionparameter λ of arriving tasks during a week. Since we setthe TP to 30 minutes, we have 336 target periods duringthe week. Blue points represent parameter values of trainingdata set in each TP and green points are parameter valuesof test data set in each TP . Solid lines represent parameterprediction values for different values of bandwidth. We setthe UP to 25 hours in Fig. 5, which means that predic-tion value is obtained based on the last 25th hours data.Parameter λ is equivalent to mean the number of arrivalsduring 30 minutes. We can observe that the graph has aregularly repeated pattern. It has seven high peaks in the

11

Figure 5: Poisson distribution parameter λ estimation ofarrival tasks

graph, which means similar patterns repeated during theweek.

7.2.2 Error Assessment

In order to quantify the accuracy of prediction, we measureMean Absolute Percentage Error (MAPE) between predic-tion model and test data set. MAPE is a measurement ofthe accuracy of prediction for constructing fitted time seriesvalue. MAPE expresses error rate as the percentage.

MAPE =1

n

n∑j=1

|Pj − Tj |Tj

(55)

Pj is the predicted value of the actual target value Tj .MAPE value is equal to zero when the prediction model is aperfect fit to target value and increased when the predictionis not properly fitted to target values.

Figure 6: MAPE measurement of arrival tasks predictionFig. 6 is the MAPE measurement graph of the Poisson

distribution parameter λ. Poisson distribution parameter λhas MAPE value between 38.84% and 52.49% in Fig. 6.The prediction model could achieve higher accuracy withlonger UP , which is equivalent to the window size, becauseincreasing the UP means employing more data from history

for prediction. However, the large UP requires the morecomplex computation. In other words, proper selection ofutilization period is required to satisfy both prediction ac-curacy and calculation time. Choosing the best bandwidthvalue is also an important issue in order to reduce predictionerror. Too small bandwidth causes very spiky estimateswhile large bandwidth leads to over-smoothing. If datavalues are spread widely, smaller bandwidth will not resultin higher prediction accuracy. In contrast, the regressionachieves higher accuracy with small bandwidth if datavalues are compacted. Fig. 6 shows higher accuracy withthe increase in bandwidth because parameter data pointsare more spread as we can see in Fig. 5.

Figure 7: NMSE comparisonThe proposed prediction algorithm is compared with

the fractal differential equation modeling based predictionmethod proposed in [21]. The Mean Square Error (MSE) ofthe proposed algorithm and comparison prediction modelis measured for CPU and memory requests and normalizedby baseline prediction algorithm. The auto-regressive pre-dictor is used for baseline model by employing 16 previoustime slot values, which is equivalent to using 16 UP inthe proposed algorithm. In memory request prediction, theproposed model achieves 25% reduction MSE compare tothe fractional modeling based predictor and 84% reducedMSE than the auto-regressive predictor. In CPU request pre-diction, the proposed algorithm shows a slightly enhancedprediction accuracy than fractal modeling based predictor,3% reduced MSE but it achieves 75% MSE reduction com-pared to the baseline prediction model.

7.3 Adaptive Data Center Activation

The optimization problem is solved using CPLEX for smalldata centers and also using the Simulated Annealing algo-rithm implemented in C. We consider heterogeneous envi-ronment data centers having different service rates of hosts.However, all switches have the same performance in eachlayer. We set the parameters of the model as shown in Table1.

Power consumption parameters of switches are esti-mated with practical power consumption of data centerswitch, HP Altoline 6712 Switch Series [22]. Since core

12Table 1: Value of key parameters

Variables Values

P staticCij

, P staticAij

, P staticTij

100W, 50W, 50W

P dynamicCij

, P dynamicAij

, P dynamicTij

300W, 150W, 150W

P staticHij ToRmn

[30, 50, 70, 90]W

P dynamicHij ToRmn

[100, 150, 200, 250]W

P portCij

, P portAij

, P portTij

0.0005W/job

PmemoryCij

, PmemoryAij

, PmemoryTij

,PmemoryHij ToRmn

25W

switches implement path calculation and management ascontrol plane, they consume more energy than aggregationand ToR switches in the data plane. Switches in the dataplane are set to consume half energy consumed by coreswitches. Hosts have different activation power parametersproportional to their service rate. Our model includes fourtypes of hosts, and therefore hosts have four levels ofactivation power consumption depending on their servicerates with high performance hosts consuming more power.Identical hosts are allocated to the same POD. Thus, hostsheterogeneity will be across PODs.

The size of requests are randomly generated by normaldistribution with µ=20MB. All switches have two 512MBmemory modules and hosts have two 1GB memory mod-ules. The latency constraint of each switch is set to 1µs basedon the reference switch data sheet and the latency constraintof hosts is set to 1ms to satisfy the QoS of data center.

The service rate of a core switches are set to 1000 tasksper unit time, and aggregation and ToR switch have theability to handle 5000 tasks per a unit time. Since wepredict the traffic distribution every 30 minutes and decidesystem activation states, a unit time is 30 minutes in oursimulation. Hosts have 80, 100, 120, and 140 service rates(jobs/sec) which are corresponding processing speed be-tween 1.6 GHz, lower performance host, to 2.4 GHz, highperformance host. Data plane switches, aggregation andToR switches, have higher service rate than control planeswitch,core switches, because they just work for forwardingtasks.

Since the problem is NP-hard, we could not obtainthe optimal solution for large size data centers. Optimalsolutions only when k is equal to 4 were obtained withina reasonable time using CPLEX. However, the computa-tion time of the problem increased significantly when weincrease the size of te data center to k that is greater than 8.

Therefore, we employ Simulated Annealing to obtain anear optimal solution of the problem. The algorithm uses1000 iterations, β is set to 1, and α is 0.9 in Algorithm 1.

Fig. 8 compares the solution of the optimal solutionand heuristic solutions when k is equal to 8. Since thecomputation time of the problem is unrealistic, we comparethe upper and lower bounds of the optimal solution whenthe gap is around 6%. It has taken around 1300 seconds untilwe reached the 6% gap and could not get to less than 6% gapeven after 3 hours of computation. Data center utilizationrate exhibits the incoming rate of tasks compared to max-imum service rate capacity of data centers. For stability ofdata centers, the incoming rate cannot exceed the maximumservice capacity of the data center. The Simulated Annealing

Figure 8: Optimal and heuristic solution comparison

solution has around 10% difference with the upper boundand 15% difference with the lower bound.

Figure 9: Power saving rate with Simulated Annealingalgorithm

Fig. 9 shows how much energy we can save with ourmodel. The power saving rate is calculated by comparingthe energy consumption of the heuristic solution and fulloperation power consumption of data center when the datacenter operates every switch and host. We measure howmuch energy we can save depending on the utilizationrate and the size of the data center. As the utilization rateincreases, the power saving rate is decreased because wecannot turn off many switches and hosts to guarantee theperformance of the data center. Also, we can observe thatthe power saving rate is increased when the size of datacenter increases.

The predicted Poisson distribution parameters which areobtained in Fig. 5 are employed as the input to the datacenter in Fig. 10. The predicted parameters include 336prediction points during a week. So each point correspondsto Poisson distribution parameter for 30 minutes. We havemade a modification in the data center parameter in orderto make it close to Google cluster environment. The portnumber k is set to 24, and therefore the data center has 24core switches, 48 ToR and Aggregation switches, and 3456

13

Figure 10: Power saving rate with Simulated Annealingalgorithm for different bandwidth values

hosts. Energy consumption and latency parameters are thesame as in Table 1 and service rates of switches and hostsare assumed as the same condition.

Figure 11: Power saving rate comparison betweenpredicted and measured user requests

The first graph in Fig. 10 presents predicted parametersduring a week and the second graph shows how powersaving rate is changed depends on λ in every 30 minutes. InFig. 10, we can observe the data center power saving rate isdecreased when the number of arriving tasks increases andit increases when the data center receives fewer requests.The algorithm saves average 47.7 to 48.2% operation energycompared to the full operation state depending on thebandwidth.

Fig. 11 shows the difference between actual parametersand predicted parameters. The prediction model makesaccurate prediction generally. However, we can observe theprediction model has a weakness in predicting traffic bursts.If the number of requests soars in a short time, the predictionmodel could not follow that variation. Power saving rateof the data center model also presents the similar pat-terns. However, the data center activation model activates

switches and hosts by forecasting the high probability trafficof given probability distribution. For example, the α is set to0.95 in (22), (28), and (38) in the experiment. Therefore, thedata center could cover in some degree of traffic burst.

Figure 12: Power saving rate comparison with LCPalgorithm

Power saving rates of proposed dynamic data center ac-tivation mode algorithm are compared with Lazy CapacityProvisioning (LCP) algorithm proposed in [40]. The LCPalgorithm decides the optimal number of activated serversby considering operating cost and transition cost, the cost ofserver on-off transition. Since the LCP algorithm has beendeveloped for homogeneous server condition and does notaffect to activation of switch layer, we modified our simu-lation model to a homogeneous data center. Heterogeneousserver service rates are replaced by a unique service rate andpower consumption of servers are set to a single value butthe total capacity of the homogeneous data center is set tosame as the heterogeneous data center model. Since the LCPalgorithm does not control the activation of switch layer, allswitches are activated if at least one server is activated inthe same POD but switches are deactivated if none of theservers are activated in the same POD. In Fig. 12, power sav-ing rate of the proposed algorithm and the LCP algorithmare compared. The proposed algorithm saves an average of9.1% more power compared to the LCP algorithm. Also,we can observe that the LCP algorithm does not performwell for traffic burst. During the time slot between 5 to25, we can observe that the data center utilization ratesvary a lot. Since the LCP algorithm minimizes operationcost and transition cost, the data center tries to keep thecurrent state of activated servers. Since the traffic burstis a common situation in cloud computing environments,considering transition cost is not the appropriate model forpower saving purposes.

8 CONCLUSIONS

This paper proposed adaptive data center activation modelwith request prediction algorithm. With accurate predictionmodel, the data center could save the energy in the moreefficient way. The prediction model exhibits accurate pre-diction compared to another prediction algorithms and theadaptive activation model presents flexible energy saving

14

rate depending on incoming rates of requests. When themodel is tested with predicted data based on real data,we could save 30 to 50 percent of energy compared to fulloperation environment.

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