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Computer Systems Power Model Estimation Breno H. M. Neves, Bruna M. J. Cruz, Raphael R. Mendes, Frederico M. Bublitz, J. J. Silva, Saulo O. D. Luiz, Angelo Perkusich and Hyggo Almeida Department of Electrical Engineering, Center for Electrical Engineering and Informatics, Universidade Federal de Campina Grande, 58.429-900 Campina Grande, Brazil Emails: {breno.neves, bruna.cruz, raphael.mendes}@ee.ufcg.edu.br, [email protected], {jaidilson,saulo,perkusic}@dee.ufcg.edu.br, [email protected] Abstract—The estimation of power models for computer systems is important for the development process of dynamic power managers. In this work, a power model is estimated based on a constrained linear least-squares technique. I. Introduction The reduction of the power consumption of computer systems is a challenging research area. For battery-powered mobile devices, such as notebooks, ultrabooks, mobile phones and tablets, there is an increasing demand for performance [1]. More powerful processors, larger memory and network in- terfaces contribute to increase the system load. However, the energy density stored in the batteries has not been increased at the same rate as the performance required by computer systems. Thus, it is necessary to develop power management techniques to reduce the power consumption of computer sys- tems, and thus increase the battery lifetime. The development of a power management technique may be optimized by means of the estimation of the system power consumption model. Models are important for battery lifetime optimization and power management in battery-powered systems [2], [3]. In this work, a power consumption model is estimated by applying constrained linear least-squares [4]. The input data used is composed of the states of the computer system devices, such as LCD (liquid crystal display), HD (hard disk), processor and network interfaces. II. The computer system power model A power manageable system is a computer system whose devices have multiple power states, each one with a spe- cific power and performance level. As shown in Fig. 1, the power manageable system is composed of a devices set P = { p i |i = 1, 2, ..., P}. Each device p i is provided with a set of power states S i = s j | j = 1, 2, ..., S i , e.g. the display brightness. For each device it is possible to assign a utilization metric μ i (device load). The power consumed y i by the device p i is a function c i ( s i i ) of the device energy state s i and its utilization μ i . The power consumption estimate ˆ y of the power manageable system is shown in (1) where Y 0 is the static power (operation of the basic circuits and maintaining the devices in the low-power state) and the component P i=1 y i represents the dynamic power, which is a function of the devices energy states and utilization. ˆ y = P i=1 y i + Y 0 = P i=1 c i ( s i i ) + Y 0 (1) Workload Power manageable system Device 1 Power manager Requests State States Device 2 Device P ... Commands Fig. 1. Power manageable system block diagram. If it is possible to represent the power component c i ( s i i ) as b i · f i ( s i i ), where b i is a constant (named parameter) and f i is a function, for all i = 1, 2, ..., P, then replacing f i ( s i i ) by u i (named input), the expression in (1) is rewritten as (2). ˆ y = P i=1 b i u i + Y 0 (2) The problem of the computer system power model estimation is therefore the evaluation of the parameters b i , i = 1, 2, ..., P, and Y 0 . The power consumption estimate ˆ y, the static power Y 0 and the power components b i u i , for all i = 1, 2, ..., P are non- negative. Therefore, if the inputs u i 0, then it is possible to consider that b i 0, for all i = 1, 2, ..., P. Therefore the estimation of the parameters b i , i = 1, 2, ..., P, and Y 0 may be formulated as a constrained linear least-squares problem [3], using the constraint b i 0, for all i = 1, 2, ..., P and Y 0 0. To evaluate the parameters, it is possible to perform m N experiments for acquiring the identification data, which is composed of a vector of power measurements Y = [ y 1 ... y m ] T and a matrix of inputs U = [u ji ], j = 1,..., m, and i = 1,..., P. Using (2) and the matrix of inputs, the relation between a vector of esti- mates ˆ Y = y 1 ... ˆ y m ] T and a parameter vector θ = [ b 1 ... b P Y 0 ] T is shown in (3). ˆ y 1 . . . ˆ y m = u 11 ··· u 1P 1 . . . . . . . . . . . . u m1 ··· u mP 1 b 1 . . . b P Y 0 (3) Let C = [U [1] m×1 ], then (3) may be written as ˆ Y = Cθ. The goal of the computer system power model estimation is to find the parameters vector θ which minimizes the squared 2-norm of the dierence between the vector of estimates and the vector of power measurements ˆ Y Y 2 2 such that each element of the 978-1-4799-1412-8/13/$31.00 ©2013 IEEE 2013 IEEE Third International Conference on Consumer Electronics - Berlin (ICCE-Berlin) 173

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Page 1: [IEEE 2013 IEEE Third International Conference on Consumer Electronics ¿ Berlin (ICCE-Berlin) - IFA Fairground, Berlin, Germany (2013.09.9-2013.09.11)] 2013 IEEE Third International

Computer Systems Power Model Estimation

Breno H. M. Neves, Bruna M. J. Cruz, Raphael R. Mendes, Frederico M. Bublitz, J. J. Silva,Saulo O. D. Luiz, Angelo Perkusich and Hyggo Almeida

Department of Electrical Engineering, Center for Electrical Engineering and Informatics,Universidade Federal de Campina Grande, 58.429-900 Campina Grande, Brazil

Emails: {breno.neves, bruna.cruz, raphael.mendes}@ee.ufcg.edu.br, [email protected],{jaidilson,saulo,perkusic}@dee.ufcg.edu.br, [email protected]

Abstract—The estimation of power models for computersystems is important for the development process of dynamicpower managers. In this work, a power model is estimated basedon a constrained linear least-squares technique.

I. Introduction

The reduction of the power consumption of computersystems is a challenging research area. For battery-poweredmobile devices, such as notebooks, ultrabooks, mobile phonesand tablets, there is an increasing demand for performance [1].More powerful processors, larger memory and network in-terfaces contribute to increase the system load. However, theenergy density stored in the batteries has not been increasedat the same rate as the performance required by computersystems. Thus, it is necessary to develop power managementtechniques to reduce the power consumption of computer sys-tems, and thus increase the battery lifetime. The developmentof a power management technique may be optimized by meansof the estimation of the system power consumption model.Models are important for battery lifetime optimization andpower management in battery-powered systems [2], [3]. In thiswork, a power consumption model is estimated by applyingconstrained linear least-squares [4]. The input data used iscomposed of the states of the computer system devices, suchas LCD (liquid crystal display), HD (hard disk), processor andnetwork interfaces.

II. The computer system power model

A power manageable system is a computer system whosedevices have multiple power states, each one with a spe-cific power and performance level. As shown in Fig. 1,the power manageable system is composed of a devices setP = {pi|i = 1, 2, ..., P}. Each device pi is provided with aset of power states Si =

{s j| j = 1, 2, ..., S i

}, e.g. the display

brightness. For each device it is possible to assign a utilizationmetric μi (device load). The power consumed yi by the devicepi is a function ci(si, μi) of the device energy state si and itsutilization μi. The power consumption estimate y of the powermanageable system is shown in (1) where Y0 is the static power(operation of the basic circuits and maintaining the devices inthe low-power state) and the component

∑Pi=1 yi represents the

dynamic power, which is a function of the devices energy statesand utilization.

y =P∑

i=1

yi + Y0 =P∑

i=1

ci(si, μi) + Y0 (1)

Workload

Power manageable system

Device 1

Powermanager

Requests

State

States

Device 2 Device P...

Commands

Fig. 1. Power manageable system block diagram.

If it is possible to represent the power component ci(si, μi) asbi · fi(si, μi), where bi is a constant (named parameter) and fiis a function, for all i = 1, 2, ..., P, then replacing fi(si, μi) byui (named input), the expression in (1) is rewritten as (2).

y =P∑

i=1

biui + Y0 (2)

The problem of the computer system power model estimationis therefore the evaluation of the parameters bi, i = 1, 2, ..., P,and Y0. The power consumption estimate y, the static power Y0and the power components biui, for all i = 1, 2, ..., P are non-negative. Therefore, if the inputs ui ≥ 0, then it is possibleto consider that bi ≥ 0, for all i = 1, 2, ..., P. Therefore theestimation of the parameters bi, i = 1, 2, ..., P, and Y0 may beformulated as a constrained linear least-squares problem [3],using the constraint bi ≥ 0, for all i = 1, 2, ..., P and Y0 ≥ 0.

To evaluate the parameters, it is possible to performm ∈ N experiments for acquiring the identification data,which is composed of a vector of power measurementsY = [ y1 . . . ym ]T and a matrix of inputs U =

[u ji], j = 1, . . . ,m, and i = 1, . . . , P. Using (2) and thematrix of inputs, the relation between a vector of esti-mates Y = [ y1 . . . ym ]T and a parameter vector θ =[ b1 . . . bP Y0 ]T is shown in (3).

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

y1...

ym

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

u11 · · · u1P 1.... . .

......

um1 · · · umP 1

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

b1...

bPY0

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦(3)

Let C = [U [1]m×1], then (3) may be written as Y = Cθ. Thegoal of the computer system power model estimation is to findthe parameters vector θ which minimizes the squared 2-normof the difference between the vector of estimates and the vectorof power measurements ‖Y−Y‖22 such that each element of the

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2013 IEEE Third International Conference on Consumer Electronics - Berlin (ICCE-Berlin)

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parameter vector is non-negative, as shown in (4).

minθ‖Cθ − Y‖22 such that θ ≥ 0 (4)

III. Case study

Considering the estimation of the power model parametersin (4) by means of the constrained linear least-squares, a casestudy is presented in this section. The experimental platformused was a netbook composed of a 10” LCD, a processor withtwo logical cores and the frequencies set {0.80 GHz, 1.07 GHz,1.33 GHz, 1.60 GHz}, 1GB RAM, 160 GB HDD, ethernet andWi-Fi.

A data acquisition module was applied to measure thevoltage and current supplied to the experimental platform. Asshown in Fig. 2, the data acquisition module was connectedto a desktop computer which was dedicated to the powermeasurements. As shown in Fig. 3, the current i was obtainedby measuring the voltage vR across a resistor R equal to0.232Ω, placed in series with the experimental platform andalso connected to the analog input 1 (AI 1) at the dataacquisition module. The voltage v was obtained by measuringthe output voltage v1 of a voltage divider (with R1 = 10055.3Ωand R2 = 9945.0Ω), because the nominal source voltage of 19Vis greater than the maximum voltage of 10V supported by dataacquisition module analog input. The output voltage v1 wasconnected to the analog input 2 (AI 2) at the data acquisitionmodule. During the data acquisition, in the desktop computer,the values of vR and v1 are converted to i and v, and the powery = vi is evaluated, as shown in Fig. 4.

Source

A

Dataacquisition

module

Desktopcomputer

VExperimental

platform

+

-

Fig. 2. Experimental setup for measuring the experimental platform powerconsumption.

Considering the experimental platform devices, the powermodel in (2) is to be estimated considering the inputs ui, i =1, 2, ..., P, defined in Table I. There are P = 9 different inputs.To estimate the model parameters bi, i = 1, 2, ..., P, and Y0,experiments were performed varying the LCD brightness (from0% to 100%), varying the cpu utilization (from 15% to 95%)and performing download and upload operations with theethernet and Wi-Fi network interfaces:

LCD Brightness Test: keep the computer idle only showingthe desktop, during 3 minutes for each test.

1) Using the background image completely black,change the LCD brightness from 0% to 100% (alwaysincreasing 10% for the next test).

2) Using the background image completely white,change the LCD brightness from 0% to 100% (alwaysincreasing 10% for the next test).

Idle Network Interface Test: keep the computer idle show-ing the desktop during 3 minutes.

Active Network Interface Test: open the browser and down-load a file from a given link. After starting the download,initiate the test during 3 minutes.

Ethernet

1) Change the Ethernet state to off and execute the IdleNetwork Interface Test.

2) Change the Ethernet state to on and execute the IdleNetwork Interface Test.

3) Change the Ethernet state to on and execute the ActiveNetwork Interface Test.

Wi-Fi

1) Change the Wi-Fi state to off and execute the IdleNetwork Interface Test.

2) Change the Wi-Fi state to on and execute the IdleNetwork Interface Test.

3) Change the Wi-Fi state to on and execute the ActiveNetwork Interface Test.

Processor Test: to evaluate the processor dynamic power,we implemented a workload resulting in an approximatelyconstant usage of the processor. In this way, it was possibleto keep constant the processor frequency and usage during thetest. The 3-minute tests were performed varying the processorusage from 15% to 95%.

TABLE I. Description of the inputs

Input Description Rangeu0 LCD brightness u0 ∈ {0, 0.1, 0.2, . . . , 1.0}u1 Ethernet turned on u1 ∈ {0, 1}u2 Wi-Fi turned on u2 ∈ {0, 1}u3 Ethernet download rate u3 ≥ 0u4 Ethernet upload rate u4 ≥ 0u5 Wi-Fi download rate u5 ≥ 0u6 Wi-Fi upload rate u6 ≥ 0u7 HD data transfer rate u7 ≥ 0u8 Memory occupancy u8 ≥ 0u9 Processor dynamic power u9 ≥ 0

u9 = 0.01 · (cpuUtilization(%) · cpuFrequency3)

A software, named ComponentsLogger, was developed tomeasure and store the inputs ui, i = 1, 2, ..., P, as defined inTable I. The sampling period for the measurements was 2seconds. A sampling period smaller than 2 seconds wouldincrease the processor utilization by the ComponentsLoggersoftware itself, thus affecting the processor measurements. Theparameters bi, i = 1, 2, ..., P, and Y0 were estimated by meansof the constrained linear least-squares problem in (4), resultingin the parameter values shown in Table II.

TABLE II. Parameter values

Parameter ValueY0 9.5193b0 0.1339b1 0.7046b2 2.8944b3 7.4662 × 10−9

b4 5.6817 × 10−15

b5 1.5273 × 10−7

b6 1.0486 × 10−7

b7 2.1808 × 10−7

b8 5.7512 × 10−10

b9 1.1961

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ExperimentalplatformSource

-

+

Dataacquisition

module

AI 1AI 2GND

-

+

Desktopcomputer

Fig. 3. Electrical circuit for measuring the experimental platform power consumption.

Three experiments were performed to validate the esti-mated model. For the Test 1, the following workloads wereexecuted during 1 minute each:

1) Idle with all of the devices off;2) Wi-Fi turned on, without network usage;3) Wi-Fi turned on, loading a video;4) Wi-Fi turned on, playing the video previously

loaded;5) Wi-Fi turned on, without network usage;6) Idle with all of the devices off;7) Ethernet turned on, without network usage;8) Idle with all of the devices off.

Dataacquisition

driver

Writemeasurement

file

Fig. 4. Data acquisition software for measuring the experimental platformpower consumption.

For the Test 2, the following workloads were executed during1 minute each:

1) Idle with all of the devices off;2) Run a workload resulting in a 30% processor usage;3) Run a workload resulting in a 30% processor usage

and play a music;4) Run a workload resulting in a 30% processor usage

and play a video;5) Run a workload resulting in a 60% processor usage;6) Run a workload resulting in a 60% processor usage

and play a music;7) Run a workload resulting in a 60% processor usage

and play a video;8) Run a workload resulting in a 90% processor usage;9) Run a workload resulting in a 90% processor usage

and play a music;

10) Run a workload resulting in a 90% processor usageand play a video;

11) Idle with all of the devices off.

For the Test 3, the power states of the following devices wereapplied during 1 minute each:

1) Idle with all of the devices off;2) Wi-Fi turned on, LCD brightness of 40%;3) Wi-Fi and webcam turned on, LCD brightness of

40%;4) Wi-Fi turned on, LCD brightness of 80%;5) Wi-Fi and webcam turned on, LCD brightness of

80%;6) Ethernet turned on, LCD brightness of 40%;7) Ethernet and webcam turned on, LCD brightness of

40%;8) Ethernet turned on, LCD brightness of 80%;9) Ethernet and webcam turned on, LCD brightness of

80%;10) Wi-Fi and Ethernet turned on, LCD brightness of

40%;11) Wi-Fi, Ethernet and webcam turned on, LCD bright-

ness of 40%;12) Wi-Fi and Ethernet turned on, LCD brightness of

80%;13) Wi-Fi, Ethernet and webcam turned on, LCD bright-

ness of 80%;14) Idle with all of the devices off.

The measured power consumption y and the estimated powery using the parameters in Table II for the Tests 1, 2 and 3are respectively shown in Figures 5, 6 and 7. For all of thetests, the measured power consumption is a signal with greatvariability, but the estimated power is close to the mean valueof the measured power.

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Fig. 5. The power consumption measured and the power estimated by meansof the computer system power model for the test 1.

Fig. 6. The power consumption measured and the power estimated by meansof the computer system power model for the test 2.

Fig. 7. The power consumption measured and the power estimated by meansof the computer system power model for the test 3.

IV. Conclusion

In this work, a computer system power model was ef-fectively estimated by means of the constrained linear least-squares. The proposed technique was evaluated in a realexperimental platform described in a case study. For all ofthe validation experiments, despite the fact that the measuredpower consumption is a signal with great variability, the esti-mated power is a good approximation of the mean measuredpower.

Acknowledgment

The authors would like to thank all the members of theEmbedded Systems and Pervasive Computing Laboratory ofthe Universidade Federal de Campina Grande. This work waspartially supported by the Electrical Engineering GraduateProgram (Programa de Pós-Graduação em Engenharia Elétrica- PPgEE) at the Universidade Federal de Campina Grande(UFCG) and CNPq.

References

[1] F. Shearer, Power Management in Mobile Devices, 1st ed. Burlington,USA: Newnes, 2008.

[2] D. Rakhmatov and S. Vrudhula, “Energy management for battery-powered embedded systems,” ACM Transactions on Embedded Comput-ing Systems, vol. 2, no. 3, pp. 277–324, 2003.

[3] S. O. D. Luiz, A. Perkusich, B. M. J. Cruz, B. H. M. Neves, andG. M. da S. Araújo, “Optimization of timeout-based power managementpolicies for network interfaces,” IEEE Trans. Consum. Electron., vol. 59,no. 1, pp. 101–106, 2013.

[4] T. Coleman and Y. Li, “A reflective newton method for minimizing aquadratic function subject to bounds on some of the variables,” SIAMJournal on Optimization, vol. 6, no. 4, pp. 1040–1058, 1996.

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