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isbn = {0-7695-2700-0},
location = {Tampa, Florida},
articleno = {107},
- url = {http://doi.acm.org/10.1145/1188455.1188567},
doi = {10.1145/1188455.1188567},
acmid = {1188567},
publisher = {ACM},
@article{2,
author = {Peraza , J. and Tiwari , A. and Laurenzano , M. and Carrington L. and Snavely},
- title = "{PMaC}'s green queue: a framework for selecting energy optimal {DVFS} configurations in large scale {MPI} applications",
- journal = "Concurrency Computat.: Pract. Exper.DOI: 10.1002/cpe",
- pages = "1-20",
- year = "2012",
+ title = {{PMaC}'s green queue: a framework for selecting energy optimal {DVFS} configurations in large scale {MPI} applications},
+ journal = {Concurrency Computat.: Pract. Exper.DOI: 10.1002/cpe},
+ pages = {1-20},
+ year = {2012}
+
}
pages = {245:1--245:13},
articleno = {245},
numpages = {13},
- url = {http://dl.acm.org/citation.cfm?id=2429759.2430090},
acmid = {2430090},
publisher = {Winter Simulation Conference}
}
location = {San Diego, CA, USA},
pages = {275--280},
numpages = {6},
- url = {http://doi.acm.org/10.1145/996566.996650},
doi = {10.1145/996566.996650},
acmid = {996650},
publisher = {ACM},
Computing Systems},
journal = {CoRR},
volume = {abs/1210.4690},
- year = {2012},
- ee = {http://arxiv.org/abs/1210.4690},
- bibsource = {DBLP, http://dblp.uni-trier.de}
+ year = {2012}
}
@techreport{7,
TTtype = "",
TTnumber = "",
TTaddress = "",
- year = "2012",
- TTmonth = "",
- TTnote = "",
+ year = {2012}
+
}
@INPROCEEDINGS{8,
month={November},
pages={1-9},
keywords={Clustering algorithms;Delay effects;Dynamic voltage scaling;Energy consumption;Frequency;Government;Laboratories;Large-scale systems;Linear programming;Processor scheduling},
-doi={10.1145/1362622.1362688},}
+doi={10.1145/1362622.1362688}
+}
@phdthesis {9,
author = "Malkowski, Konrad",
address = "USA",
year = "2009",
pages = "227",
- MMmonth = "",
+
}
month={Sept},
pages={215-222},
keywords={cores;microprocessor chips;optimisation;power consumption;resource allocation;scaling circuits;scheduling;ILP;crown scheduling;data flows;discrete voltage-frequency scaling;dynamic discrete frequency scaling;dynamic rescaling;energy-efficient resource allocation;energy-optimal code;integer linear programming;malleable streaming tasks;many-core processor;mapping;optimization;pipelined task graph;power consumption;processor cores;streaming task collections;Dynamic scheduling;Optimization;Processor scheduling;Radio spectrum management;Resource management;Schedules},
-doi={10.1109/PATMOS.2013.6662176},}
+doi={10.1109/PATMOS.2013.6662176}
+}
@INPROCEEDINGS{11,
author={Kimura, H. and Sato, M. and Hotta, Y. and Boku, T. and Takahashi, D.},
pages={1-10},
keywords={directed graphs;parallel programming;power aware computing;AMD Turion;PC clusters;PowerWatch;Transmeta Crusoe;control library;directed acyclic task graph;dynamic voltage scaling;energy consumption;energy reduction;frequency scaling;high performance computing;microprocessors;parallel programs;power consumption;power monitoring tools;slack reclamation;Clustering algorithms;Concurrent computing;Dynamic voltage scaling;Energy consumption;Energy efficiency;Frequency synchronization;Gears;Libraries;Microprocessors;Monitoring},
doi={10.1109/CLUSTR.2006.311839},
-ISSN={1552-5244},}
+ISSN={1552-5244}
+}
@article{12,
author = {Lively, Charles and Xingfu Wu and Taylor, Valerie and Moore, Shirley and Chang, Hung-Ching and Cameron, Kirk},
issn = {1094-3420},
pages = {342--350},
numpages = {9},
- url = {http://dx.doi.org/10.1177/1094342011414749},
doi = {10.1177/1094342011414749},
acmid = {2020813},
publisher = {Sage Publications, Inc.},
}
@ARTICLE{13,
- author = "Lizhe Wang a,b, Samee U. Khan c , Dan Chen a , Joanna Kołodziej d , Rajiv Ranjan e , Cheng-zhong Xu f ,Albert Zomaya",
- title = "Energy-aware parallel task scheduling in a cluster",
- journal = "Future Generation Computer Systems",
+ author = {Lizhe Wang a,b, Samee U. Khan c , Dan Chen a , Joanna Kołodziej d , Rajiv Ranjan e , Cheng-zhong Xu f ,Albert Zomaya},
+ title = {Energy-aware parallel task scheduling in a cluster},
+ journal = {Future Generation Computer Systems},
volume = {29},
number = {7},
- pages = "1661–1670",
- year = "2013",
+ pages = {1661–1670},
+ year = {2013}
+
}
@INPROCEEDINGS{14,
month={May},
pages={68-75},
keywords={parallel processing;power aware computing;workstation clusters;cluster computer;eco-friendly daemon;energy consumption reduction;energy-efficient cluster computing;power consumption reduction;processor stall cycles;workload characterization;Application software;Clustering algorithms;Energy consumption;Energy efficiency;Frequency;Grid computing;Hardware;High performance computing;Runtime;Voltage},
-doi={10.1109/CCGRID.2009.88},}
+doi={10.1109/CCGRID.2009.88}
+}
@article{15,
author = {Zhuo, Jianli and Chakrabarti, Chaitali},
pages = {17:1--17:25},
articleno = {17},
numpages = {25},
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doi = {10.1145/1331331.1331341},
acmid = {1331341},
publisher = {ACM},
year = {2007},
isbn = {0-7695-2933-X},
pages = {19--},
- url = {http://dx.doi.org/10.1109/ICPP.2007.39},
doi = {10.1109/ICPP.2007.39},
acmid = {1306033},
publisher = {IEEE Computer Society},
year = {2005},
isbn = {0-7695-2312-9},
pages = {4.1--},
- url = {http://dx.doi.org/10.1109/IPDPS.2005.214},
doi = {10.1109/IPDPS.2005.214},
acmid = {1054466},
publisher = {IEEE Computer Society},
location = {New York, New York, USA},
pages = {230--238},
numpages = {9},
- url = {http://doi.acm.org/10.1145/1122971.1123006},
doi = {10.1145/1122971.1123006},
acmid = {1123006},
publisher = {ACM},
@inproceedings{21,
added-at = {2011-12-01T00:00:00.000+0100},
author = {Rauber, Thomas and Rünger, Gudula},
- biburl = {http://www.bibsonomy.org/bibtex/21cd7e6aa9e6f55f1185c3157b9cde5c1/dblp},
booktitle = {SpringSim (CNS)},
crossref = {conf/springsim/2011-3},
editor = {Abhari, Abdolreza},
publisher = {SCS/ACM},
timestamp = {2011-12-01T00:00:00.000+0100},
title = {Modeling the energy consumption for concurrent executions of parallel tasks.},
- url = {http://dblp.uni-trier.de/db/conf/springsim/springsim2011-3.html#RauberR11},
- year = 2011
+ year = {2011}
}
@inproceedings{22,
year = {2005},
isbn = {1-59593-061-2},
pages = {34--},
- url = {http://dx.doi.org/10.1109/SC.2005.57},
doi = {10.1109/SC.2005.57},
acmid = {1105799},
publisher = {IEEE Computer Society},
year = {2005},
isbn = {0-7695-2312-9},
pages = {34--},
- url = {http://dx.doi.org/10.1109/IPDPS.2005.346},
doi = {10.1109/IPDPS.2005.346},
acmid = {1054376},
publisher = {IEEE Computer Society},
@inproceedings{24,
added-at = {2009-11-27T00:00:00.000+0100},
author = {Chen, Yen-Jun and Hsu, Ching-Hsien and Li, Kuan-Ching and Chang, Hsi-Ya and Wang, Shuen-Tai},
- biburl = {http://www.bibsonomy.org/bibtex/24601b8a777bdf956bb48fa611b7556f5/dblp},
booktitle = {Infoscale},
crossref = {conf/infoscale/2009},
date = {2009-11-27},
series = {Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering},
timestamp = {2009-11-27T00:00:00.000+0100},
title = {Power Consumption Optimization of {MPI} Programs on Multi-core Clusters.},
- url = {http://dblp.uni-trier.de/db/conf/infoscale/infoscale2009.html#ChenHLCW09},
- volume = 18,
- year = 2009
+ volume = {18},
+ year = {2009}
}
@inproceedings{25,
location = {Bordeaux, France},
pages = {79--90},
numpages = {12},
- url = {http://dl.acm.org/citation.cfm?id=2033345.2033356},
acmid = {2033356},
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issn = {0743-7315},
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acmid = {1998949},
publisher = {Academic Press, Inc.},
issn = {0278-0070},
pages = {676--689},
numpages = {14},
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doi = {10.1109/TCAD.2009.2015740},
acmid = {1656937},
publisher = {IEEE Press},
month={March},
pages={204-209},
keywords={circuit optimisation;embedded systems;integrated circuit design;low-power electronics;microprocessor chips;nonlinear programming;thermal management (packaging);DVFS-enabled processors;application peak temperature;cooling costs;dynamic voltage voltage;embedded systems;energy consumption;frequency scaling;nonlinear programming;power optimization;run-time thermal emergencies;system thermal profile;thermal optimization;thermal-constrained energy optimization;Cooling;Cost function;Design optimization;Dynamic voltage scaling;Embedded system;Energy consumption;Frequency;Power system planning;Runtime;Temperature},
-doi={10.1109/ISQED.2007.158},}
+doi={10.1109/ISQED.2007.158}
+}
@INPROCEEDINGS{29,
author={Fen Xie and Martonosi, M. and Malik, S.},
month={Aug},
pages={287-292},
keywords={approximation theory;energy conservation;low-power electronics;power consumption;power supply circuits;DVFS policy;discrete voltage/frequency voltage level;dynamic voltage scaling;dynamic voltage/frequency scaling;energy reduction technique;exponential algorithm;linear-time heuristic approximation;power reduction technique;switching cost;Approximation algorithms;Costs;Dynamic voltage scaling;Energy consumption;Frequency;Linear approximation;Power system modeling;Runtime;Semiconductor device modeling;Upper bound},
-doi={10.1109/LPE.2005.195529},}
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+}
@INPROCEEDINGS{30,
author={Lizhe Wang and von Laszewski, G. and Dayal, J. and Fugang Wang},
month={May},
pages={368-377},
keywords={environmental factors;parallel processing;power aware computing;scheduling;workstation clusters;dynamic voltage frequency scaling technique;energy aware scheduling heuristics;green service level agreement;high end computing;precedence constrained parallel tasks;Computational modeling;Concurrent computing;Costs;Dynamic voltage scaling;Energy consumption;Frequency;Grid computing;High performance computing;Power engineering computing;Processor scheduling;Cluster Computing;Green Computing;Task Scheduling},
-doi={10.1109/CCGRID.2010.19},}
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+}
@article{31,
author = {Yu-Liang Chou and Shaoshan Liu and Eui-Young Chung and Jean-Luc Gaudiot},
pages = {1},
doi = {http://doi.ieeecomputersociety.org/10.1109/L-CA.2013.1},
publisher = {IEEE Computer Society},
-address = {Los Alamitos, CA, USA},
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}
@article{32,
note = "S.I.Energy efficiency in grids and clouds ",
issn = "1569-190X",
doi = "http://dx.doi.org/10.1016/j.simpat.2013.04.007",
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-keywords = "Grid computing",
-keywords = "Cloud computing",
-keywords = "Simulation",
-keywords = "Energy-efficiency",
-keywords = "\{DVFS\} "
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}
@INPROCEEDINGS{33,
month={Nov},
pages={33-33},
keywords={Computer science;Dynamic voltage scaling;Energy consumption;Energy efficiency;Frequency;Gears;Jitter;Microprocessors;Performance loss;Permission},
-doi={10.1109/SC.2005.39},}
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+}
@inproceedings{34,
author = {Cochran, Ryan and Hankendi, Can and Coskun, Ayse and Reda, Sherief},
location = {San Jose, California},
pages = {608--615},
numpages = {8},
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note = "",
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doi = "http://dx.doi.org/10.1016/j.jnca.2013.10.009",
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-keywords = "Homogeneous clusters",
-keywords = "Dynamic voltage scaling (DVS)",
-keywords = "Task duplication",
-keywords = "Adaptive threshold",
-keywords = "Energy efficiency "
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}
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issn = {0018-9162},
pages = {68--75},
numpages = {8},
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acmid = {957974},
publisher = {IEEE Computer Society Press},
location = {Porto Alegre, Brazil},
pages = {175--185},
numpages = {11},
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acmid = {2155641},
publisher = {ACM},
month={Aug},
pages={207-212},
keywords={Linux;computer aided instruction;multiprogramming;power aware computing;program compilers;system monitoring;Intel PXA27x;Linux 2.6.9;dynamic voltage frequency scaling;multitasking systems;online learning;processors runtime statistics;Batteries;Computer applications;Delay;Dynamic voltage scaling;Embedded system;Energy consumption;Frequency estimation;Linux;Power engineering computing;Statistics;dynamic voltage frequency scaling;online learning},
-doi={10.1145/1283780.1283825},}
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+}
@inproceedings{40,
author = {Azevedo, A. and Issenin, I. and Cornea, R. and Gupta, R. and Dutt, N. and Veidenbaum, A. and Nicolau, A.},
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isbn = {0-7695-1471-5},
pages = {168-175},
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acmid = {874373},
publisher = {IEEE Computer Society},
address = {Washington, DC, USA}
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pages = {155--165},
numpages = {11},
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acmid = {2457493},
publisher = {IEEE Computer Society},
pages={676-689},
keywords={power aware computing;DPM policies;Intel PXA27x core;device leakage characteristics;dynamic power management;dynamic voltage-frequency scaling problems;hard disk drive;online learning;system-level power management;workload characterization;Dynamic voltage frequency scaling;energy-performance trade-off;online learning;power management},
doi={10.1109/TCAD.2009.2015740},
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doi = {10.1109/UKSIM.2008.28},
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+``{TOP500 Supercomputers Sites}.'' [Online]. Available:
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+\bibitem{44}
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+{NASA Advanced Supercomputing Division}, ``{NAS} parallel benchmarks,'' Mar.
+ 2012. [Online]. Available:
+ \url{http://www.nas.nasa.gov/publications/npb.html}
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+
+\bibitem{Casanova:2008:SGF:1397760.1398183}
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+ large-scale distributed experiments,'' in \emph{Proceedings of the Tenth
+ International Conference on Computer Modeling and Simulation}, ser. UKSIM
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+ Computer Society, 2008, pp. 126--131.
+
+\bibitem{3}
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+ the energy-time tradeoff in {MPI} programs on a power-scalable cluster,'' in
+ \emph{Proceedings of the 19th IEEE International Parallel and Distributed
+ Processing Symposium (IPDPS'05) - Papers - Volume 01}, ser. IPDPS '05.\hskip
+ 1em plus 0.5em minus 0.4em\relax Washington, DC, USA: IEEE Computer Society,
+ 2005, pp. 4.1--.
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+ ``Bounding energy consumption in large-scale {MPI} programs,'' in
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+ ser. ICCAD '11.\hskip 1em plus 0.5em minus 0.4em\relax Piscataway, NJ, USA:
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+ learning,'' \emph{Computer-Aided Design of Integrated Circuits and Systems,
+ IEEE Transactions on}, vol.~28, no.~5, pp. 676--689, May 2009.
+
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University of Franche-Comté\\
IUT de Belfort-Montb\'{e}liard, Rue Engel Gros, BP 27, 90016 Belfort, France\\
Fax : (+33)~3~84~58~77~32\\
- Email: \{jean-claude.charr, ahmed.fanfakh, raphael.couturier, arnaud.giersch\}@univ-fcomte.fr
+ Email: \{jean-claude.charr, raphael.couturier, ahmed.fanfakh, arnaud.giersch\}@univ-fcomte.fr
}
}
\maketitle
-\AG{Use Capital letters for only the first letter in the title of a section, table, figure, ...}
\begin{abstract}
Dynamic Voltage Frequency Scaling (DVFS) can be applied to modern CPUs.
This technique is usually used to reduce the energy consumed by a CPU while
the power consumed by the CPU. However, it can also significantly affect the
performance of the executed program if it is compute bound and a low CPU
frequency is selected. The performance degradation ratio can even be higher than
-the saved energy ratio.Therefore, the chosen scaling factor must give the best possible tradeoff
+the saved energy ratio. Therefore, the chosen scaling factor must give the best possible tradeoff
between energy reduction and performance.
In this paper we present an algorithm
using the simulator SimGrid/SMPI v3.10~\cite{Casanova:2008:SGF:1397760.1398183}
over an homogeneous distributed memory architecture. Furthermore, we compare the
proposed algorithm with Rauber and Rünger methods~\cite{3}.
-The comparison's results show that our
-algorithm gives better energy-time tradeoff.
+The comparison's results show that our algorithm gives better energy-time tradeoff.
This paper is organized as follows: Section~\ref{sec.relwork} presents related works
from other authors. Section~\ref{sec.exe} shows the execution of parallel
tasks and sources of idle times. It resumes the energy
model of homogeneous platform. Section~\ref{sec.mpip} evaluates the performance
of MPI program. Section~\ref{sec.compet} presents the energy-performance tradeoffs
-objective function. Section~\ref{sec.optim} demonstrates the proposed
-energy-performance algorithm. Section~\ref{sec.expe} verifies the performance prediction
+objective function. Section~\ref{sec.optim} demonstrates the proposed energy-performance algorithm. Section~\ref{sec.expe} verifies the performance prediction
model and presents the results of the proposed algorithm. Also, It shows the comparison results. Finally,
we conclude in Section~\ref{sec.concl}.
-\section{Related Works}
+\section{Related works}
\label{sec.relwork}
\AG{Consider introducing the models sec.~\ref{sec.exe} maybe before related works}
The online scaling factor selection methods are executed during the runtime of the program. They are usually integrated into iterative programs where the same block of instructions is executed many times. During the first few iterations, many informations are measured such as the execution time, the energy consumed using a multimeter, the slack times, ... Then a method will exploit these measurements to compute the scaling factor values for each processor. This operation, measurements and computing new scaling factor, can be repeated as much as needed if the iterations are not regular. Kimura, Peraza, Yu-Liang et al. ~\cite{11,2,31} used learning methods to select the appropriate scaling factor values to eliminate the slack times during runtime. However, as seen in ~\cite{39,19}, machine learning methods can take a lot of time to converge when the number of available gears is big. To reduce the impact of slack times, in~\cite{1}, Lim et al. developed an algorithm that detects the
communication sections and changes the frequency during these sections
only. This approach might change the frequency of each processor many times per iteration if an iteration
-contains more than one communication section. In ~\cite{3}, Rauber et al. used an analytical model that after measuring the energy consumed and the execution time with the highest frequency gear, it can predict the energy consumed and the execution time for every frequency gear . These predictions may be used to choose the optimal gear for each processor executing the parallel program to reduce energy consumption.
+contains more than one communication section. In ~\cite{3}, Rauber and Rünger used an analytical model that after measuring the energy consumed and the execution time with the highest frequency gear, it can predict the energy consumed and the execution time for every frequency gear . These predictions may be used to choose the optimal gear for each processor executing the parallel program to reduce energy consumption.
To maintain the performance of the parallel program , they
-set the processor with the biggest load to the highest gear and then compute the scaling factor values for the rest pf the processors. Although this model was built for parallel architectures, it can be adapted to distributed architectures by taking into account the communications.
+set the processor with the biggest load to the highest gear and then compute the scaling factor values for the rest of the processors. Although this model was built for parallel architectures, it can be adapted to distributed architectures by taking into account the communications.
The primary contribution of this paper is presenting a new online scaling factor selection method which has the following characteristics :
\begin{enumerate}
\item Based on Rauber's analytical model to predict the energy consumption and the execution time of the application with different frequency gears.
\end{enumerate}
-\section{Execution and Energy of Parallel Tasks on Homogeneous Platform}
+\section{Execution and energy of parallel tasks on homogeneous platform}
\label{sec.exe}
-\AG{The whole subsection ``Parallel Tasks Execution on Homogeneous Platform'', can be deleted if we need space, we can just say we are interested in this paper in homogeneous clusters}
-\subsection{Parallel Tasks Execution on Homogeneous Platform}
+%\AG{The whole subsection ``Parallel Tasks Execution on Homogeneous Platform'', can be deleted if we need space, we can just say we are interested in this paper in homogeneous clusters}
+\subsection{Parallel tasks execution on homogeneous platform}
A homogeneous cluster consists of identical nodes in terms of hardware and software.
Each node has its own memory and at least one processor which can
be a multi-core. The nodes are connected via a high bandwidth network. Tasks
platform. These tasks can exchange the data via synchronous message passing.
\begin{figure*}[t]
\centering
- \subfloat[Sync. Imbalanced Communications]{\includegraphics[scale=0.67]{commtasks}\label{fig:h1}}
- \subfloat[Sync. Imbalanced Computations]{\includegraphics[scale=0.67]{compt}\label{fig:h2}}
- \caption{Parallel Tasks on Homogeneous Platform}
+ \subfloat[Sync. imbalanced communications]{\includegraphics[scale=0.67]{commtasks}\label{fig:h1}}
+ \subfloat[Sync. imbalanced computations]{\includegraphics[scale=0.67]{compt}\label{fig:h2}}
+ \caption{Parallel tasks on homogeneous platform}
\label{fig:homo}
\end{figure*}
Therefore, the execution time of a task consists of the computation time and the
This happens when processing different amounts of data on each processor (see figure~(\ref{fig:h2})).
In this case the fastest tasks have to wait at the synchronization barrier for the
slowest ones to begin the next task. In both cases the overall execution time
-of the program is the execution time of the slowest task as in equation \ref{eq:T1}.
+of the program is the execution time of the slowest task as in EQ~(\ref{eq:T1}).
\begin{equation}
\label{eq:T1}
\textit{Program Time} = \max_{i=1,2,\dots,N} T_i
\end{equation}
where $T_i$ is the execution time of task $i$ and all the tasks are executed concurrently on different processors.
-\subsection{Energy Model for Homogeneous Platform}
+\subsection{Energy model for homogeneous platform}
Many researchers~\cite{9,3,15,26} divide the power consumed by a processor to two power metrics: the
static and the dynamic power. While the first one is consumed as long as the computing unit is on, the latter is only consumed during computation times. The dynamic power
$P_{dyn}$ is related to the switching activity $\alpha$, load capacitance $C_L$,
-the supply voltage $V$ and operational frequency $f$, as shown in equation ~\ref{eq:pd}.
+the supply voltage $V$ and operational frequency $f$, as shown in EQ~(\ref{eq:pd}).
\begin{equation}
\label{eq:pd}
P_\textit{dyn} = \alpha \cdot C_L \cdot V^2 \cdot f
quadratically the dynamic power which may cause degradation in performance and thus, the increase of the static energy because the execution time is increased~\cite{36}. If the tasks are sorted according to their execution times before scaling in a descending order, the total energy consumption model for a parallel
homogeneous platform, as presented by Rauber et al.~\cite{3}, can be written as a function of the scaling factor \emph S, as in EQ~(\ref{eq:energy}).
-\AG{Are you sure of the following equation}
\begin{equation}
\label{eq:energy}
E = P_\textit{dyn} \cdot S_1^{-2} \cdot
\end{equation}
where \emph N is the number of parallel nodes, $T_i \ and \ S_i \ for \ i=1,...,N$ are the execution times and scaling factors of the sorted tasks. Therefore, $T1$ is the time of the slowest task, and $S_1$ its scaling factor which should be the highest because they are proportional to
the time values $T_i$. The scaling factors are computed as in EQ~(\ref{eq:si}).
-\AG{This equation does not make sense either, what's S? there is no F}
\begin{equation}
\label{eq:si}
S_i = S \cdot \frac{T_1}{T_i}
= \frac{F_\textit{max}}{F_\textit{new}} \cdot \frac{T_1}{T_i}
\end{equation}
-\AG{The Rauber model was used for a parallel machine not a homogeneous platform}
-where $F$ is the number of available frequencies. In this paper we depend on
+In this paper we depend on
Rauber and Rünger energy model EQ~(\ref{eq:energy}) for two reasons: (1) this
-model is used for homogeneous platform that we work on in this paper, and (2) we
+model is used for any number of concurrent tasks, and (2) we
compare our algorithm with Rauber and Rünger scaling factor selection method which is based on
EQ~(\ref{eq:energy}). The optimal scaling factor is computed by minimizing the derivation for this equation which produces EQ~(\ref{eq:sopt}).
-\AG{what's the small n in the equation}
\begin{equation}
\label{eq:sopt}
- S_\textit{opt} = \sqrt[3]{\frac{2}{n} \cdot \frac{P_\textit{dyn}}{P_\textit{static}} \cdot
+ S_\textit{opt} = \sqrt[3]{\frac{2}{N} \cdot \frac{P_\textit{dyn}}{P_\textit{static}} \cdot
\left( 1 + \sum_{i=2}^{N} \frac{T_i^3}{T_1^3} \right) }
\end{equation}
\AG{The following 2 sections can be merged easily}
-\section{Performance Evaluation of MPI Programs}
+\section{Performance evaluation of MPI programs}
\label{sec.mpip}
The performance (execution time) of parallel synchronous MPI applications depend on
\end{equation}
In this paper, this prediction method is used to select the best scaling factor for each processor as presented in the next section.
-
-\section{Performance to Energy Competition}
+\section{Performance to energy competition}
\label{sec.compet}
This section demonstrates our approach for choosing the optimal scaling
\begin{multline}
\label{eq:enorm}
E_\textit{Norm} = \frac{ E_\textit{Reduced}}{E_\textit{Original}} \\
- {} = \frac{P_\textit{dyn} \cdot S_i^{-2} \cdot
+ {} = \frac{P_\textit{dyn} \cdot S_1^{-2} \cdot
\left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
- P_\textit{static} \cdot T_1 \cdot S_i \cdot N }{
+ P_\textit{static} \cdot T_1 \cdot S_1 \cdot N }{
P_\textit{dyn} \cdot \left(T_1+\sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
P_\textit{static} \cdot T_1 \cdot N }
\end{multline}
\end{equation}
\begin{figure*}
\centering
- \subfloat[Converted Relation.]{%
+ \subfloat[Converted relation.]{%
\includegraphics[width=.4\textwidth]{file.eps}\label{fig:r1}}%
\qquad%
- \subfloat[Real Relation.]{%
+ \subfloat[Real relation.]{%
\includegraphics[width=.4\textwidth]{file3.eps}\label{fig:r2}}
\label{fig:rel}
- \caption{The Energy and Performance Relation}
+ \caption{The energy and performance relation}
\end{figure*}
Then, we can modelize our objective function as finding the maximum distance
between the energy curve EQ~(\ref{eq:enorm}) and the inverse of performance
following form:
\begin{equation}
\label{eq:max}
- \textit{MaxDist} = \max (\overbrace{P^{-1}_\textit{Norm}}^{\text{Maximize}} -
- \overbrace{E_\textit{Norm}}^{\text{Minimize}} )
+ Max Dist = \max_{j=1,2,\dots,F} (\overbrace{P^{-1}_\textit{Norm}(S_j)}^{\text{Maximize}} -
+ \overbrace{E_\textit{Norm}(S_j)}^{\text{Minimize}} )
\end{equation}
-Then we can select the optimal scaling factor that satisfy
+where F is the number of available frequencies. Then we can select the optimal scaling factor that satisfy
EQ~(\ref{eq:max}). Our objective function can work with any energy model or
static power values stored in a data file. Moreover, this function works in
optimal way when the energy curve has a convex form over the available frequency scaling
factors as shown in~\cite{15,3,19}.
-\section{Optimal Scaling Factor for Performance and Energy}
+\section{Optimal scaling factor for performance and energy}
\label{sec.optim}
Algorithm~\ref{EPSA} compute the optimal scaling factor according to the objective function described above.
\begin{algorithm}[tp]
\State Set $P_{states}$ to the number of available frequencies.
\State Set the variable $F_{new}$ to max. frequency, $F_{new} = F_{max} $
\State Set the variable $F_{diff}$ to the difference between two successive frequencies.
- \For {$i=1$ to $P_{states} $}
+ \For {$j:=1$ to $P_{states} $}
\State - $F_{new}=F_{new} - F_{diff} $
\State - $S = \frac{F_\textit{max}}{F_\textit{new}}$
- \State - $S_i = S \cdot \frac{T_1}{T_i}= \frac{F_\textit{max}}{F_\textit{new}} \cdot \frac{T_1}{T_i} \ for \ i=1,...,N$
- \State - $E_\textit{Norm} = \frac{P_\textit{dyn} \cdot S_i^{-2} \cdot
+ \State - $S_i = S \cdot \frac{T_1}{T_i}= \frac{F_\textit{max}}{F_\textit{new}} \cdot \frac{T_1}{T_i} \
+ for \ i=1,...,N$
+ \State - $E_\textit{Norm} = \frac{P_\textit{dyn} \cdot S_1^{-2} \cdot
\left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
- P_\textit{static} \cdot T_1 \cdot S_i \cdot N }{
+ P_\textit{static} \cdot T_1 \cdot S_1 \cdot N }{
P_\textit{dyn} \cdot \left(T_1+\sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
P_\textit{static} \cdot T_1 \cdot N }$
\State - $P_{NormInv}=T_{old}/T_{new}$
\If{ $(P_{NormInv}-E_{Norm} > Dist$) }
- \State $S_{optimal} = S$
+ \State $S_{opt} = S$
\State $Dist = P_{NormInv} - E_{Norm}$
\EndIf
\EndFor
- \State Return $S_{optimal}$
+ \State Return $S_{opt}$
\end{algorithmic}
\end{algorithm}
\caption{DVFS}
\label{dvfs}
\begin{algorithmic}[1]
- \For {$J:=1$ to $Some-Iterations \; $}
+ \For {$k:=1$ to $Some-Iterations \; $}
\State -Computations Section.
\State -Communications Section.
- \If {$(J=1)$}
+ \If {$(k=1)$}
\State -Gather all times of computation and\par\hspace{13 pt} communication from each node.
\State -Call algorithm~\ref{EPSA} with these times.
- \State -Compute the new frequency from the returned optimal scaling factor.
+ \State -Compute the new frequency from the \par\hspace{13 pt} returned optimal scaling factor.
\State -Set the new frequency to the CPU.
\EndIf
\EndFor
they have balanced workloads, otherwise, they take different frequencies when
having imbalanced workloads. Thus, EQ~(\ref{eq:fi}) adapts the frequency of the CPU to the nodes' workloads to maintain performance.
-\section{Experimental Results}
+\section{Experimental results}
\label{sec.expe}
Our experiments are executed on the simulator SimGrid/SMPI
-v3.10. We configure the simulator to use a a homogeneous cluster with one core per
+v3.10. We configure the simulator to use a homogeneous cluster with one core per
node. The
detailed characteristics of our platform file are shown in the
table~(\ref{table:platform}).
frequencies. The simulated network link is 1 GB Ethernet (TCP/IP).
The backbone of the cluster simulates a high performance switch.
\begin{table}[htb]
- \caption{Platform File Parameters}
+ \caption{Platform file parameters}
% title of Table
\centering
\begin{tabular}{|*{7}{l|}}
\end{tabular}
\label{table:platform}
\end{table}
-\subsection{Performance Prediction Verification}
+\subsection{Performance prediction verification}
In this section we evaluate the precision of our performance prediction method based on EQ~(\ref{eq:tnew}) by applying it the NAS benchmarks. The NAS programs are executed with the class B option for comparing the
real execution time with the predicted execution time. Each program runs offline
frequency by the new one see EQ~(\ref{eq:s}).
\begin{figure*}[t]
\centering
- \includegraphics[width=.4\textwidth]{cg_per.eps}\qquad%
- \includegraphics[width=.4\textwidth]{mg_pre.eps}
- \includegraphics[width=.4\textwidth]{bt_pre.eps}\qquad%
- \includegraphics[width=.4\textwidth]{lu_pre.eps}
+ \includegraphics[width=.328\textwidth]{cg_per.eps}\hfill%
+ \includegraphics[width=.328\textwidth]{mg_pre.eps}\hfill%
+ % \includegraphics[width=.4\textwidth]{bt_pre.eps}\qquad%
+ \includegraphics[width=.328\textwidth]{lu_pre.eps}\hfill%
\caption{Comparing predicted to real execution time}
\label{fig:pred}
\end{figure*}
In our cluster there are 18 available frequency states for each processor.
This lead to 18 run states for each program. We use seven MPI programs of the
NAS parallel benchmarks: CG, MG, EP, FT, BT, LU
-and SP. Figure~(\ref{fig:pred}) presents plots of the real execution times and the simulated ones. The average normalized errors between the predicted execution time and
-the real time (SimGrid time) for all programs is between 0.0032 to 0.0133.
-\AG{why compute the average error not the max}
-\subsection{The experimental results}
+and SP. Figure~(\ref{fig:pred}) presents plots of the real execution times and the simulated ones. The maximum normalized error between the predicted execution time and the real time (SimGrid time) for all programs is between 0.0073 to 0.031. The better case is for CG and the worse case is for LU.
+\subsection{The experimental results for the scaling algorithm }
The proposed algorithm was applied to seven MPI programs of the NAS
benchmarks (EP, CG, MG, FT, BT, LU and SP) which were run with three classes (A, B and
C). For each instance the benchmarks were executed on a number of processors
same time from all available scaling factors.
\begin{figure*}[t]
\centering
- \includegraphics[width=.33\textwidth]{ep.eps}\hfill%
- \includegraphics[width=.33\textwidth]{cg.eps}\hfill%
- \includegraphics[width=.33\textwidth]{sp.eps}
- \includegraphics[width=.33\textwidth]{lu.eps}\hfill%
- \includegraphics[width=.33\textwidth]{bt.eps}\hfill%
- \includegraphics[width=.33\textwidth]{ft.eps}
- \caption{Optimal scaling factors for The parallel NAS benchmarks}
+ \includegraphics[width=.328\textwidth]{ep.eps}\hfill%
+ \includegraphics[width=.328\textwidth]{cg.eps}\hfill%
+ \includegraphics[width=.328\textwidth]{sp.eps}
+ \includegraphics[width=.328\textwidth]{lu.eps}\hfill%
+ \includegraphics[width=.328\textwidth]{bt.eps}\hfill%
+ \includegraphics[width=.328\textwidth]{ft.eps}
+ \caption{Optimal scaling factors for predicted energy and performance of NAS benchmarks}
\label{fig:nas}
\end{figure*}
\begin{table}[htb]
- \caption{The Scaling Factors Results}
+ \caption{The scaling factors results}
% title of Table
\centering
\begin{tabular}{|l|*{4}{r|}}
example BT and EP. Our algorithm selects big scaling factor value when the
communication and the other slacks times are big and smaller ones in opposite
cases. In EP there are no communications inside the iterations. This make our
-EPSA to selects smaller scaling factor values (inducing smaller energy savings).
+algorithm to selects smaller scaling factor values (inducing smaller energy savings).
-\subsection{Comparing Results}
+\subsection{Results comparison}
In this section, we compare our scaling factor selection method with Rauber and Rünger
methods~\cite{3}. They had two scenarios, the first is to reduce energy to the
refer to this scenario as $R_{E}$. The second scenario is similar to the first
except setting the slower task to the maximum frequency (when the scale $S=1$)
to keep the performance from degradation as mush as possible. We refer to this
-scenario as $R_{E-P}$. The comparison is made in tables~(\ref{table:compare
- Class A},\ref{table:compare Class B},\ref{table:compare Class C}). These
+scenario as $R_{E-P}$. While we refer to our algorithm as EPSA. The comparison is made in tables~(\ref{table:compareA},\ref{table:compareB},\ref{table:compareC}). These
tables show the results of our method and Rauber and Rünger scenarios for all the
NAS benchmarks programs for classes A,B and C.
\begin{table}[p]
- \caption{Comparing Results for The NAS Class A}
+ \caption{Comparing results for the NAS class A}
% title of Table
\centering
\begin{tabular}{|l|l|*{4}{r|}}
% is used to refer this table in the text
\end{table}
\begin{table}[p]
- \caption{Comparing Results for The NAS Class B}
+ \caption{Comparing results for the NAS class B}
% title of Table
\centering
\begin{tabular}{|l|l|*{4}{r|}}
\end{table}
\begin{table}[p]
- \caption{Comparing Results for The NAS Class C}
+ \caption{Comparing results for the NAS class C}
% title of Table
\centering
\begin{tabular}{|l|l|*{4}{r|}}
gives the highest positive energy to performance tradeoffs while Rauber and Rünger method
($R_{E-P}$) gives in some time negative tradeoffs such as in BT and
EP.
-\begin{figure}[t]
+\begin{figure*}[t]
\centering
- \includegraphics[width=.33\textwidth]{compare_class_A.pdf}
- \includegraphics[width=.33\textwidth]{compare_class_B.pdf}
- \includegraphics[width=.33\textwidth]{compare_class_c.pdf}
- \caption{Comparing our method to Rauber and Rünger Methods}
+ \includegraphics[width=.328\textwidth]{compare_class_A.pdf}
+ \includegraphics[width=.328\textwidth]{compare_class_B.pdf}
+ \includegraphics[width=.328\textwidth]{compare_class_c.pdf}
+ \caption{Comparing our method to Rauber and Rünger methods}
\label{fig:compare}
-\end{figure}
+\end{figure*}
\section{Conclusion}
\label{sec.concl}
-In this paper, we have presented a new online scaling factor selection method that optimizes simultaneously the energy and performance of a distributed application running on an homogeneous cluster. It uses the computation and communication times measured at the first iteration to predict energy consumption and the performance of the parallel application at every available frequency. Then, it selects the scaling factor that gives the best tradeoff between energy reduction and performance which is the maximum distance between the energy and the inverted performance curves. To evaluate this method, we have applied it to the NAS benchmarks and it was compared to Rauber's methods while being executed on the simulator SimGrid. The results showed that our method, outperforms Rauber's methods in terms of energy-performance ratio.
+In this paper, we have presented a new online scaling factor selection method that optimizes simultaneously the energy and performance of a distributed application running on an homogeneous cluster. It uses the computation and communication times measured at the first iteration to predict energy consumption and the performance of the parallel application at every available frequency. Then, it selects the scaling factor that gives the best tradeoff between energy reduction and performance which is the maximum distance between the energy and the inverted performance curves. To evaluate this method, we have applied it to the NAS benchmarks and it was compared to Rauber and Rünger methods while being executed on the simulator SimGrid. The results showed that our method, outperforms Rauber and Rünger methods in terms of energy-performance ratio.
In the near future, we would like to adapt this scaling factor selection method to heterogeneous platforms where each node has different characteristics. In particular, each CPU has different available frequencies, energy consumption and performance. It would be also interesting to develop a new energy model for asynchronous parallel iterative methods where the number of iterations is not known in advance and depends on the global convergence of the iterative system.
As a PhD student, M. Ahmed Fanfakh, would like to thank the University of
Babylon (Iraq) for supporting his work.
-\AG{delete the online paths for each reference}
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+%%CreationDate: Mon Mar 24 16:08:33 2014
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+ /CreationDate (Mon Mar 24 16:08:33 2014)
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