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06/08/13 16:43:18 (12 years ago)
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wojtekp
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papers/SMPaT-2012_DCWoRMS
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  • papers/SMPaT-2012_DCWoRMS/elsarticle-DCWoRMS.aux

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  • papers/SMPaT-2012_DCWoRMS/elsarticle-DCWoRMS.tex

    r1076 r1077  
    397397 
    398398\begin{equation} 
    399 P = P_{idle} + L*P_{cpubase}*c^{(f-f_{base})/100} + P_{app}, \label{eq:model} 
     399P = P_{idle} + L*P_{cpubase}*c^{(f-f_{base})/100} + P_{app} \label{eq:model} 
    400400\end{equation} 
    401401 
    … …  
    531531 
    532532\textbf{Application} 
    533 This model refers to the Application specific approach presented in Section~\ref{sec:power}. Relative error of this model, with respect to the measured values, is equal to 10.85\%.  In this model we face possible deviation from the average caused by power usage fluctuations not explained by variables used in models. These deviations reached around 7\%. Power usage was defined using the equation presented in \ref{eq:model}. 
     533This model refers to the Application specific approach presented in Section~\ref{sec:power}. Power usage was defined using the equation presented in \ref{eq:model}. 
    534534 
    535535Table~\ref{nodeBasePowerUsage} and Table~\ref{appPowerUsage} contain values of $P_{cpubase}$ and $P_{app}$, respectively, obtained for the particular application and resource architectures. Lack of the corresponding value means that the application did not run on the given type of node. 
    … …  
    555555\hline 
    556556Abinit & 3.3 &  - &  - \\ 
    557 Linpactiny & 2.5 & - & 0.2 \\ 
    558 Linpack3gb &  6 &  -  & -  \\ 
     557Linpack - tiny & 2.5 & - & 0.2 \\ 
     558Linpack - 3Gb &  6 &  -  & -  \\ 
    559559C-Ray & 4 & 1 & 0.05 \\ 
    560560FFT & 3.5 & 2 & 0.1 \\ 
    … …  
    569569Within this model we applied the measured values for each application exactly to the power model. Neither dependencies with load nor application profiles are modeled. Obviously this approach is contaminated only with the inaccuracy of the measurements and variability of power usage (caused by other unmeasured factors). 
    570570 
     571 
     572The following table (Table~\ref{expPowerModels}) contains the relative errors of the models with respect to the measured values 
     573\begin {table}[h!] 
     574\centering 
     575\begin{tabular}{cccc} 
     576\hline 
     577Static & Dynamic & Application  & Mapping \\ 
     578\hline 
     57913.74 & 5.2 &  10.85 & 0 \\ 
     580\hline 
     581\end{tabular} 
     582\caption {\label{expPowerModels} Power models error in \%} 
     583\end {table} 
     584 
     585Obviously, 0\% error in the case of the Mapping model is caused by the use of a tabular data, which for each application stores a specific power usage. Nevertheless, in all models we face possible deviations from the average caused by power usage fluctuations not explained by variables used in models. These deviations reached around 7\% for each case. 
     586 
     587 
    571588For the evaluation of resource management policies we decided to use the latter model. Thus, we introduce into the simulation environment exact values obtained within our testbed, to build both the power profiles of applications as well as the application performance models, denoting their execution times. 
    572 In the experiments addressing the verification of models we investigated the Dynamic model by comparing appropriate results to the ones derived from the Mapping approach. 
     589In the experiments addressing the verification of models we investigated all models by comparing the appropriate results to the ones derived from the Mapping approach. 
    573590 
    574591 
    … …  
    709726\subsection{Verification of models}  
    710727 
    711 This section contains more detailed comparison of two types of power consumption models that can be applied, among others, within the DCworms. The first one, called Mapping approach, was applied to the experiments in the previous section. As mentioned within this model, the values measured on the CoolEmAll testbed for each application were applied directly to the power consumption model used in DCworms.  
    712  
    713 Model evaluated in this section is a variation of Dynamic model by additional modeling of dependencies with the processor load for the given type of application. Within this model, we benefited from the power profiles based on the measurements made on CoolEmAll testbed (and adopted also by the previous model). However, data applied to the simulation environment consisted only of measurements gathered for applications ran in mode resulting in lowest and highest processor load. For all load levels between the given two values we assumed the linear dependency between the load and power consumption. Thus, the power consumption for the given processor load can be expressed using the equation (\ref{eq:modelLoadApp}). 
    714  
     728This section contains more detailed and experimental comparison of power consumption models that can be applied, among others, within the DCworms. As a reference model, called Mapping approach, we used model that was applied to the experiments in the previous section. As mentioned within this model, the values measured on the CoolEmAll testbed for each application were applied directly to the power consumption model used in DCworms.  
     729 
     730\paragraph{Static} 
     731TODO 
     732 
     733\paragraph{Dynamic} 
     734This model assumes additional modeling of dependencies with the processor load for the given type of application. Within this model, we benefited from the power profiles based on the measurements made on CoolEmAll testbed. However, data applied to the simulation environment consisted only of measurements gathered for applications ran in mode resulting in lowest and highest processor load. For all load levels between the given two values we assumed the linear dependency between the load and power consumption. Thus, the power consumption for the given processor load can be expressed using the equation (\ref{eq:modelLoadApp}). 
    715735 
    716736\begin{equation} 
    717 P_{L_{app}} = P_{LL_{app}} + (L_{app}-LL_{app})*(P_{HL_{app}}-P_{LL_{app}})/(HL_{app}-LL_{app}), \label{eq:modelLoadApp} 
     737P_{L_{app}} = P_{LL_{app}} + (L_{app}-LL_{app})*(P_{HL_{app}}-P_{LL_{app}})/(HL_{app}-LL_{app}) \label{eq:modelLoadApp} 
    718738\end{equation} 
    719739 
    720740where $L_{app}$ is a given processor load, $LL_{app}$ is the lowest measured processor load, $HL_{app}$ is the highest measured processor load, $P_{L_{app}}$ denotes power consumption for a given processor load, $P_{LL_{app}}$ is a power consumption measured for the lowest processor load and $P_{HL_{app}}$ stands for power consumption measured for the highest processor load. All these values refer to the execution of the application of the given type. 
    721741 
    722  
    723 Table \ref{modelAccuracy} contains the results obtained for two examined models for five resource management strategies presented in the previous section. 
     742\paragraph{Application} 
     743TODO 
     744 
     745Table \ref{modelsResults} contains the results obtained for all examined models for five resource management strategies presented in the previous section, while Table \ref{modelsAccuracy} summarize their accuracy. 
     746 
     747%\begin {table}[h!] 
     748%\centering 
     749%\begin{tabular}{l| c | c | c } 
     750%\hline 
     751%Policy / Model  & Mapping & Dynamic  & Accuracy [\%]\\ 
     752%\hline 
     753%R & 46.883 & 44.476 &  94.87 \\ 
     754%R+NPM & 36.705 & 34.298 & 93.44\\ 
     755%EO & 46.305 & 44.050 &  95.13\\ 
     756%EO+NPM & 30.568 &      28.250 &  92.42 \\ 
     757%R+LF  & 77.109 & 75.277 & 97.62\\ 
     758%\hline 
     759%\end{tabular} 
     760%\caption {\label{modelAccuracy} Comparison of energy usage estimations [kWh] obtained for two power consumption %models. R - Random, R+NPM - Random + node power management, EO - Energy optimization, EO+NPM - Energy %optimization + node power management, R+LF - Random + lowest frequency} 
     761%\end {table} 
     762 
    724763 
    725764\begin {table}[h!] 
    726765\centering 
    727 \begin{tabular}{l| c | c | c } 
    728 \hline 
    729 Policy / Model  & Mapping & Dynamic  & Accuracy [\%]\\ 
    730 \hline 
    731 R & 46.883 & 44.476 &  94.87 \\ 
    732 R+NPM & 30.568 &        28.250 &  92.42 \\ 
    733 EO & 36.705 & 34.298 & 93.44\\ 
    734 EO+NPM & 46.305 & 44.050 &  95.13\\ 
    735 R+LF  & 77.109 & 75.277 & 97.62\\ 
     766\begin{tabular}{l| c | c | c | c} 
     767\hline 
     768Policy / Model  & Mapping & Static &  Dynamic  & Application \\ 
     769\hline 
     770R & 46.883 & 48.969 &46.857 & 45.024 \\ 
     771R+NPM &  36.705 & 38.790        & 36.679  & 34.846 \\ 
     772EO & 46.305 & 49.254 & 46.746 & 44.585 \\ 
     773EO +NPM & 30.568 &      33.915 & 30.31 & 28.728\\ 
     774R+LF  & 77.109 &  78.371 & 76.5  &      81.919\\ 
    736775\hline 
    737776\end{tabular} 
    738 \caption {\label{modelAccuracy} Comparison of energy usage estimations [kWh] obtained for two power consumption models. R - Random, R+NPM - Random + node power management, EO - Energy optimization, EO+NPM - Energy optimization + node power management, R+LF - Random + lowest frequency} 
     777\caption {\label{modelsResults} Comparison of energy usage estimations [kWh] obtained for investigated power consumption models. R - Random, R+NPM - Random + node power management, EO - Energy optimization, EO+NPM - Energy optimization + node power management, R+LF - Random + lowest frequency} 
    739778\end {table} 
    740779 
    741 %R & 46.883 & 44.476 & 48.444 & 94.87 \\ 
    742 %R+NPM & 30.568 &       28.250 & 32.619 & 92.42 \\ 
    743 %EO & 36.705 & 34.298 & 42.386 & 93.44\\ 
    744 %EO+NPM & 46.305 & 44.050 & 26.319 & 95.13\\ 
    745 %R+LF  & 77.109 & 75.277 &      80.905 & 97.62\\ 
    746  
    747 As it can be observed, the accuracy of the Dynamic based model is high and exceeds visibly 90\%. Satisfactory accuracy suggests that applying various power consumption models, while verifying different approaches or in case of lack of detailed measurements, does not lead to deterioration of overall results. This fact confirms also the important role of simulations in the experiments related to the distributed computing systems.  
     780 
     781 
     782\begin {table}[h!] 
     783\centering 
     784\begin{tabular}{l| c | c | c | c} 
     785\hline 
     786Policy / Model  & Mapping & Static &  Dynamic  & Application \\ 
     787\hline 
     788R & 100 & 95.55&        99.94   &96.03 \\ 
     789R+NPM & 100 & 94.32&    99.93&  94.94 \\ 
     790EO & 100 & 93.63        &99.05  &96.29\\ 
     791EO +NPM &  100 &        89.05&  99.16&  93.98\\ 
     792R+LF  &  100 &  98.36   &99.21& 93.76\\ 
     793\hline 
     794\end{tabular} 
     795\caption {\label{modelsAccuracy} Comparison of accuracy [\%] obtained for investigated power consumption models. R - Random, R+NPM - Random + node power management, EO - Energy optimization, EO+NPM - Energy optimization + node power management, R+LF - Random + lowest frequency} 
     796\end {table} 
     797 
     798As it can be observed, the accuracy of the all models is high and exceeds visibly 90\%. Satisfactory accuracy suggests that applying various power consumption models, while verifying different approaches or in case of lack of detailed measurements, does not lead to deterioration of overall results. This fact confirms also the important role of simulations in the experiments related to the distributed computing systems.  
    748799 
    749800 
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