number of nodes composing them. To minimize the operating costs of these
platforms many techniques have been used. Dynamic voltage and frequency
scaling (DVFS) is one of them. It reduces the frequency of a CPU to lower its
- energy consumption. However, lowering the frequency of a CPU might increase
+ energy consumption. However, lowering the frequency of a CPU may increase
the execution time of an application running on that processor. Therefore,
the frequency that gives the best trade-off between the energy consumption and
the performance of an application must be selected.
The need for more computing power is continually increasing. To partially
satisfy this need, most supercomputers constructors just put more computing
-nodes in their platform. The resulting platforms might achieve higher floating
+nodes in their platform. The resulting platforms may achieve higher floating
point operations per second (FLOPS), but the energy consumption and the heat
dissipation are also increased. As an example, the Chinese supercomputer
Tianhe-2 had the highest FLOPS in November 2014 according to the Top500 list
\dots{} DVFS is a widely used process to reduce the energy consumption of a
processor by lowering its frequency
\cite{Rizvandi_Some.Observations.on.Optimal.Frequency}. However, it also reduces
-the number of FLOPS executed by the processor which might increase the execution
+the number of FLOPS executed by the processor which may increase the execution
time of the application running over that processor. Therefore, researchers use
different optimization strategies to select the frequency that gives the best
trade-off between the energy reduction and performance degradation ratio. In
DVFS is a technique used in modern processors to scale down both the voltage and
the frequency of the CPU while computing, in order to reduce the energy
consumption of the processor. DVFS is also allowed in GPUs to achieve the same
-goal. Reducing the frequency of a processor lowers its number of FLOPS and might
+goal. Reducing the frequency of a processor lowers its number of FLOPS and may
degrade the performance of the application running on that processor, especially
if it is compute bound. Therefore selecting the appropriate frequency for a
processor to satisfy some objectives while taking into account all the
strategies to tackle this problem. Some of them developed online methods that
compute the new frequency while executing the application, such
as~\cite{Hao_Learning.based.DVFS,Spiliopoulos_Green.governors.Adaptive.DVFS}.
-Others used offline methods that might need to run the application and profile
+Others used offline methods that may need to run the application and profile
it before selecting the new frequency, such
as~\cite{Rountree_Bounding.energy.consumption.in.MPI,Cochran_Pack_and_Cap_Adaptive_DVFS}.
The methods could be heuristics, exact or brute force methods that satisfy
The overall execution time of a distributed iterative synchronous application
over a heterogeneous platform consists of the sum of the computation time and
the communication time for every iteration on a node. However, due to the
-heterogeneous computation power of the computing nodes, slack times might occur
+heterogeneous computation power of the computing nodes, slack times may occur
when fast nodes have to wait, during synchronous communications, for the slower
nodes to finish their computations (see Figure~\ref{fig:heter}). Therefore, the
overall execution time of the program is the execution time of the slowest task
modern processors, that reduces the energy consumption of a CPU by scaling
down its voltage and frequency. Since DVFS lowers the frequency of a CPU
and consequently its computing power, the execution time of a program running
-over that scaled down processor might increase, especially if the program is
+over that scaled down processor may increase, especially if the program is
compute bound. The frequency reduction process can be expressed by the scaling
factor S which is the ratio between the maximum and the new frequency of a CPU
as in (\ref{eq:s}).
\Es = \Ps \cdot (\Tcp \cdot S + \Tcm)
\end{equation}
-In the considered heterogeneous platform, each processor $i$ might have
+In the considered heterogeneous platform, each processor $i$ may have
different dynamic and static powers, noted as $\Pd[i]$ and $\Ps[i]$
respectively. Therefore, even if the distributed message passing iterative
application is load balanced, the computation time of each CPU $i$ noted
-$\Tcp[i]$ might be different and different frequency scaling factors might be
+$\Tcp[i]$ may be different and different frequency scaling factors may be
computed in order to decrease the overall energy consumption of the application
and reduce slack times. The communication time of a processor $i$ is noted as
$\Tcm[i]$ and could contain slack times when communicating with slower nodes,
presented in Table~\ref{table:platform}, it takes on average \np[ms]{0.04} for 4
nodes and \np[ms]{0.15} on average for 144 nodes to compute the best scaling
factors vector. The algorithm complexity is $O(F\cdot N)$, where $F$ is the
-number of iterations and $N$ is the number of computing nodes. The algorithm
-needs from 12 to 20 iterations to select the best vector of frequency scaling
-factors that gives the results of the next sections.
+maximum number of available frequencies, and $N$ is the number of computing
+nodes. The algorithm needs from 12 to 20 iterations to select the best vector of
+frequency scaling factors that gives the results of the next sections.
\begin{table}[!t]
\caption{Heterogeneous nodes characteristics}
