-The energy saving percentage is computed as the ratio between the reduced
-energy consumption, equation (\ref{eq:energy}), and the original energy consumption,
-equation (\ref{eq:eorginal}), for all benchmarks as in figure \ref{fig:eng_s}.
-This figure shows that the energy saving percentages of one site scenario for
-16 and 32 nodes are bigger than those of the two sites scenario. This is because
-the computations to communications ratio in one site scenario is higher
-than the ratio of the two sites scenarios, due to the increase in the communication
-times. Moreover, the frequencies selecting algorithm selects smaller frequencies, bigger
-scaling factors, when the computations times are higher than communication times,
-producing smaller energy consumption, because the dynamic energy consumption
-is decreased linearly with computation times that decreased exponentially with
-scaling factors. On the other side, the increase in the number of computing nodes can be
-increase the communication times and thus producing less energy saving depending on the
-benchmarks being executed. The benchmarks CG, MG, BT and FT show more
-energy saving percentage in one site scenario when executed over 16 nodes comparing to 32 nodes. While
-the benchmarks LU and SP showed the inverse, because there computations to
-communications ratio is not effected to the increase in local site communications.
-While all benchmarks are effected by the long distance communications in the two sites
-scenarios, except EP benchmarks. In EP benchmark there is no communications
-in their iterations, then it is independent from the effect of local and long
-distance communications. Therefore, the energy saving percentage of this benchmarks is
-depend on differences between the computing powers of the computing nodes, for example
-in the one site scenario, the graphite cluster is selected but in the two sits scenario
-this cluster is replaced with Taurus cluster that be more powerful in computing power.
-Therefore, the energy saving of EP benchmarks are bigger in the two site scenario due
-to increase in the differences between the computing powers of the nodes. This means, the higher
-differences between the nodes' computing powers make the proposed frequencies selecting
-algorithm to selects smaller frequencies in the nodes of the higher computing power,
-producing less energy consumption and thus more energy saving.
-The best energy saving percentage was for one site scenario with 16 nodes, on average it
-saves the energy consumption up to 30\%.
-
-Figure \ref{fig:per_d}, presents the performance degradation percentages for all benchmarks.
-It shows that the performance degradation percentages of the one site scenario with
-32 nodes, on average equal to 10\%, is higher than the performance degradation of one 16 nodes,
-which on average equal to 3\%. This because selecting smaller frequencies in the one site scenarios,
-when the computations grater than the communications , increase the number of the critical nodes
-when the number of nodes increased. The inverse happens in the tow sites scenario,
-this due to the lower computations to communications ratio that decreased with highest
-communications. Therefore, the number of the critical nodes are decreased. The average performance
-degradation for the two sites scenario with 16 nodes is equal to 8\% and for 32 nodes is equal to 4\%.
-The EP benchmarks is gives the bigger performance degradation ratio, because there is no
-communications and no slack times in this benchmarks that is always their performance effected
-by selecting big or small frequencies.
-The tradeoff between these scenarios can be computed as in the trade-off function \ref{eq:max}.
-Figure \ref{fig:dist}, presents the tradeoff distance for all benchmarks over all
-platform scenarios. The one site scenario with 16 and 32 nodes had the best tradeoff distance
-compared to the two sites scenarios, because the increase in the communications as mentioned before.
-The one site scenario with 16 nodes is the best scenario in term of energy and performance tradeoff,
-which on average is up 26\%. Then, the tradeoff distance is related linearly to the energy saving
-percentage. Finally, the best energy and performance tradeoff depends on the increase in all of:
-1) the computations to communications ratio, 2) the differences in computing powers
-between the computing nodes and 3) the differences in static and the dynamic powers of the nodes.
-
-\subsection{The experimental results of multi-cores clusters}
-\label{sec.res}
