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add equations of ops/sec

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1 parent 051f29f commit 5794c19b0bd82500c0a410bcf890d6f568e235ee Ming committed Dec 13, 2012
Showing with 92 additions and 33 deletions.
  1. +2 −2 doc/report/abstract.tex
  2. +72 −18 doc/report/eval.tex
  3. +8 −3 doc/report/main.aux
  4. BIN doc/report/main.dvi
  5. +10 −10 doc/report/main.log
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4 doc/report/abstract.tex
@@ -16,9 +16,9 @@
be stored efficiently in terms of performance and cost. We
implemented the system based on LevelDB, and benchmarked the system
using a two-tiered store including a Flash tier and a HDD tier. Our
-system presents up to 6.8$\times$ speedup of throughput over the
+system presents up to 5.78$\times$ speedup of throughput over the
single-tier store using HDD. Particularly, for a workload emulating
-Facebook's photo requests, we observe a sppedup of 5.3$\times$ of the
+Facebook's photo requests, we observe a speedup of 4.46$\times$ of the
throughput using only a small Flash of 5.9\% of the total storage
capacity.
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90 doc/report/eval.tex
@@ -233,37 +233,91 @@ \subsection{MRIS Read}
Figure~\ref{fig:mrisread} presents the read throughput in term of
ops/sec. For all ratios, SSD shows the highest throughput among the
-three setups, followed by Hybrid and then SATA. The ops/sec of SSD is
-3.9$\times$ to 8.0$\times$ faster than SATA. The speedup of SSD over
-SATA also grows as ratio gets larger (except one point). This is
-because as the ratio increases, the I/Os contain more small random
-reads, which exploits more of SSD's superior random performance to
-SATA. Another interesting observation is that the speedup of Hybrid
-over SATA grows rapidly from to as ratio increases.
-
-\NOTE{Ming}{TODO: consitify terms, such as images and objects, HDD and
-SATA}
-
-Notice that the average size of an operation depends on the ratio.
-$$
-\mbox{avg\_op\_size} = \frac{ratio \times \mbox{small} +
- \mbox{large}}{ratio + 1}
-$$
+three setups, followed by Hybrid and then SATA. As shown in
+Table~\ref{tbl:speedup}, the ops/sec of SSD is 3.89$\times$ to
+7.64$\times$ faster than SATA. The speedup of SSD over SATA also grows
+as ratio gets larger (except one point). This is because as the ratio
+increases, the I/Os contain more small random reads, which exploits
+more of SSD's superior random performance to SATA. Another interesting
+observation is that the speedup of Hybrid over SATA grows rapidly from
+0.44 to 5.78 as ratio increases.
\begin{table}[tc]
{\centering \footnotesize
\begin{tabular}{c|c|c|c|c|c|c|c}
\hline
- Speedup & \multicolumn{7}{c}{Placement of Objects} \\ \cline{2-8}
+ Speedup & \multicolumn{7}{c}{Ratio} \\ \cline{2-8}
over SATA & 1 & 2 & 4 & 8 & 16 & 32 & 64 \\ \hline
SSD & 3.89 & 4.68 & 5.79 & 7.52 & 8.04 & 7.60 & 7.64 \\
Hybrid & 0.44 & 0.86 & 1.39 & 2.69 & 3.56 & 4.46 & 5.78 \\ \hline
\end{tabular}
- \caption{Speedup of SSD and Hybrid over SATA.}
+ \caption{Speedup of SSD and Hybrid over SATA in term of ops/sec.}
\label{tbl:speedup}
}
\end{table}
+To help analyze the results, we use variables in
+Table~\ref{tbl:variable} to represent the costs of involved read
+operations in term of time. Then, ops/sec of SSD and SATA can be
+expressed in (\ref{eqn:ssdops}) and (\ref{eqn:sataops}).
+
+\begin{equation}
+\label{eqn:ssdops}
+ 1000000 \frac{ratio + 1}{t_{SF} * ratio + t_{LF}}
+\end{equation}
+
+\begin{equation}
+\label{eqn:sataops}
+ 1000000 \frac{ratio + 1}{t_{SH} * ratio + t_{LH}}
+\end{equation}
+
+By linear regression, we obtained the estimation of the variables
+(shown in Table~\ref{tbl:variable}) from our benchmark data.
+Approxmiately, the ops/sec of Hybrid can be expressed in
+(\ref{eqn:hybridops}).
+
+\begin{equation}
+\label{eqn:hybridops}
+ 1000000 \frac{ratio + 1}{t_{SF} * ratio + t_{LH}}
+\end{equation}
+
+\begin{table}[tc]
+{\centering \footnotesize
+\begin{tabular}{c|c|c}
+\hline
+ Read Type & Flash SSD & SATA HDD \\ \hline
+ Small Image & $t_{SF} = 1482$ & $t_{SH} = 6542$ \\
+ Large Image & $t_{LF} = 13238$ & $t_{LH} = 37599$ \\ \hline
+\end{tabular}
+ \caption{Costs of read operations in time ($\mu$s). For instance,
+$t_{SF}$ means the time taken to read Small image from the Flash SSD.}
+\label{tbl:variable}
+}
+\end{table}
+
+Use (\ref{eqn:hybridops}) and the values in Table~\ref{tbl:variable},
+we can expect the ops/sec of Hybrid. The results, together with
+measured ops/sec in benchmarks, are presented in
+Figure~\ref{fig:readesti}.
+
+\begin{figure}[t]
+\begin{centering}
+\epsfig{file=figures/read_estimate.eps,width=1.00\linewidth}
+\caption{Read performance of Hybrid}
+\label{fig:readesti}
+\end{centering}
+\end{figure}
+
+
+\NOTE{Ming}{TODO: consitify terms, such as images and objects, HDD and
+SATA}
+
+Notice that the average size of an operation depends on the ratio.
+$$
+\mbox{avg\_op\_size} = \frac{ratio \times \mbox{small} +
+ \mbox{large}}{ratio + 1}
+$$
+
The results are shown in Figure~\ref{fig:mrisread}. Specifically, the
speedup for Facebook and Wikipedia workload is XXX and YYY.
View
11 doc/report/main.aux
@@ -39,10 +39,11 @@
\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}MRIS Read}{5}}
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces MRIS Read Performance. Each operation represents a read of an image.}}{5}}
\newlabel{fig:mrisread}{{9}{5}}
-\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Speedup of SSD and Hybrid over SATA.}}{5}}
+\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Speedup of SSD and Hybrid over SATA in term of ops/sec.}}{5}}
\newlabel{tbl:speedup}{{2}{5}}
-\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces MRIS Read Performance by iostat}}{5}}
-\newlabel{fig:mrisiostat}{{10}{5}}
+\newlabel{eqn:ssdops}{{1}{5}}
+\newlabel{eqn:sataops}{{2}{5}}
+\newlabel{eqn:hybridops}{{3}{5}}
\citation{eurosys_hfs}
\bibstyle{plain}
\bibdata{../references}
@@ -56,6 +57,10 @@
\bibcite{wikimedia-foundation}{8}
\bibcite{wikipedia-web}{9}
\bibcite{eurosys_hfs}{10}
+\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Costs of read operations in time ($\mu $s). For instance, $t_{SF}$ means the time taken to read Small image from the Flash SSD.}}{6}}
+\newlabel{tbl:variable}{{3}{6}}
+\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces MRIS Read Performance by iostat}}{6}}
+\newlabel{fig:mrisiostat}{{10}{6}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Related Work}{6}}
\newlabel{sec:related}{{4}{6}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Conclusions}{6}}
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BIN doc/report/main.dvi
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20 doc/report/main.log
@@ -1,4 +1,4 @@
-This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=latex 2011.6.28) 13 DEC 2012 17:19
+This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=latex 2011.6.28) 13 DEC 2012 18:27
entering extended mode
%&-line parsing enabled.
**main.tex
@@ -541,10 +541,10 @@ File: figures/mris-write-thput.eps Graphic file (type eps)
<figures/mris-write-thput.eps>
File: figures/mris_ratio_ops.eps Graphic file (type eps)
- <figures/mris_ratio_ops.eps>
+ <figures/mris_ratio_ops.eps> [5]
File: figures/mris_ratio_iostat_ops.eps Graphic file (type eps)
-<figures/mris_ratio_iostat_ops.eps>) (./related.tex [5]) (./conclusion.tex)
+<figures/mris_ratio_iostat_ops.eps>) (./related.tex) (./conclusion.tex)
(./main.bbl
Underfull \hbox (badness 10000) in paragraph at lines 50--55
\OT1/ptm/m/n/10 life-time. $\OT1/ptm/m/sl/8 https : / / groups . google . com
@@ -559,12 +559,12 @@ Underfull \hbox (badness 10000) in paragraph at lines 62--64
) [6] (./main.aux) )
Here is how much of TeX's memory you used:
- 9152 strings out of 495062
- 153254 string characters out of 1182644
- 209031 words of memory out of 3000000
- 12069 multiletter control sequences out of 15000+50000
- 19086 words of font info for 58 fonts, out of 3000000 for 9000
+ 9166 strings out of 495062
+ 153404 string characters out of 1182644
+ 212063 words of memory out of 3000000
+ 12079 multiletter control sequences out of 15000+50000
+ 20631 words of font info for 64 fonts, out of 3000000 for 9000
29 hyphenation exceptions out of 8191
- 54i,9n,51p,376b,345s stack positions out of 5000i,500n,10000p,200000b,50000s
+ 54i,11n,51p,376b,345s stack positions out of 5000i,500n,10000p,200000b,50000s
-Output written on main.dvi (6 pages, 43220 bytes).
+Output written on main.dvi (6 pages, 45044 bytes).

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