1,3d0
< Ted,
< My comments begin with Ted:.
< You can see my other changes by doing a diff.
5,16d1
< My changes are mostly stylistic, though I had to add some clarification
< to the theoretical portion.
< Please check the diffs there carefully.
< There are one or two other places where I had to ask you questions. 
< 
< Finally, there is the note to reviewers at the beginning.
< I think, from my own experience on program committees, that this
< will help since we make if very clear what the genesis of this paper is.
< Dennis
< P.S. Did you ever get the Swiss Bank traces? That would be great to include.
< 
< 
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< other buffer management algorithms, such as GCLOCK \cite{Sm78,EH84,NDD92},
---
> other buffer management algorithms, such as Gclock \cite{Sm78,EH84,NDD92},
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> %Dennis: no, the sigmetrics paper NDD92 talks a lot about tuning.
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< from the same process (so-called ``correlated''
< accesses) 
---
> from the same process (so-called ``correlated'' accesses) 
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> %Dennis: fine.
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< In this section, we show that 2Q is better than LRU and is comparable
< to LRU/2.
---
> In this section, we show that 2Q is better than LRU and Gclock,
> and is comparable to LRU/2.
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> We implemented the Gclock algorithm as described in \cite{NDD92}:
> every page has a history count attached.  When a page is referenced,
> we set the history count of its buffer to {\em init\_count}. 
> If a free buffer is required,
> we scan through the buffers (starting from the previous stopping point)
> and examine the history counts.  If the history count of a buffer is non-zero,
> then we decrement the history count and move on to the next page.
> Otherwise, we choose that buffer for replacement.
> We tested Gclock with an {\em init\_count} parameter set to 2 and 4,
> and report the best results.  We found that Gclock usually has a slightly
> lower hit rate than LRU, so we report Gclock results in the tables only,
> for clarity.
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> 
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< rate than LRU. 
---
> rate than LRU and Gclock. 
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< \begin{tabular}{|c| c c c c|}
---
> \begin{tabular}{|c| c c c c c|}
765,786c764,785
< Number of page slots &	LRU/2 &	LRU	 & 2Q	& 2Q \\
<                      &        &          & Kin=30\% & Kin=20\% \\ \hline
< 50       &          .345  & .317    &   .349 &  .349 \\ \hline
< 100      &          .432  & .413    &   .444 &  .430 \\ \hline
< 200      &          .516  & .512    &   .521 &  .510 \\ \hline
< 500      &          .610  & .606    &   .624 &  .611 \\ \hline
< 700      &          .639  & .630    &   .658 &  .648 \\ \hline
< 1000     &          .665  & .654    &   .686 &  .681 \\ \hline
< 1200     &          .678  & .667    &   .698 &  .695 \\ \hline
< 1500     &          .693  & .683    &   .711 &  .712 \\ \hline
< 1700     &          .702  & .691    &   .719 &  .720 \\ \hline
< 2000     &          .712  & .704    &   .729 &  .730 \\ \hline
< 2500     &          .727  & .718    &   .742 &  .744 \\ \hline
< 3000     &          .738  & .730    &   .750 &  .753 \\ \hline
< 3500     &          .747  & .740    &   .759 &  .760 \\ \hline
< 4000     &          .755  & .748    &   .767 &  .766 \\ \hline
< 5000     &          .768  & .762    &   .778 &  .777 \\ \hline
< 6000     &          .778  & .773    &   .785 &  .786 \\ \hline
< 7000     &          .786  & .781    &   .791 &  .791 \\ \hline
< 8000     &          .792  & .789    &   .795 &  .795 \\ \hline
< 9000     &          .798  & .795    &   .798 &  .799 \\ \hline
< 10000    &          .802  & .801    &   .801 &  .801 \\ \hline
---
> Number of page slots &	LRU/2 &	LRU	& Gclock	 & 2Q	& 2Q \\
>          &                &        &          & Kin=30\% & Kin=20\% \\ \hline
> 50       &          .345  & .317    & .313	&   .349 &  .349 \\ \hline
> 100      &          .432  & .413    & .407	&   .444 &  .430 \\ \hline
> 200      &          .516  & .512    & .506 	&  .521 &  .510 \\ \hline
> 500      &          .610  & .606    & .602 	&  .624 &  .611 \\ \hline
> 700      &          .639  & .630    & .627	&  .658 &  .648 \\ \hline
> 1000     &          .665  & .654    & .651 	&  .686 &  .681 \\ \hline
> 1200     &          .678  & .667    & .664	&  .698 &  .695 \\ \hline
> 1500     &          .693  & .683    & .680	&  .711 &  .712 \\ \hline
> 1700     &          .702  & .691    & .688 	&  .719 &  .720 \\ \hline
> 2000     &          .712  & .704    & .700	&  .729 &  .730 \\ \hline
> 2500     &          .727  & .718    & .715	&  .742 &  .744 \\ \hline
> 3000     &          .738  & .730    & .726	&  .750 &  .753 \\ \hline
> 3500     &          .747  & .740    & .736	&  .759 &  .760 \\ \hline
> 4000     &          .755  & .748    & .744	&  .767 &  .766 \\ \hline
> 5000     &          .768  & .762    & .758	&  .778 &  .777 \\ \hline
> 6000     &          .778  & .773    & .768	&  .785 &  .786 \\ \hline
> 7000     &          .786  & .781    & .777	&  .791 &  .791 \\ \hline
> 8000     &          .792  & .789    & .784	&  .795 &  .795 \\ \hline
> 9000     &          .798  & .795    & .790	&  .798 &  .799 \\ \hline
> 10000    &          .802  & .801    & .796	&  .801 &  .801 \\ \hline
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< provide a significantly higher hit rate than LRU. 
---
> provide a significantly higher hit rate than LRU and Gclock. 
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< over LRU.
---
> over LRU and Gclock.
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< \begin{tabular}{|c| c c c c|}
---
> \begin{tabular}{|c| c c c c c|}
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< Number of page slots &	LRU/2 &	LRU	 & 2Q	& 2Q \\
<                      &        &          & Kin=30\% & Kin=20\% \\ \hline
< 4          &  .443   &   .428  &      .457   &     .457 \\ \hline
< 6          &  .504   &   .479  &      .533   &     .532 \\ \hline
< 8          &  .551   &   .536  &      .598   &     .598 \\ \hline
< 10         &  .602   &   .578  &      .662   &     .661 \\ \hline
< 12         &  .678   &   .655  &      .722   &     .721 \\ \hline
< 14         &  .740   &   .713  &      .762   &     .765 \\ \hline
< 16         &  .762   &   .730  &      .785   &     .792 \\ \hline
< 18         &  .790   &   .759  &      .815   &     .816 \\ \hline
< 20         &  .809   &   .772  &      .832   &     .836 \\ \hline
< 22         &  .825   &   .795  &      .836   &     .844 \\ \hline
< 24         &  .852   &   .825  &      .845   &     .849 \\ \hline
< 26         &  .866   &   .839  &      .858   &     .866 \\ \hline
< 28         &  .877   &   .849  &      .876   &     .879 \\ \hline
< 30         &  .883   &   .861  &      .894   &     .896 \\ \hline
< 32         &  .893   &   .876  &      .911   &     .913 \\ \hline
< 34         &  .917   &   .909  &      .923   &     .926 \\ \hline
< 36         &  .930   &   .925  &      .932   &     .934 \\ \hline
< 38         &  .937   &   .935  &      .940   &     .941 \\ \hline
< 40         &  .943   &   .946  &      .946   &     .946 \\ \hline
---
> Number of page slots &	LRU/2 &	LRU & Gclock	 & 2Q	& 2Q \\
>                      &        &       &          & Kin=30\% & Kin=20\% \\ \hline
> 4          &  .443   &   .428  & .427 &     .457   &     .457 \\ \hline
> 6          &  .504   &   .479  & .484 &     .533   &     .532 \\ \hline
> 8          &  .551   &   .536  & .530 &     .598   &     .598 \\ \hline
> 10         &  .602   &   .578  & .577 &     .662   &     .661 \\ \hline
> 12         &  .678   &   .655  & .657 &     .722   &     .721 \\ \hline
> 14         &  .740   &   .713  & .703 &     .762   &     .765 \\ \hline
> 16         &  .762   &   .730  & .722 &     .785   &     .792 \\ \hline
> 18         &  .790   &   .759  & .754 &     .815   &     .816 \\ \hline
> 20         &  .809   &   .772  & .767 &     .832   &     .836 \\ \hline
> 22         &  .825   &   .795  & .797 &     .836   &     .844 \\ \hline
> 24         &  .852   &   .825  & .818 &     .845   &     .849 \\ \hline
> 26         &  .866   &   .839  & .832 &     .858   &     .866 \\ \hline
> 28         &  .877   &   .849  & .845 &     .876   &     .879 \\ \hline
> 30         &  .883   &   .861  & .858 &     .894   &     .896 \\ \hline
> 32         &  .893   &   .876  & .881 &     .911   &     .913 \\ \hline
> 34         &  .917   &   .909  & .910 &     .923   &     .926 \\ \hline
> 36         &  .930   &   .925  & .924 &     .932   &     .934 \\ \hline
> 38         &  .937   &   .935  & .932 &     .940   &     .941 \\ \hline
> 40         &  .943   &   .946  & .939 &     .946   &     .946 \\ \hline
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< \begin{tabular}{|c| c c c|}
---
> \begin{tabular}{|c| c c c c|}
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< Number of page slots &	LRU/2 &	LRU	 & 2Q \\
---
> Number of page slots &	LRU/2 &	LRU & Gclock	 & 2Q \\
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< \multicolumn{4}{|c|}{$\alpha=.5$}  \\
---
> \multicolumn{5}{|c|}{$\alpha=.5$}  \\
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< 5\%  & .141 & .105 & .162 \\
---
> 5\%  & .141 & .105 &  .104 & .162 \\
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< 10\% & .222 & .183 & .238 \\
---
> 10\% & .222 & .183 & .181  & .238 \\
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< 20\% & .347 & .313 & .356 \\
---
> 20\% & .347 & .313 & .311  & .356 \\
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< 40\% & .544 & .529 & .535 \\
---
> 40\% & .544 & .529 & .519  & .535 \\
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< \multicolumn{4}{|c|}{$\alpha=.86$}  \\
---
> \multicolumn{5}{|c|}{$\alpha=.86$}  \\
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< 5\%  & .584 & .528 & .595 \\
---
> 5\%  & .584 & .528 & .524  & .595 \\
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< 10\% & .661 & .618 & .667 \\
---
> 10\% & .661 & .618 & .613 & .667 \\
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< 20\% & .745 & .718 & .744 \\
---
> 20\% & .745 & .718 & .713 & .744 \\
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< 40\% & .838 & .826 & .827 \\
---
> 40\% & .838 & .826 & .821 & .827 \\
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< Let us call this probability $p_{accept}$
---
> Let us call this probability $p_{accept}$.
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< and applies when
< the miss ratio is under 10\%.)
---
> and has less than 4\% error when $m/f \le .1$).
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> %Dennis: the above ia a more exact statement.
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< Next, given $p$ and $m$, we can ask what $f=f_{crit}$ gives
---
> %Dennis: I changed it to p_{i}, since its a data item reference probability.
> Next, given $p_{i}$ and $m$, we can ask what $f=f_{crit}$ gives
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< f_{crit}=&-\frac{m\ln(2)}{\ln(1-p)} \\
< &\approx m\ln(2)/p
---
> f_{crit}=&-\frac{m\ln(2)}{\ln(1-p_{i})} \\
> &\approx m\ln(2)/p_{i}
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< The approximation follows because $\ln(1-p) \approx -p$.
---
> The approximation follows because $\ln(1-p_{i}) \approx -p_{i}$.
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< is $(1-m)/B$.  Substituting for $p$ in the formula for $f_{crit}$,
---
> is $(1-m)/B$.  Substituting for $p_{i}$ in the formula for $f_{crit}$,
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< for values of $m$ under about 10\%.
---
> for values of $m$ between 10\% and 90\%.
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> %Dennis: I changed it to a more accurate statement.
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> 
> 
