<s>
The	O
power	O
law	O
for	O
cache	B-General_Concept
misses	O
was	O
first	O
established	O
by	O
C	O
.	O
K	O
.	O
Chow	O
in	O
his	O
1974	O
paper	O
,	O
supported	O
by	O
experimental	O
data	O
on	O
hit	O
ratios	O
for	O
stack	B-Application
processing	O
by	O
Richard	O
Mattson	O
in	O
1971	O
.	O
</s>
<s>
The	O
power	B-General_Concept
law	I-General_Concept
of	I-General_Concept
cache	I-General_Concept
misses	I-General_Concept
can	O
be	O
used	O
to	O
narrow	O
down	O
the	O
cache	B-General_Concept
sizes	O
to	O
practical	O
ranges	O
,	O
given	O
a	O
tolerable	O
miss	O
rate	O
,	O
as	O
one	O
of	O
the	O
early	O
steps	O
while	O
designing	O
the	O
cache	B-General_Concept
hierarchy	I-General_Concept
for	O
a	O
uniprocessor	B-Operating_System
system	I-Operating_System
.	O
</s>
<s>
where	O
M	O
is	O
the	O
miss	O
rate	O
for	O
a	O
cache	B-General_Concept
of	O
size	O
C	O
and	O
M0	O
is	O
the	O
miss	O
rate	O
of	O
a	O
baseline	O
cache	B-General_Concept
.	O
</s>
<s>
The	O
power	O
law	O
can	O
only	O
give	O
an	O
estimate	O
of	O
the	O
miss	O
rate	O
only	O
up	O
to	O
a	O
certain	O
value	O
of	O
cache	B-General_Concept
size	O
.	O
</s>
<s>
A	O
large	O
enough	O
cache	B-General_Concept
eliminates	O
capacity	O
misses	O
and	O
increasing	O
the	O
cache	B-General_Concept
size	O
further	O
will	O
not	O
reduce	O
the	O
miss	O
rate	O
any	O
further	O
,	O
contrary	O
to	O
the	O
power	O
law	O
's	O
prediction	O
.	O
</s>
<s>
The	O
validity	O
of	O
the	O
power	B-General_Concept
law	I-General_Concept
of	I-General_Concept
cache	I-General_Concept
misses	I-General_Concept
also	O
depends	O
on	O
the	O
size	O
of	O
the	O
working	O
memory	O
set	O
in	O
a	O
given	O
process	O
and	O
also	O
on	O
the	O
temporal	O
re-reference	O
pattern	O
of	O
cache	B-General_Concept
blocks	O
in	O
a	O
process	O
.	O
</s>
<s>
If	O
a	O
process	O
has	O
a	O
small	O
working	O
memory	O
set	O
relative	O
to	O
the	O
cache	B-General_Concept
size	O
,	O
capacity	O
misses	O
are	O
unlikely	O
and	O
the	O
power	O
law	O
does	O
not	O
hold	O
.	O
</s>
<s>
plotted	O
the	O
number	O
of	O
cache	B-General_Concept
block	O
re-accesses	O
versus	O
their	O
re-reference	O
times	O
for	O
a	O
large	O
number	O
of	O
workloads	O
and	O
found	O
that	O
most	O
also	O
follow	O
an	O
exponential	O
relationship	O
.	O
</s>
<s>
Theoretically	O
,	O
it	O
was	O
proved	O
that	O
the	O
power	O
laws	O
of	O
cache	B-General_Concept
re-reference	O
and	O
cache	B-General_Concept
miss	O
rate	O
are	O
related	O
by	O
the	O
equation	O
.	O
</s>
<s>
This	O
means	O
that	O
for	O
workloads	O
that	O
do	O
not	O
follow	O
the	O
re-reference	O
power	O
law	O
,	O
the	O
power	B-General_Concept
law	I-General_Concept
of	I-General_Concept
cache	I-General_Concept
misses	I-General_Concept
does	O
not	O
hold	O
true	O
.	O
</s>
<s>
In	O
a	O
multilevel	O
cache	B-General_Concept
hierarchy	I-General_Concept
,	O
the	O
miss	O
pattern	O
of	O
the	O
higher	O
level	O
cache	B-General_Concept
becomes	O
the	O
re-reference	O
pattern	O
of	O
the	O
immediate	O
lower	O
level	O
cache	B-General_Concept
.	O
</s>
<s>
found	O
that	O
whereas	O
the	O
cache	B-General_Concept
misses	O
for	O
lower	O
levels	O
do	O
not	O
follow	O
a	O
strict	O
power	O
law	O
,	O
as	O
long	O
as	O
the	O
lower	O
level	O
cache	B-General_Concept
is	O
considerably	O
larger	O
than	O
the	O
higher	O
level	O
cache	B-General_Concept
,	O
the	O
miss	O
rate	O
function	O
can	O
be	O
approximated	O
to	O
the	O
power	O
law	O
.	O
</s>
