News
Abstract
An article written by Dr. Robert Blackburn, z/TPF Performance and Design, that was previously published in the TPF Technical Systems Newsletter. This article discusses how to calculate the approximate VFA hit ratio when the size of VFA is changed.
Content
TPF customers will often alter the size of virtual file access (VFA), while holding the VFA candidate list constant, and want to know the effect on the VFA hit ratio. This is a difficult question to answer in general because it depends on the locality of reference of the records in the cache, the record size, and the VFA candidate list.
However, there is an empirically based approximation that has been quite accurate. WRITEs could work as well as READs assuming there were no FILE Immediates. The formula is that the number of references per cache miss is proportional to the square root of the cache size. For example, letting:
cache references
R = ------------------ (1)
cache misses
R = ------------------ (1)
cache misses
S = cache size
For some constant K, we have:
_____
R2 = K | S (2)
\|
_____
R2 = K | S (2)
\|
Letting be two references per cache miss and two cache sizes, respectively, and dividing the corresponding equations, we have:
_____
R2 | S2
--- = | --- (3)
R1 \| S1
_____
R2 | S2
--- = | --- (3)
R1 \| S1
An Example
Assume that the hit ratio is .92 with 100 MB of VFA. We would like to know the hit ratio with 180 MB of VFA, assuming the VFA candidate list remains constant.
The hit ratio of .92 means that with 100 total references there are 8 misses, so there are 12.5 references per VFA miss. Thus:
R1 = 12.5
R1 = 12.5
Using the two cache sizes, S1 and S2, we see that:
_____
| S2
| --- =
\| S1
_____
| S2
| --- =
\| S1
_____
| 180
| --- = 1.34
\| 100
| 180
| --- = 1.34
\| 100
Using (3)
R2
-- = 1.34 (4)
R1
R2
-- = 1.34 (4)
R1
so that:
R2 = 12.5(1.34) = 16.8.
R2 = 12.5(1.34) = 16.8.
Now, converting back to hit ratios we have:
1
------- = .06
16.8
1
------- = .06
16.8
So, the new hit ratio with 180 MB of VFA is .94. While it might seem that a change in hit ratio from .92 to .94 is very small, this is not really the case. This is because the miss ratio was .08 and now is .06 for a 25% reduction.
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Document Information
Modified date:
13 April 2020
UID
ibm16188085