Cache Algorithms
Ilya Lintsbah,
Symmetrix Performance Research Group, intern
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Symmetrix
Symmetrix is an enterprise storage
array
Symmetrix DMX-4 characteristics:
– Up to 1920 drives
– Each drive capacity up to 1Tb
– Up to 512 GB cache memory
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Cache
Disk array
Cache hit
Cache
Cache miss
Cache hit – cache contains the requested page
Cache miss – cache doesn’t contain the requested page, page should be
fetched from disk array
Hit rate is the percentage of requests that result in cache hits
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Cache Replacement Policies
Request that result as cache hit is processed much faster than request
that result as cache miss
When cache miss happens, we need to put a requested page to cache
If cache is full we should at first discard some page from cache
Cache replacement policy decides which page should be discarded in
this situation
Performance of cache replacement policy can be measured in hit rate
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Offline Optimal Replacement Policy
Offline replacement policy knows future information
MIN algorithm replaces the page that has the greatest forward distance
It is an optimal replacement policy in terms of hit rate, but it can’t be
used for page replacement
MIN provides an upper bound on the achievable hit rate by any on-line
policy
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Basic Cache Replacement Policies
MRU LRU
LRU
Least Recently Used item is discarded
Simple to implement as a bidirectional list
On a cache hit referenced page is moved to MRU position
LFU
Least Frequently Used item is discarded
Counts number of requests for each track
Disadvantage: LFU accumulates stale pages with high
frequency counts that may no longer be useful
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LRFU and FBR
LRFU
Item with the least recency/frequency value is discarded
A spectrum of policies that subsumes the LRU, LFU and intermediate
policies
FBR
Cache is divided into three parts, each page has a reference count
Factoring out locality: page reference count is increased only if this page
is referenced, when it is in Middle or Old sections
Page with least reference count from old section is replaced
MRU LRU
New Middle Old
Section Section Section
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ARC Algorithm
ARC contains two LRU lists: L1 and L2
L1 contains pages that were referenced only once L1 L2
recently
L2 contains pages that were referenced at least twice T1
recently T2
Each list is divided into two parts: top and bottom B1
B2
B1 and B2 are used as history, they are not stored in
cache. They are called “ghost caches”
Real cache consists of T1 and T2 Ghost caches
T1 and T2 compete with each other for size
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ARC Adaptation
History is used to change sizes of T1 and T2
dynamically
L1 L2
Hits in history change the target size of T1 (p)
If there is a hit in B1, p is increased T1
T2
If there is a hit in B2, p is decreased
B1
On a cache miss: B2
– If |T1| > p, LRU page from T1 is replaced
– Else LRU page from T2 is replaced
Ghost caches
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ARC Advantages
Long sequence of one-time-only reads will pass through L1, without
flushing out possibly important pages in L2, so ARC is scan-resistant
ARC has no parameters
ARC is adaptive
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Simulations
Trace LRU LFU FBR LRFU ARC MIN
Trace 1 45.1% 31.8% 45.9% 45.6% 46.7% 54.5%
Trace 2 72.7% 26.1% 74.8% 72.7% 73.1% 82.7%
Trace 3 72.4% 26.7% 74.7% 72.4% 72.1% 82.2%
Trace 4 50.4% 19.2% 50.7% 50.4% 51.1% 60.8%
Trace 5 39.6% 13.9% 41.1% 39.6% 40.0% 55.3%
Trace 6 81.7% 63.1% 82.8% 82.1% 83.2% 90.1%
Trace 7 78.5% 46.8% 78.6% 78.6% 78.6% 83.7%
Trace 8 60.7% 21.7% 63.6% 60.6% 60.1% 70.7%
Trace 9 85.4% 70.5% 85.9% 85.4% 85.4% 90.1%
Trace 10 67.5% 60.7% 69.7% 67.5% 69.2% 79.9%
Cache size 64 Gb
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ARC Modifications
ARC is announced to outperform LRU, but on Symmetrix traces they
both do rather similar hit rate
One of the reasons of that is that more tracks then needed are moved to
second list
We propose two solutions for this problem: ARCM1 and ARCM2
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Relative Improvement
1
To compare algorithms with LRU the following
characteristic could be used: 0.9
Hit ratio(Alg) − Hit ratio(LRU) 0.8
Relative Improvement =
Hit ratio(MIN) − Hit ratio(LRU) 0.7
0.6
Relative improvement shows the improvement offered by
algorithm over LRU as a fraction of the difference 0.5
between MIN and LRU
0.4
If algorithm performance is worse than LRU the relative
improvement is negative 0.3
LRU Alg MIN
Example: 0.2
– Hit Ratio(LRU) = 0.6
– Hit Ratio(MIN) = 0.7 0.1
– Hit Ratio(Alg) = 0.64
– Rel.Improvement(Alg) = (0.64-0.6)/(0.7-0.6) = 0.4 0
1
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Results: Relative Improvement
Relative improvement over LRU
50,0%
40,0%
30,0%
Rel. improvement
20,0%
10,0%
0,0%
Trace 1 Trace 3 Trace 5 Trace 6 Trace 7 Trace 8 Trace 9 Trace 10
-10,0%
Traces
ARCM1 ARCM2 ARC
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