LRFU (Least Recently/Frequently Used) Block Replacement Policy

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LRFU (Least Recently/Frequently Used)Block
Replacement Policy

• Sang Lyul Min
• Dept. of Computer Engineering
• Seoul National University

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Why file cache?
Processor - Disk Speed Gap
1950s
1990s

• Processor - IBM 701
• 17,000 ins/sec
• Disk - IBM 305 RAMAC
• Density - 0.002 Mbits/sq. in
• Average seek time - 500 ms

• Processor - IBM PowerPC 603e
• 350,000,000 ins/sec
• Disk - IBM Deskstar 5
• Density - 1,319 Mbits/sq. in
• Average seek time - 10 ms

x 20,000
x 600,000
x 50
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File Cache
main memory
disk controller
processor
disks
file cache or buffer cache
disk cache
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Operating System 101

• LRU Replacement

• LFU Replacement

O(1) complexity
O(n) complexity
O(log n) complexity
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Operating System 101

• LRU
• Advantage
• High Adaptability
• Disadvantage
• Short sighted

• LFU
• Advantage
• Long sighted
• Disadvantage
• Cache pollution

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Motivation

• Cache size 20 blocks

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• Cache size 60 blocks

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• Cache size 100 blocks

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• Cache size 200 blocks

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• Cache size 300 blocks

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• Cache size 500 blocks

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Observation

• Both recency and frequency affect the
  likelihood of future references
• The relative impact of each is largely determined
  by cache size

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Goal

• A replacement algorithm that allows a flexible
  trade-off between recency and frequency

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Results

• LRFU (Least Recently/Frequently Used) Replacement
  Algorithm that
• (1) subsumes both the LRU and LFU algorithms
• (2) subsumes their implementations
• (3) yields better performance than them

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CRF (Combined Recency and Frequency) Value
Current time tc
?1
?2
?3
time
t3
t2
t1
Ctc(b) F(?1) F(?2) F(?3)

tc - t1 tc - t2
tc - t3
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CRF (Combined Recency and Frequency) Value

• Estimate of how likely a block will be referenced
  in the future
• Every reference to a block contributes to the CRF
  value of the block
• A references contribution is determined by
  weighing function F(x)

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Hints and Constraints on F(x)

• should be monotonically decreasing
• should subsume LRU and LFU
• should allow efficient implementation

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Conditions for LRU and LFU

• LRU Condition
• If F(x) satisfies the following condition, then
  the LRFU algorithm becomes the LRU algorithm
• LFU Condition
• If F(x) c, then the LRFU algorithm becomes the
  LFU algorithm

current time
i
block a
x
block b x x x x x x x x
i1
i2
? ? ? ? ?
i3
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Weighing function F(x)

• F(x) (?)?x

Meaning a references contribution to the target
blocks CRF value is halved after every 1/ ?
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Properties of F(x) (?)?x

• Property 1
• When ? 0, (i.e., F(x) 1), then it becomes LFU
• When ? 1, (i.e., F(x) (?)x ), then it becomes
  LRU
• When 0 lt ? lt 1, it is between LFU and LRU

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Results

• LRFU (Least Recently/Frequently Used) Replacement
  Algorithm that
• ?(1) subsumes both the LRU and LFU algorithms
• (2) subsumes their implementations
• (3) yields better performance than them

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Difficulties of Naive Implementation

• Enormous space overheads
• Information about the time of every reference to
  each block
• Enormous time overheads
• Computation of the CRF value of every block at
  each time

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Update of CRF value over time
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Properties of F(x) (?)?x

• Property 2
• With F(x) (?)?x, Ctk(b) can be computed from
  Ctk-1(b) as follows
• Ctk(b) Ctk-1(b) F (?) F (0)
• 
  tk - tk-1
• Implications Only two variables are required for
  each block for maintaining the CRF value
• One for the time of the last reference
• The other for the CRF value at that time

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Difficulties of Naive Implementation

• Enormous space overheads
• Information about the time of every reference to
  each block
• Enormous time overheads
• Computation of the CRF value of every block at
  each time

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Properties of F(x) (?)?x

• Property 3
• If Ct(a) gt Ct(b) and neither a or b is referenced
  after t, then Ct'(a) gt Ct'(b) for all t' gt t
• Why?
• Ct'(a) Ct(a) F(?) gt Ct(b) F(?) Ct'(b)
  (since F(?) gt 0 )
• Implications
• Reordering of blocks is needed only upon a block
  reference
• Heap data structure can be used to maintain the
  ordering of blocks with O(log n) time complexity

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Optimized Implementation
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Optimized Implementation
Reference to a new block
Reference to a block in the linked list
Reference to a block in the heap
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Question What is the maximum number of blocks
that can potentially compete with a currently
referenced block?
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(No Transcript)
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Properties of F(x) (?)?x

• Property 4

Archi Network LAB
Seoul National University
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Optimized implementation (Contd)
Archi Network LAB
Seoul National University
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Results

• LRFU (Least Recently/Frequently Used) Replacement
  Algorithm that
• ?(1) subsumes both the LRU and LFU algorithms
• ?(2) subsumes their implementations
• (3) yields better performance than them

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Correlated References
correlated references
correlated references
correlated references
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LRFU with correlated references

• Masking function Gc(x)
• C'tk(b), CRF value when correlated references are
  considered, can be derived from C'tk-1(b)
• C'tk(b) F(tk - tk) F(tk - ti )Gc(ti1
  - ti )
• F( tk - tk-1) F(0) Gc( tk -
  tk-1) C'tk-1(b) - F(0) F(0)

Archi Network LAB
Seoul National University
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Trace-driven simulation

• Sprite client trace
• Collection of block references from a Sprite
  client
• contains 203,808 references to 4,822 unique
  blocks
• DB2 trace
• Collection of block references from a DB2
  installation
• Contains 500,000 references to 75,514 unique
  blocks

Archi Network LAB
Seoul National University
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Effects of ? on the performance
Archi Network LAB
Seoul National University
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Combined effects of ? and correlated period
Archi Network LAB
Seoul National University
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Previous works

• FBR (Frequency-Based Replacement) algorithm
• Introduces correlated reference concept
• LRU-K algorithm
• Replaces blocks based on time of the Kth-to-last
  non-correlated references
• Discriminates well the frequently and
  infrequently used blocks
• Problems
• Ignores the K-1 references
• linear space complexity to keep the last K
  reference times
• 2Q and sLRU algorithms
• Use two queues or two segments
• Move only the hot blocks to the main part of the
  disk cache
• Work very well for used-only-once blocks

Archi Network LAB
Seoul National University
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Comparison of the LRFU policy with other policies
Archi Network LAB
Seoul National University
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Implementation of the LRFU algorithm

• Buffer cache of the FreeBSD 3.0 operating system
• Benchmark SPEC SDET benchmark
• Simulates a multi-programming environment
• consists of concurrent shell scripts each with
  about 150 UNIX commands
• gives results in scripts / hour

Archi Network LAB
Seoul National University
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SDET benchmark results
Hit rate
SDET Throughput (scripts/ hour)
Hit Rate
?
Archi Network LAB
Seoul National University
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Conclusions

• LRFU (Least Recently/Frequently Used) Replacement
  Algorithm that
• ?(1) subsumes both the LRU and LFU algorithms
• ?(2) subsumes their implementations
• ?(3) yields better performance than them

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Future Research

• Dynamic version of the LRFU algorithm
• LRFU algorithm for heterogeneous workloads
• File requests vs. VM requests
• Disk block requests vs. Parity block requests
  (RAID)
• Requests to different files (index files, data
  files)

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People

• REAL PEOPLE
• (Graduate students)
• Lee, Donghee
• Choi, Jongmoo
• Kim, Jong-Hun

• Guides
• (Professors)
• Noh, Sam H.
• Min, Sang Lyul
• Cho, Yookun
• Kim, Chong Sang

http//archi.snu.ac.kr/symin/
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Adaptive LRFU policy

• Adjust ? periodically depending on the evolution
  of workload
• Use the LRU policy as the reference model to
  quantify how good (or bad) the locality of the
  workload has been
• Algorithm of the Adaptive LRFU policy
• if ( gt
  )
• ? value for period i1 is updated in the same
  direction
• else
• the direction is reversed

Archi Network LAB
Seoul National University
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Results of the Adaptive LRFU
Client Workstation 54
DB2
Archi Network LAB
Seoul National University