Practical LFU implementation for Web Caching

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Practical LFU implementation for Web Caching

• George Karakostas
• Telcordia
• Dimitrios N. Serpanos
• University of Patras

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A simple caching environment
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Basic assumptions
1. The number of all Web pages N is known. 2.
The system is closed. 3. The requests for Web
pages follow Zipfs Law. 4. The requests are
statistically independent.
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(only order of magnitude matters)
(yeah, rightbut we wont care) (plenty of
experimental evidence) (very strong
assumption - counterintuitive(?))
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Zipf-like distributions
More generally
where a is a constant between 0.6-0.9, depending
on the particular request stream.
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Popularities according to Zipf
where a1.
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Our motivation

• Serpanos Wolf prove analytically the optimality
  of Perfect-LFU under assumptions 3 and 4.
• Breslau et al. studied the implications of
  assumptions 3 and 4. Give evidence for Zipf-like
  distribution of page requests, and for the
  optimality of Perfect-LFU as a cache replacement
  policy.

But, if so...
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Why people dont use Perfect-LFU?
Answer Because it is Perfect (i.e.
impractical). Perfect-LFU needs to store
statistics for all the pages requested from the
beginning of cache operation. Hence the resources
(time/space) needed are of order N.
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Our contribution We show that under assumptions
1-4 we can efficiently approximate the
Perfect-LFU hit rate within any constant e.
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Chernoff bounds
Theorem Chernoff The sum of R i.i.d. random
variables is close to its expected value with
very high probability
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Observation 1 Under our assumptions, the number
of requests for a page in a random trace is
close to its expected value, i.e. proportional to
its popularity. Observation 2 With a small R we
can distinguish the most popular objects.
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Window-LFU

• Simple variation of Perfect-LFU.
• Instead of keeping statistics for all pages, keep
  only for a sample of the request stream (called
  window) of size where
  C is the cache size, and e is the error
  parameter.
• Cache the C most frequent pages in the sample.

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Theorem Under our assumptions,
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Window placement
Observation Under our assumptions, any sample
of size W will achieve the Perfect-LFU hit rate.
Request stream
New request
CACHE
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Locality

• Two different types of locality phenomena
• Temporal
• Popularity

Our window will be the W most recent requests
to take advantage of temporal locality as well.
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Simulation results
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Conclusions / Open problems

• Window-LFU is an efficient implementation of LFU
• It takes advantage of the different types of
  locality to achieve in practice better
  performance than Perfect-LFU.
• How can we determine the window size dynamically?
  (simple doubling heuristic performs very
  well)
• How can we detect that the Zipf-like distribution
  parameters (N,a) have changed?