Abstract:
Comparing strength of locality of reference – Popularity, majorization, and some folk theorems Abstract — The performance of demand-driven caching depends on the locality of reference exhibited by the stream of requests made to the cache. In particular, it is expected that the stronger the locality of reference, the smaller the miss rate of the cache. For the Independent Reference Model, this amounts to a smaller miss rate when the popularity distribution of requested objects in the stream is more skewed. In this paper, we formalize this “folk theorem ” through the companion concepts of majorization and Schur-concavity. This folk theorem is established for caches operating under a Random On-demand Replacement Algorithm (RORA). However, the result fails to hold in general under the (popular) LRU and CLIMB policies, but can be established when the input has a Zipf-like popularity pmf with large skewness parameter. In addition, we explore how the majorization of popularity distributions translates into comparisons of three well-known locality of reference metrics, namely the inter-reference time, the working set size and the stack distance. Keywords: Locality of reference in request streams, Popularity, Majorization/Schur-concavity.
Citations
|
554
|
Web Caching and Zipf-like Distributions: Evidence and Implications
– Breslau, Cao, et al.
- 1999
|
|
387
|
A study of replacement algorithms for virtual storage computers. IBMSystems Journal
– Belady
- 1966
|
|
329
|
Inequalities: Theory of Majorization and its Applications
– Marshall, Olkin
- 1979
|
|
194
|
Evaluation techniques for storage hierarchies
– Mattson, Gecsei, et al.
|
|
173
|
The working set model for program behavior
– DENNING
- 1968
|
|
95
|
Stochastic Orders and Their Applications
– Shaked, Shanthikumar
- 1994
|
|
62
|
Characterizing reference locality
– Almeida, Bestavros, et al.
- 1996
|
|
52
|
Implications of Certain Assumptions in Database Performance Evaluation
– Christodoulakis
- 1984
|
|
46
|
GreedyDual* Web caching algorithm: exploiting the two sources of temporal locality in Web request streams
– Jin, Bestavros
- 2001
|
|
45
|
Web caching and content distribution: a view from the interior
– Gadde, Chase, et al.
- 2000
|
|
39
|
Birthday paradox, coupon collector, caching algorithms and self-organizing search
– Flajolet, Gardy, et al.
- 1992
|
|
36
|
An Inter-Reference Gap Model for Temporal Locality in Program Behavior
– Phalke, Gopinath
- 1995
|
|
32
|
Sources and characteristics of Web temporal locality
– Jin, Bestavros
- 2000
|
|
27
|
Temporal locality and its impact on Web proxy cache performance,” Performance Evaluation
– Mahanti, Eager, et al.
- 2000
|
|
18
|
Temporal locality in Web request streams: Sources, characteristics, and caching implication (poster
– Jin, Bestavros
- 2000
|
|
18
|
On the optimality of the probability ranking scheme in storage applications
– Yue, Wong
- 1973
|
|
16
|
Properties of the working set model
– Denning, Schwartz
- 1972
|
|
14
|
Asymptotic approximation of the move-to-front search cost distribution and least-recently-used caching fault probabilities
– Jelenković
- 1999
|
|
7
|
Asymptotic insensitivity of least-recently-used caching to statistical dependency
– Jelenković, Radovanović
- 2003
|
|
4
|
The output of a cache under the independent reference model: where did the locality of reference go
– Vanichpun, Makowski
- 2004
|
|
3
|
Application of multifractals in the characterization of WWW traffic
– Balamash, Krunz
- 2002
|
|
2
|
A unified approach to the evaluation of a class of replacement algorithms
– Gelenbe
- 1973
|
|
1
|
Stochastic Analysis of
– Aven, Coffman, et al.
- 1987
|
|
1
|
On the intrinsic locality of Web reference streams
– Fonseca, Almeida, et al.
- 2003
|
|
1
|
A majorization theorem for the number of distinct outcomes
– Wong, Yue
- 1973
|
