GreedyDual* Web Caching Exploiting the Two Sources of Locality in Web Request Streams

1. GreedyDual* Web Caching Exploiting the Two Sources of Locality in Web Request Streams Azer Bestavros and Shudong Jin Computer Science Department Boston University May 23, 2000

2. Characterizing Temporal Locality Use PDF of Request Inter-Arrivals (RIA) [Breslau et al:1999] Temporal locality of a document is inversely proportional to the time elapsed since the last access to that document Is that all there is? NO!

3. Sources of Temporal Locality Popularity • Example: …XabcXdefgXhijkXlmnXopqrsX… • Frequency over long time scales (e.g. days) • Persists in the face of scrambling Temporal Correlation • Example: …abcdYYfYeYghijklmnopqrs • Frequency over short time scales (e.g minutes) • Does not persist in the face of scrambling

4. Scramble Heavy-tailed with constant g Heavy-tailed with constant g PDF of Request Inter-Arrivalsfor “All” Documents

5. Scramble Heavy-tailed with constant g Heavy-tailed with constant g PDF of Request Inter-Arrivalsfor “All” Documents

6. From Popularity to Temporal Correlation Theorem: g = (2-1/a)

7. Zipf  RIA PDF What happens to the RIA PDF when we marginalize the effect of popularity?

8. Scramble Heavy-tailed with constant b Uniform PDF of Request Inter-Arrivals for “Equally-Popular” Documents

9. Scramble Heavy-tailed with constant b Uniform PDF of Request Inter-Arrivals for “Equally-Popular” Documents

10. Values of b Values ofbare trace dependent but consistent for each trace Value ofbcan be estimated on-line

11. Values of b What are the implications of measuring b on Web Caching Algorithms?

12. Cache Management Strategies to Exploit Temporal Locality Use “Recency of Last Access” (LRU-like) • Captures both popularity and temporal correlation • But, may result in “myopic” replacement decisions Use “Frequency of Accesses” (LFU-like) • Captures only popularity • Thus, may miss short-term caching opportunities Use a “Hybrid” • The problem is to find the “sweet spot” that balances the two approaches!

13. Exploiting Temporal Locality A Taxonomy of Existing Cache Management Strategies None of these techniques can dynamically adjust its sensitivity to popularity versus temporal correlation

14. GreedyDual* Cache Management • A generalization of GDS [CaoIrani:1997] • Utility of cached page ~ freq(p)*[cost(p)/size(p)] • Uses an aging mechanism to account for recency • … that dynamically adjusts the merits of popularity versus temporal correlation • Done by tuning the “speed” of aging based on the strength of b in the reference stream

15. Aging Speed Utility Function GreedyDual* Cache Management

16. GreedyDual*: Illustration • Consider two documents “a” and “b” • Assume that u(a) = 2 u(b) • If b >> 1, then “a” and “b” are equally competitive if time since last access for “a” is ~ that of “b” • If b = 1, then “a” and “b” are equally competitive if time since last access for “a” is 2 times that of “b” • If b = 0.5, then “a” and “b” are equally competitive if time since last access for “a” is 4 times that of “b” • If b = 0.2, then “a” and “b” are equally competitive if time since last access for “a” is 32 times that of “b”

17. GreedyDual*: Special Cases GreedyDual* when b >> 1 • Reduces to LRU (worst performer!) GreedyDual* when b = 0 • Reduces to a variant of LFU (LFU-DA) GreedyDual* when b = 1 • Reduces to a variant of GDS called (GDSF) GreedyDual* when 0 < b < 1 • A family of algorithms spanning LFU  GDS

18. Experimental Evaluation Traces Used for Simulations Performance Metrics

19. Experimental Evaluation Performance under “Constant Cost” Assumption

20. Experimental Evaluation Performance under “Constant Cost” Assumption

21. Experimental Evaluation Performance under “Packet Cost” Assumption

22. Experimental Evaluation Performance under “Packet Cost” Assumption

23. Experimental Evaluation Summary of performance improvements for cache size = 2.5% of total “Web Size”

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