File popularity characterisation
Summary (2 min read)
- WWW caching has proved a valuable technique for scaling up the internet [ABR95, BAE 97].
- It is often said that this popularity curve follows Zipf's law, Popularity = K* ranking-a, with a being close to 1 (e.g. [CUN95]); others argue that the curve does not follow Zipf's law [ALM98].
- This would be useful because previous observations of Zipf’s law have been largely culture independent, and if some culture independent cache metrics could be established cache models would not need to take account of cultural effects.
- It is not at all clear that cache logs reflect human choices, since not all of a user’s web requests reach the network cache.
- Derived from the literature and their own imagination, and propose tests of the explanations.the authors.
- One possible hypothesis (derived from a related proposal by Zipf [ZIP49]) is that caches at different levels of the hierarchy have different exponents for best-fit power laws, and caches higher up the hierarchy would have smaller exponents.
- This is because requests for more popular files are reduced more than requests for less popular files, since only the first request for a file from a low level cache reaches a high level cache.
- This can be tested by accurately determining the exponent for a range of caches, at the same position in the hierarchy, and finding a correlation between exponent and size.
- If the behaviour of individuals is strongly correlated (e.g. by information waves) on a range of timescales with an infinite variance, then the popularity curve exponent will exhibit variation regardless of sample size or timescale.
- From consideration of the work of Zipf on word use in different cultures, it seems likely that cultural differences will often be expressed through differences in the K factor in the power curve rather than the exponent.
- To analyse file popularity, cache logs are usually needed, the only alternative being the correctly processed output from such a cache log.
- The authors are indebted to several sources for making their logs available, and hope this is fully shown in the acknowledgements.
- At the moment cache logs do not contain the means to discriminate between the physical request made by the client and files that are requested by linkage (linked image file, redirections etc) to the requested files.
- Another analysis irregularity is that some researchers look at the popularity of generic hosts and not files.
- The quality of the fit was checked using the standard R2 test.
4. Variability of Locality.
- In order to compare data from different caches reliably it is necessary to ensure that differences are real and not due to insufficiently large samples.
- This cache receives about 10000 requests per day from a research community.
- The least squares procedure can then be used to find the slope of the line with best fit.
- If the data shows longrange dependence the sample size required to get a reliable estimate of the slope of the popularity curve will be considerably larger than might be expected for normal Poisson statistics.
- The exponent converges to a stable value for samples of 300 000 or more requests, for all the caches the authors have analysed.
- The authors have been able to obtain samples in excess of 500000 file requests for 5 very different caches.
- The authors show in figures 7 and 8 the popularity curves for these caches, and the curves fitted to the data using the techniques outlined in section 3.
- In table 1 the authors show the estimated value of the exponent in the power law, together with the error interval and the confidence limit established by the R2 test.
- FUNET and Spain are national caches, RMPLC and PISA are local caches serving very different communities.
- Error estimates were calculated using several methods, the ones shown were the largest calculated.
- The data in section 5 supported the notion that the variation in cache popularity curves is simply due to the hierarchical position of the cache.
- Figure 9 shows cache size plotted against exponent.
- It is hard to imagine a user community more different from the undergraduates, lecturers and researchers at Pisa university.
- The lack of significant differences between caches at similar apparent levels in the hierarchy means that client effect are not significant either.
- These models require an accurate description of real cache behavior so their performance can be accurately assessed.
- The analysis of cache popularity curves requires careful definition of what is to be analysed and, since the data displays significant long range dependency, very large sample sizes.
- Further data should be analysed to fully confirm the relative independence of the metric.
- The authors would like to thank Pekka Järveläinen for supplying us with anonymised logs for the Funet proxy cache, Simon Rainey , Javier Puche (Centro Superior de Investigaciones Cientificas) and Luigi Rizzo (Pisa).
- World-Wide Web Conference, Boston, MA, Dec. 1995. [BAE97] M Baentsch, L Baum, G Molter, S Rothkugel and P Sturm.
- 'On the implications of Zipf's Law for web caching'. in 3W3Cache Workshop, Manchester, June 1998. [CUN95] C Cunha, A Bestavros, and M Crovella.
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Cites background from "File popularity characterisation"
...,  and , we will extend it to our detection in the rest of this paper....
"File popularity characterisation" refers background in this paper
...We show that locality can be characterised with a single parameter, which primarily varies with the topological position of the cache, and is largely independent of the culture of the cache users....
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