1. October 14, 2002MASCOTS 20021 Workload Characterization in Web Caching Hierarchies Guangwei Bai Carey Williamson Department of Computer Science University of Calgary

2. October 14, 2002MASCOTS 20022 Talk Outline 1.Problem Statement 2.Experimental Methodology 3.Simulation Results 4.Modeling Results 5.Summary and Conclusions

3. October 14, 2002MASCOTS 20023 1. Introduction  World Wide Web: One of the most popular applications on today’s Internet  Web proxy caching: A technique used for improving performance and scalability of the Internet

4. October 14, 2002MASCOTS 20024 Internet Web Server Web Proxy Caching System …Web Clients… Illustration of Web Proxy Cache Filtering Effect Original Request Stream Filtered Request Stream

5. October 14, 2002MASCOTS 20025 Example of Web cache filter effect Time ID 0.001 A 0.025 B 0.150 C 0.689 A 0.890 D 1.358 B 1.777 B 2.190 A 2.460 E Arriving Request StreamFiltered Request Stream Time ID 0.001 A 0.025 B 0.150 C 0.890 D 1.358 B 2.460 E Web Proxy Cache … …

6. October 14, 2002MASCOTS 20026 Example of Web cache filter effect Time ID 0.001 A 0.025 B 0.150 C 0.689 A 0.890 D 1.358 B 1.777 B 2.190 A 2.460 E Arriving Request StreamFiltered Request Stream Time ID 0.001 A 0.025 B 0.150 C 0.890 D 1.358 B 2.460 E Web Proxy Cache Frequency-domain effect … …

7. October 14, 2002MASCOTS 20027 Example of Web cache filter effect Time ID 0.001 A 0.025 B 0.150 C 0.689 A 0.890 D 1.358 B 1.777 B 2.190 A 2.460 E Arriving Request StreamFiltered Request Stream Time ID 0.001 A 0.025 B 0.150 C 0.890 D 1.358 B 2.460 E … Web Proxy Cache Time-domain effect …

8. October 14, 2002MASCOTS 20028 Goal of this Work: Time-domain analysis of cache filter effects in Web caching hierarchies : o Study impact of a cache on the structural characteristics of Web request workload (mean, peak, variance, self-similarity) o Sensitivity of filter effect to cache configuration (cache size and cache replacement policy) o Characterizing aggregate Web request streams in a multi-level Web proxy caching hierarchy

9. October 14, 2002MASCOTS 20029 Multi-Level Web Proxy Caching System Web Proxy Cache 1 Web Proxy Cache 2Web Proxy Cache 3 1 2 3 3 2 1 Child Level Parent Level

10. October 14, 2002MASCOTS 200210 Experimental Methodology  Trace-driven simulation  Web proxy cache simulator  Synthetic Web proxy workloads o Controllable characteristics o Trace length: about 1M requests o Zipf slope: -0.75, -0.8 o Request arrival process: Deterministic, Poisson, Self-Similar

11. October 14, 2002MASCOTS 200211 0 20004000 12000 14000 60008000 10000 Time (sec) 0 0.2 0.4 0.6 0.8 1 Hit Ratio 16:00 15:3012:30 12:00 Requests per 5-minute Interval 0 4000 2000 14000 12000 10000 8000 6000 Time (sec) 0 4000 12000 16000 20000 16:0015:30 12:3012:00 8000  General Observations: Filter Effects Arrival Counts Cache Hit Ratio

12. October 14, 2002MASCOTS 200212  Effect of Cache Configuration  Experimental factors: Cache size determines the maximum number of Web Content bytes that can be held in the cache at one time Cache Replacement Policy determines what object(s) to remove from the cache when more space is needed to store an incoming object (e.g. RAND, FIFO, LRU, LFU, GDS)  (Assumption: arrival process is Poisson)

13. October 14, 2002MASCOTS 200213 Effect of Cache Size on Traffic Structure 020406080100120 0 5 10 15 20 25 Frequency in Percent Requests per 1-minute Interval (a) Effect of cache size Marginal Distribution Plot (pdf)

14. October 14, 2002MASCOTS 200214 Effect of Cache Replacement Policy Frequency 120 100806040200 0 5 10 15 20 25 Requests per 1-minute Arrival (b) Effect of cache policy (8 KB)

15. October 14, 2002MASCOTS 200215  Input: Deterministic Arrival Process Main Observations:  Reduces mean arrival rate of filtered request stream  Increases variance of the filtered request stream Statistics Before Cache Cache Size (MB) Mean Standard Deviation Hit Ratio 4166425610241 38.8%47.8%52.7%55.5%59.1%62.7% 60.0036.8831.4528.7127.3125.3723.03 0.004.844.604.014.004.314.78

16.  Input: Poisson Arrival Process Main Observations:  Large impact on mean; little impact on variance  Variance-to-mean ratio increases with cache size  For small cache sizes, the filtered stream is well-characterized as a Poisson process. Statistics Before Cache Cache Size (MB) Mean Standard Deviation Hit Ratio 4166425610241 38.8%47.8%52.7%55.5%59.1%62.7% 60.1036.8131.3828.6527.2625.3323.00 7.826.776.075.435.315.395.62

17. Input: Self-Similar Arrival Process Main Observations:  Large impact on mean; little impact on variance  Variance-to-mean ratio increases with cache size  Filtered request stream retains self-similar structure Statistics Before Cache Cache Size (MB) Mean Standard Deviation Hit Ratio 4166425610241 38.8%47.8%52.7%55.5%59.1%62.7% 62.8738.5032.7929.8828.2726.0523.49 12.249.037.987.126.947.027.14

18. October 14, 2002MASCOTS 200218  Network traffic self-similarity The statistical characterization of the traffic is essentially invariant with time scale.  Main measure Hurst parameter: 0.5 < H < 1  Examination o autocorrelation (long-range dependence) o variance-time plot o rescaled adjusted range statistic (R/S)  Background: Self-Similar Traffic

19. October 14, 2002MASCOTS 200219 Traffic Characterization in a Web Proxy Caching Hierarchy  Filter effects of the first-level cache on Web workload  Statistical multiplexing of filtered Web request streams after the first-level cache  Modeling aggregate request stream offered to the second-level cache

20. October 14, 2002MASCOTS 200220 Multi-Level Web Proxy Caching System Web Proxy Cache 1 Web Proxy Cache 2Web Proxy Cache 3 1 2 3 3 2 1 Child Level Parent Level

21. October 14, 2002MASCOTS 200221 Synthetic Self-Similar Workload Traces offered to the first-level cache Trace 1 (H=0.70, Zipf slope=0.75) Trace 2 (H=0.80, Zipf slope=0.80) 40001200008000 60 100 140 20 180 Time (sec.) Requests per Interval 80000400012000 20 60 100 140 Time (sec.) Requests per Interval

22. Evidence of Self-Similar Request Arrival Process for Filtered Web Proxy Workload 04000800012000 0 20 40 60 Time Interval Count of Arrival /Interval (a) Time Series 1 020406080100 -0.4 0 0.4 0.8 Lag Autocorrelation (b) Autocorrelation 01234 -4 -3 -2 0 Log10(Aggregation level) Log10(Variance) (c) Variance-Time Plot 1234 0 1 2 3 4 Log10(R/S) Log10(Sample Size) (d) R/S Pox Plot H=0.699 1 `

23. October 14, 2002MASCOTS 200223 Superposition of Web Workload in time-domain 3 2 1 020406080100120140 0 2 4 6 8 Request Arrival Frequency (%) Characteristics of aggregate request arrival process 3

24. Evidence of Self-Similarity for Aggregate Request Arrival Process 3 2000600010000 0 40 80 120 Requests per Interval Time(sec.) (a) Time series 020406080100 -0.4 0 0.4 0.8 Lag Autocorrelation (b) Autocorrelation function 0 1 23 4 0 -2 -3 -4 Log10(variance) Log10(aggregation level) (c) Variance-Time Plot 12 3 4 0 1 2 3 4 Log10(sample size) Log10(R/S) (d) R/S Pox Plot H=0.76

25. October 14, 2002MASCOTS 200225 Gamma Distribution βΓ( ) x-μ β ()e β ( ) - f(x) = : shape parameter β: scale parameter μ: location parameter Modeling of Aggregate Workload

26. October 14, 2002MASCOTS 200226 Modeling of Aggregate Workload

27. October 14, 2002MASCOTS 200227 Summary and Conclusions Recap: Trace-driven simulation of Web proxy caching hierarchy, with synthetic Web workloads Cache reduces peak and mean request arrival rate Cache filter effect does not remove self-similarity Superposition of Web request streams results in a bursty aggregate request stream Gamma distribution: a flexible and robust means to characterize request arrival count distribution at different stages in a Web caching hierarchy

28. October 14, 2002MASCOTS 200228 Future Work Bigger traces, more general workloads Studying the mathematical relationships between gamma (shape) and beta (scale) parameters versus cache size and hit ratio For more information: –Email: {bai,carey}@cpsc.ucalgary.ca –http://www.cpsc.ucalgary.ca/~carey