Workload Characterization in Web Caching Hierarchies

1
Workload Characterizationin Web Caching
Hierarchies

• Guangwei Bai
• Carey Williamson
• Department of Computer Science
• University of Calgary

2
Talk Outline

• Problem Statement
• Experimental Methodology
• Simulation Results
• Modeling Results
• Summary and Conclusions

3
1. Introduction

• World Wide Web One of the most
• popular applications on todays Internet

• Web proxy caching

A technique used for improving performance and
scalability of the Internet
4
Illustration of Web Proxy Cache Filtering Effect
Internet
Filtered Request Stream
Web Proxy Caching System
Original Request Stream
Web Clients
5
Example of Web cache filter effect
Arriving Request Stream
Filtered Request Stream
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
Time ID 0.001 A 0.025 B 0.150 C 0.890
D 1.358 B 2.460 E
Web Proxy Cache


6
Example of Web cache filter effect
Arriving Request Stream
Filtered Request Stream
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
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
Example of Web cache filter effect
Arriving Request Stream
Filtered Request Stream
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
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
Goal of this Work
Time-domain analysis of cache filter effects in
Web caching hierarchies

• Study impact of a cache on the structural
• characteristics of Web request workload
• (mean, peak, variance, self-similarity)
• Sensitivity of filter effect to cache
  configuration
• (cache size and cache replacement policy)
• Characterizing aggregate Web request streams
• in a multi-level Web proxy caching hierarchy

9
Multi-Level Web Proxy Caching System
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Experimental Methodology

• Trace-driven simulation
• Web proxy cache simulator
• Synthetic Web proxy workloads
• Controllable characteristics
• Trace length about 1M requests
• Zipf slope -0.75, -0.8
• Request arrival process
• Deterministic, Poisson, Self-Similar

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• General Observations Filter Effects

Arrival Counts
Cache Hit Ratio
1600
1530
1230
1200
1600
1530
1230
1200
20000
1
16000
0.8
Requests per 5-minute Interval
12000
0.6
Hit Ratio
8000
0.4
4000
0.2
0
0
0
0
4000
8000
6000
2000
12000
14000
10000
2000
4000
6000
8000
12000
10000
14000
Time (sec)
Time (sec)
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• 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)

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Effect of Cache Size on Traffic Structure
Marginal Distribution Plot (pdf)
14
Effect of Cache Replacement Policy
(8 KB)
15

• Input Deterministic Arrival Process

Cache Size (MB)
Before Cache
Statistics
4
16
64
256
1024
1
60.00
36.88
31.45
28.71
27.31
25.37
23.03
Mean
Standard Deviation
0.00
4.84
4.60
4.01
4.00
4.31
4.78
38.8
47.8
52.7
55.5
59.1
62.7
Hit Ratio

• Main Observations
• Reduces mean arrival rate of filtered request
  stream
• Increases variance of the filtered request stream

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• Input Poisson Arrival Process

Cache Size (MB)
Before Cache
Statistics
4
16
64
256
1024
1
60.10
36.81
31.38
28.65
27.26
25.33
23.00
Mean
Standard Deviation
7.82
6.77
6.07
5.43
5.31
5.39
5.62
38.8
47.8
52.7
55.5
59.1
62.7
Hit Ratio

• 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.

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Input Self-Similar Arrival Process

Cache Size (MB)
Before Cache
Statistics
4
16
64
256
1024
1
62.87
38.50
32.79
29.88
28.27
26.05
23.49
Mean
Standard Deviation
12.24
9.03
7.98
7.12
6.94
7.02
7.14
38.8
47.8
52.7
55.5
59.1
62.7
Hit Ratio

• 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

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• Background Self-Similar Traffic

• Network traffic self-similarity
• The statistical characterization of the traffic
• is essentially invariant with time scale.
• Main measure
• Hurst parameter 0.5 lt H lt 1
• Examination
• autocorrelation (long-range dependence)
• variance-time plot
• rescaled adjusted range statistic (R/S)

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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

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Multi-Level Web Proxy Caching System
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Synthetic Self-Similar Workload Traces
offered to the first-level cache
Trace 1 (H0.70, Zipf slope0.75)
Trace 2 (H0.80, Zipf slope0.80)
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Evidence of Self-Similar Request Arrival Process
for Filtered Web Proxy Workload

1
1
H0.699
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Superposition of Web Workload in
time-domain
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H0.76
25
Modeling of Aggregate Workload

• Gamma Distribution

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Modeling of Aggregate Workload
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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

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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_at_cpsc.ucalgary.ca
• http//www.cpsc.ucalgary.ca/carey