arallel and Distributed Information Systems, Miami Beacbest/research/talks/Locality... · 2006. 3. 17. · arallel and Distributed Information Systems, Miami Beac h, FL Characterizing

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%Boston University / Computer Science Department PDIS'96

Parallel and Distributed Information Systems, Miami Beach, FL

Characterizing Reference Locality in the WWW

Azer Bestavros & Mark Crovella

Computer Science Department

Boston University

Virgilio Almeida & Adriana de Oliveira

Computer Science Department

Universidade Federal de Minas Gerais

Thursday December 19th 1996

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Talk Outline

� Introduction, Motivation, and Applications

� Experimental Environment and Data Collection

� Characterizing Web Document Popularity

� Characterizing Web Reference Locality

{ Temporal Locality: Evidence and Model

{ Spatial Locality: Evidence and Model

� Synthetic Web Reference Trace Generation

� Related Work

� Current and Future Work

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Introduction

� The characteristics of Web access patterns fall into

two categories:

{ Static (e.g. popularity pro�les)

{ Dynamic (e.g. reference locality)

� Characterizing Web access patterns is crucial for

performance tuning and evaluation.

{ Client/server caching and prefetching protocols

{ Scheduling and load balancing protocols

{ Networking issues

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Evaluating A Workload Model

Workload System

M o d e l

Systemρ

� A workload model W is a perfect representation of

the real workload R if the performance metrics �

obtained using W and R in the same system are

indistiguishable.

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Data Collection

Log NCSA SDSC EPA BU

Duration 1 day 1 day 1 day 2 weeks

Start Date Dec 19 Aug 22 Aug 29 Oct 08

Total requests 46,955 28,338 47,748 80,518

Unique requests 4,851 1,267 6,518 4,471

Summary of Access Log Data

ClientIP : TimeStamp : RequestURL : Size

Data in a Typical Log Record

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Characterizing Document Popularity

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log1

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log10(Document Rank)

Zipf's Law Applied to Web Documents

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Characterizing Document Popularity

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Length 1Length 2Length 3

Zipf's Law Applied to Sequences

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Measuring Locality of Reference

O1O2O3O4O5

OiOi+1

OiO1O2O3O4

Oi-1Oi+1

Object O is

referencedi

LRU stack distance

LRU Stack Distance Model

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Measuring Locality of Reference

� For any string of requests R = r1:r2:r3 : : : we can

compute a corresponding string of stack distances

D = d1:d2:d3 : : :

� The request and distance strings are equivalent in

terms of the locality of reference information they

capture.

� The average stack distance of D is a measure of

the number of intervening requests to unique objects

between recurrring requests.

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Evidence of Temporal Locality

� Consider a scrambled request string R0 that

corresponds to a random permutation of R.

� R and R0 have the same Zipf popularity pro�le since

they are permutations of each other.

� The di�erence in stack distance distribution for R

and R0 would be a measure of temporal locality.

BU Trace Original Scrambled

Mean Stack Distance 479.798 645.586

Standard Deviation 941.430 968.840

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Characterizing Temporal Locality

� If FD is the distribution of the stack distance D,

then the miss rate M (C) of a cache that can hold

C �les is

M (C) = P [D > C] = 1� FD(C)

Knowledge of FD provides enough information to

predict the performance of a cache of any size for

the given trace.

� Our analysis shows that FD has a long tail, yet it

does not seem to follow a power-law (e.g. Pareto).

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� Lognormal distributions with parameters � and �

seem to provide the best �t for the distributions of

the stack distance in the traces we considered.

BU NCSA SDSC EPA

�̂ 1.829 1.730 1.568 2.150

�̂ 0.947 0.836 0.827 0.921

Lognormal Distribution Parameters

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Stack Distance Distributions (BU, NCSA, SDSC, EPA)

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Lognormal Distributions and Fit (BU, NCSA, SDSC, EPA)

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Temporal Locality Modeling Accuracy

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Actual DataModel

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Actual and Predicted Miss Rates (BU, NCSA, SDSC, EPA)

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SDSC (m = 1.6, s = .83)NCSA (m = 1.7, s = .84)

BU (m = 1.8, s = .95)EPA (m = 2.2, s = .92)

Comparative Predicted Miss Rates (BU, NCSA, SDSC, EPA)

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Evidence of Spatial Locality

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Sequence Length

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BU1 Server Trace

BU1 Server Trace (Random Permutation)

BU1 Client Trace

Unique sequences observed in the BU trace

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Characterizing Spatial Locality

� Stack distance series are bursty at all timescales

; They exhibit self-similar characteristics.

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Stack Distance Scaling Behavior of Original (left) and Scrambled (right) BU Traces

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� Stack distance self-similarity is evidence of very

long-range correlations, which correspond to long

periods of very large stack distances|caused by

phase changes in referencing behavior.

� The degree of self-similarity is captured by theHurst

parameter H , which takes values between 0.5 and

1.0. As H ! 1, the burstiness becomes more

pronounced at high levels of aggregation.

�We use four methods to estimate the H parameter

for our datasets: the variance-time plot, the R/S

plot, the periodogram, and the Whittle estimator,

which provides con�dence intervals as well.

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Graphical Estimators of H for BU Trace

V-T R/S Per. Wtl. (95% conf.)

BU .82 .78 .87 .85 (0.84, 0.87)

NCSA .71 .74 .74 .74 (0.73, 0.77)

SDSC .71 .68 .69 .68 (0.66, 0.71)

EPA .64 .66 .66 .65 (0.64, 0.67)

Estimates of H for Original Traces

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Original Trace Scrambled Trace

V-T R/S Per. Wtl. V-T R/S Per. Wtl.

BU .82 .78 .87 .85 .50 .55 .50 .50

NCSA .71 .74 .74 .74 .50 .51 .51 .49

SDSC .71 .68 .69 .68 .52 .54 .50 .50

EPA .64 .66 .66 .65 .51 .55 .47 .50

H for Original vs Scrambled Traces

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Synthetic Web Reference Trace Generation

Step 1 :

Select parameters � and � re ecting temporal

locality, and H re ecting spatial locality|based on

empirical measurement of traces to be imitated, or

based on our results.

Step 2 :

Generate a stack distance trace with marginal

distribution determined by � and � and long-range

dependence determined by H using the two-phase

approach described in [Huang et al: 1995].

Step 3 :

Invert the stack distance trace to form a sequence of

�le names.

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Related Work

Traditional Memory Systems

� Fundamentals of reference locality in hierarchical

memories [Denning and Schwartz: 1972].

� Stack distance analysis and algorithms [Mattson

et al: 1970].

� Establish the existence of long-range dependence

in reference strings [Spirn: 1976].

� Relate the fractal dimension of cache misses to

software complexity [Voldman et al: 1983].

�Model memory access pattern as a random walk

with fractal dimension [Thiebaut: 1989].

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Related Work

Large-scale Information Systems

� Caching and replication for distributed �le

systems [Howard et al: 1988].

�Model Web access using Zipf-based popularity

pro�les [Glassman: 1994].

�Model Web access using frequency and recency

rates of past accesses [Recker and Pitkow: 1994].

� Characteristics of client access patterns [Cunha,

Bestavros, and Crovella: 1995].

� Used Markov processes to model access inter-

dependencies [Cunha and Bestavros: 1995, 1996].

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Current and Future Work

� Incorporate �le size information in the access

pattern characterization.

� Study the e�ect of increased multiprogramming

levels on access pattern characteristics.

� Study the implication on caching and prefetching

algorithms at clients and servers.

� Use measured characteristics to design benchmarks

for evaluating client and server software.

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