Workload characterization in Web caching hierarchies

Abstract

The paper uses trace-driven simulation and synthetic Web workloads to study the request arrival process at each level of a simple Web proxy caching hierarchy. The simulation results show that a Web cache reduces both the peak and the mean request arrival rate for Web traffic workloads. However, the variability of the request arrival process may either increase, decrease, or remain the same after the cache, depending on the input arrival process and the configuration of the cache. If the input request arrival process is self-similar, then the filtered request arrival process remains self-similar, though with reduced mean. Furthermore, the superposition of Web request streams from multiple child caches results in a bursty aggregate request stream. Finally, we find that a gamma distribution provides a flexible means of modeling the request arrival count distribution in hierarchical Web caching architectures.

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Workload Characterization in Web Caching Hierarchies
Guangwei Bai Carey Williamson
Department of Computer Science, University of Calgary
{bai,carey}@cpsc.ucalgary.ca
Abstract
This paper uses trace-driven simulation and synthetic
Web workloads to study the request arrival process at each
level of a simple Web proxy caching hierarchy. The simula-
tion results show that a Web cache reduces both the peak
and the mean request arrival rate for Web traffic work-
loads. However, the variability of the request arrival pro-
cess may either increase, decrease, or remain the same af-
ter the cache, depending on the input arrival process and
the configuration of the cache. If the input request arrival
process is self-similar, then the filtered request arrival pro-
cess remains self-similar, though with reduced mean. Fur-
thermore, the superposition of Web request streams from
multiple child caches results in a bursty aggregate request
stream. Finally, we find that a Gamma distribution provides
a flexible means of modeling the request arrival count dis-
tribution in hierarchical Web caching architectures.
1. Introduction
As the tremendous growth of the World Wide Web con-
tinues, multi-level Web proxy caching systems are being
used to improvethe performanceof the Internet [15, 16, 18,
23]. WebcachingproxieshelpbyreducingWebserverload,
Internet bandwidth consumption, and the round-trip delays
associated with Web object retrieval. In many cases, users
perceiveimprovedresponsetimes fordocumentdownloads.
The primary purpose of a proxy cache is to reduce the
number of client requests that traverse the Internet to the
origin Web server. Obviously, the presence of a Web proxy
cache changes the Web workload seen by a Web server,
since many requests are filtered (removed) from the Web
server request stream when they are satisfied at the proxy.
The same argument applies between the levels of caches in
a multi-level Web proxy caching hierarchy.
The “filtering” effect of the cache manifests itself in two
distinctly different ways. First, it removes many requests
for highly-popular Web objects, making the object pop-
ularity profile seen by a higher-level cache or the origin
server distinctly un-Zipf-like [23]. Second, it changes the
structuralcharacteristicsoftherequestarrivalprocess,since
many of the requests during peak bursty periods are satis-
fied by the first level of cache. We refer to the changes in
the document popularity profile as frequency-domain cache
filter effects, and the changes in the request arrival pro-
cess as time-domain cache filter effects. The frequency-
domain effect has been fairly well-studied in the litera-
ture [10, 12, 14, 23], while the time-domain effect has re-
ceivedlittleattention[5]. Itisthelatter(time-domain)effect
that is the focus of this paper.
The precise manifestation of the cache filter effect is
highly dependent upon the architecture of the Web proxy
caching system, the cache size used, and the cache re-
placement policy [5, 10, 23]. Since the goal in Web proxy
caching is to improve overall “system-level” performance,
it is important to design an appropriate caching system ar-
chitecture. For this purpose, knowledge of Web workloads
and a thorough understanding of cache filter effects are in-
dispensable. This knowledge will provide valuable insight
intocachingsystem designandthe mechanismsforefficient
cooperation between caches at different levels.
The research questions addressed in this paper are:
• How significantly are the mean and the variance of
the Web request arrival process transformed by the
presence of a proxy cache?
• How sensitive are the cache filter effects to the
characteristics of the input request workload?
• How can we model the aggregate Web request streams
in a multi-level Web proxy caching hierarchy?
We address these questions using trace-driven simula-
tions of a multi-level Web proxy caching hierarchy. The
simulation experiments quantify the filter effects of a Web
cache on the request arrival process, for synthetically-
generated aggregate Web client workloads. For simplicity,
we consider only a two-level Web proxy caching hierarchy,
as shown in Figure 1. Assuming that λ1and λ2represent
the Web request arrivalprocesses(fromclients) enteringthe
child-level caches, we are interested in the filtered arrival
processes λ?
terested in how they multiplex to form λ3, which itself is
transformed into λ?
1and λ?
2after these caches. We are also in-
3before entering the Internet.

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λ3
’
λ1
’
λ2
’
λ3
λ1
λ2
Web Proxy Cache 3
Web Proxy Cache 1Web Proxy Cache 2
Parent Level
Child Level
Figure 1. Example of Web caching hierarchy
The simulation experiments show the obvious result that
a Web cache reduces the mean request arrival rate for Web
traffic workloads. However, the variability (burstiness) of
the request arrival process may either increase, decrease,
or remain the same after the cache, depending on the in-
put arrival process and the configuration of the cache. The
study also demonstrates that the superposition of Web re-
quest streams from multiple child caches in a Web proxy
caching hierarchy does not result in a smoothing of traf-
fic. Rather, multiplexing bursty request streams tends to
produce a bursty aggregate stream. Finally, we find that a
Gamma distribution provides a flexible means of character-
izing Web workloads in Web caching hierarchies.
The remainder of this paper is organized as follows.
Section 2 discusses background information on Web proxy
caching and related work on Web workload characteriza-
tion and cache filter effects. Section 3 describes the exper-
imental methodology for our study, and the synthetic Web
proxy workloads used. Section 4 presents simulation re-
sults for Web cache filter effects on the request arrival pro-
cess. Section 5 focuses on the superposition of self-similar
Web workload streams in a multi-level caching hierarchy,
and the modeling of aggregate Web workload in the time-
domain. Finally,Section6concludesthepaperandsuggests
directions for future research.
2. Background and Related Work
2.1. Web Proxy Caching
Web proxy caching is a technique used for improving
Web performance on the Internet. Web proxy caches are
located between Web clients (browsers) and Web servers.
Proxies accept client requests and forward them to Web
servers only as necessary. When a requested document is
returned by a Web server, the proxy sends the document
to the client and stores a copy of the document in its local
cache, in the hope that the proxycan satisfy future client re-
quests for the same document without contacting the origin
server, thus reducing user-perceived response time.
Caching effectiveness is traditionally measured by two
quantities: the (document) hit ratio is the percentage of the
total requests that are satisfied directly by documents stored
in the cache; and the byte hit ratio is the percentage of the
total requested Web content bytes that are satisfied directly
bydocumentsstored in thecache. Bothmetrics are required
since Web objects vary significantly in size. Other metrics
such as user-perceived response time are dependent upon
the hit ratio and the byte hit ratio, as well as network band-
width, round-trip delay, and server load.
To enhancethe performanceof Web caching, multi-level
Web caching hierarchies have recently received increasing
research attention [10, 15, 18, 23]. In a hierarchical config-
uration, proxies at or near the end-user constitute the lowest
level of the hierarchy, often with sibling-sibling relation-
ships with one another. The lowest level proxies may have
a child-parent relationship to a higher level proxy, usually a
(geographically) regional proxy [23]. A regional proxy can
in turn connect to a higher level proxy, such as a national
proxy [18]. A request that cannot be satisfied by one proxy
cache can be sent to a nearby sibling or to the parent us-
ing an Inter-Cache Protocol. Contacting the origin server to
obtain the document serves as the last resort [23].
2.2. Web Workload Characterization
Web workload characterization studies have focussed on
Web client [7], Web server [3], and Web proxy workload
characteristics [2, 5, 18]. Common workload characteris-
tics observedinclude a high degreeof one-time referencing,
a Zipf-like document popularity distribution, heavy-tailed
file and transfer size distributions, and a temporal locality
property in the document referencing behaviour [3, 9, 18].
Among these characteristics, the slope of the Zipf-like
document popularity distribution is most relevant to Web
caching performance [9]. Zipf’s law expresses a power-law
relationship between the popularity P of an item (i.e., its
frequency of reference) and its rank r (i.e., relative rank
among the referenced items, based on frequency of refer-
ence). This relationship is of the form P = c/rβ, where c
is a constant, and β is often close to 1. When the slope is
steep, requests are highly concentrated on a small subset of
the Web content, and caching works well.
2.3. Web Proxy Cache Performance
Several recent research papers have explored the rela-
tionships between Web workload characteristics and Web
proxy caching performance, particularly in caching hier-
archies [10, 12, 14]. However, most of this research fo-
cuses on the frequency-domain aspect of the Web cache
filter effect. For example, Doyle et al. [14] refer to this
as the “trickle down” effect, and conduct a detailed sim-
ulation study to quantify its impact. Che et al. [12] pro-

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pose a frequency-basedcachinghierarchy,where the lower-
level cache handles requests for high-frequency items, and
the higher-level cache handles requests for low-frequency
items. Busari and Williamson [10] propose a “heteroge-
neous” Web proxy caching hierarchy that uses different
caching policies at different levels of a caching hierarchy.
Few papers explicitly address the structural changes in
the request arrival process in multi-level Web caching hier-
archies. Our own previous work [5] studied time-domain
cache filter effects using an empirical Web proxy workload,
but only for a single-level Web proxy cache. This current
paper extends our work to caching hierarchies, and general-
izes our results to a broader set of (synthetically-generated)
Web workload characteristics.
3. Experimental Methodology
Our experimental methodology has two main steps.
First, we generate a set of synthetic Web proxy workloads
to use in our study. We validate these workloads to ensure
thattheyhavetheintendedworkloadcharacteristics,andare
similar to empirical Web proxy workloads used in our ear-
lier studies [5, 9, 10, 18, 23]. Second, we conduct a set of
trace-driven simulation experiments, using an application-
level Web proxy caching simulator and the generated work-
loads. Theoutput“miss” streamsfromtheWebproxycache
simulationsareusedtoquantifythefiltereffectofthecache,
as a function of cache size and cache replacement policy.
The workload generation and cache simulation steps are
describedin moredetailin Section 3.1and3.2,respectively.
3.1. Workload Generation
There are two reasons for the use of synthetic Web proxy
workloads in our study, rather than empirical workloads.
First, synthetic workload generation offers greater control
over workload characteristics, and allows us to study the
sensitivity of our results to particular workload characteris-
tics. Second, it allows us to generate traces that are as long
or as short as needed for our study, without having to worry
about non-stationary behaviour, which can be significant in
empirical Web proxy workloads [5].
In the workload generation step, there are two workload
parameters of interest: Zipf slope, and request arrival pro-
cess. The Zipf slope refers to slope of the Zipf-like doc-
ument popularity profile in the input Web workload. This
slopeaffectsthemagnitudeoftheWebcachefilteringeffect,
since a steep Zipfslope tends to producea highcache hit ra-
tio, while a flat Zipf slope does not. The request arrival pro-
cess refers to the timestamps generated for the Web client
requests. We consider three different arrival processes: an
(unrealistic) deterministic arrival process that is simple to
analyze; an (unrealistic) Poisson arrival process that is also
Table 1. Web workload characteristics
Item
Total Requests
Total Documents
Unique Documents
One-timer Documents
One-timers
Zipf Slope
Total Bytes of Docs (MB)
Smallest Doc Size (bytes)
Largest Doc Size (MB)
Mean Doc Size (bytes)
Total Transferred Bytes (MB)
Mean Transfer Size (bytes)
Trace 1
837,972
299,513
35.74%
209,504
69.95%
-0.75
3,706
0
39.475
12,977
9,304
11,370
Trace 2
893,943
300,000
33.56%
209,693
69.90%
-0.80
3,712
32
39.475
12,976
8,960
10,264
easy to analyze; and a self-similar arrival process that rep-
resents a realistic Web request arrival process.
In our work, the ProWGen (Proxy Workload Genera-
tion) [11] tool is used to synthesize Web proxy workloads.
ProWGen captures the salient characteristics of Web proxy
workloads: one-time referencing, Zipf-like document pop-
ularity, heavy-tailed file size distribution, and temporal lo-
cality. These characteristics affect Web proxy cache perfor-
mance [9, 11], and are easy to analyze using the WebTraff
tool [19]. By design, the two synthetic workloads differ in
the Zipf-like document popularity profile, which influences
the cache hit ratio [8, 9, 22]. Table 1 summarizes the char-
acteristics of the synthetic traces used.
For each of the synthetic traces shown in Table 1, three
arrival-time time series were generated, using determinis-
tic, Poisson and self-similar request arrival processes, re-
spectively. In fact, two instances of the self-similar case are
studied, so that we can generalize our traffic characteriza-
tion and modeling results. Note that the generation of the
traffic arrival process (i.e., the timestamps on the Web doc-
ument requests) is independent of the techniques used to
generate the Web document requests (i.e., ProWGen’s file
popularity and temporal locality models).
The resulting synthetic workloads are used to investigate
cache filter effects in a two-level Web caching hierarchy.
3.2. Web Proxy Cache Simulation
In the Web cache simulation step, two experimental fac-
tors are used: cache size, and cache replacement policy.
The cache size determines the maximum number of Web
content bytes that can be held in the cache at one time.
The cache replacement policy determines what objects to
remove from the cache when more space is needed to store
an incoming object. Five cache replacement policies are
considered: removing objects at random (RAND), remov-

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ing objects in the order in which they arrived (First-In-
First-Out, FIFO), removingobjects based on recency of use
(Least-Recently-Used, LRU), removing unpopular objects
(Least-Frequently-Used, LFU), and removing large objects
(Greedy-Dual-Size, GDS).
In our simulation experiments, the synthetic Web work-
load (a timestamped series of Web document requests) is
provided as input to the Web proxy cache simulator. The
network topology modeled is shown in Figure 1. The sim-
ulator generates as output the cache hit ratio for the experi-
ment, and a timestamped series indicating the requests that
result in cache misses. The latter output constitutes the fil-
tered request stream used for traffic analysis.
The experiments use cache hit ratio and byte hit ratio
as the primary performance metrics for cache performance,
and the mean and variance of the request arrival process as
theprimarymeansofcharacterizingcachefiltereffects. The
caching simulation results follow in Section 4.
4. Simulation Results: Cache Filter Effects
This section focuses on analysis and understanding of
the cache filter effects in the time-domain. Section 4.1
makes general observations about cache filter effects, while
the effects of cache configuration parameters (Section 4.2)
and input workload characteristics (Section 4.3) follow.
4.1. General Observations
The first experiment is designed to provide an intuitive
understanding of the filter effect of a cache, and a qualita-
tive assessment of its impact. For this experiment, a single
workload (Trace 1) is provided as input to the Web proxy
cache simulator. For simplicity, we assume a deterministic
request arrival process, with an (arbitrary) average rate of
60 requests per second. This represents a trace duration of
about 4 hours for Trace 1.
Figure 2 illustrates the general impacts of a proxy cache
on the Web workload, using two time series plots. Fig-
ure2(a) shows the requestarrival countprocessfor the orig-
inal and filtered request streams, with request counts cumu-
lated over 5 minute intervals. Figure 2(b) shows the corre-
sponding cache hit ratio results for this trace.
Figure 2(a) clearly shows that the presence of the Web
cache reduces both the peak and the mean rate of the re-
quest arrival process. The larger the cache size, the more
pronouncedthe filter effect. These results are as expected.
Figure 2(b) shows the average document hit ratio in the
cache for different cache sizes. These results are plotted
using the average cache hit ratio over each 5 minute inter-
val of the trace. The cache is initially empty at the start-
ing point of the trace, and proceeds to fill as the simulation
progresses, invoking the cache replacement policy when
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12:30
(a) Time Series
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12:00 12:3015:30 16:00
(b) Hit Ratio
Figure 2. Illustration of cache filter effects
needed to manage the contents of the cache. As expected,
the cache hit ratio increases with cache size.
There are non-stationarybehavioursevident in these two
graphs, particularly for large cache sizes. A brief warmup
period occurs initially before the cache hit ratio begins to
stabilize. Some “end effects” are also visible, wherein the
cachehit ratioincreasesat theendofthe trace,sincemostof
the Web content (particularlythe popularcontent) fits in the
cache when the cache size is large. The increasing hit ra-
tio produces a corresponding drop in the request rate of the
filtered request stream. For modest cache sizes, however,
the hit ratio and the filtered request arrival process appear
to be stationary for most of the trace (e.g., 3-hour portion
between the vertical lines). We focus only on the stationary
portion in our subsequent analyses.
4.2. Effect of Cache Configuration Parameters
The second experiment illustrates the effect of cache
configuration parameters on the cache filter effect. In par-
ticular, we focus on the impact of cache size and cache re-
placement policy. For simplicity, these experiments assume
a Poisson arrival process for Web requests.
The characteristics of the filtered arrival process are il-
lustrated in Figure 3. The primary impact of the cache is
to reduce the mean arrival rate, shifting the request arrival
count distribution to the left (see Figure 3(a)). In general,
the filter effect increases with cache size, as expected.
Figure 3(b) shows the impact of cache replacement pol-
icy on the workload characteristics. Examining the plot
shows that the filter effects of each policy are similar. We
thus use the LFU replacement policy as a canonical exam-
ple in most of the remaining experiments.
4.3. Effect of Input Arrival Process
The next set of experiments studies the influence of the
input request arrival process.
namely deterministic, Poisson, and self-similar arrival pro-
cesses. In all three cases, we use 60 requests per second
as the (arbitrary)average request arrival rate, representing a
We consider three cases,

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Probability Density Function (PDF)
Before cache
LFU
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GDS
FIFO
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(a) Effect of Cache Size (LFU Policy)(b) Effect of Cache Replacement Policy (8 MB Cache)
Figure 3. Characteristics of the filtered arrival process as a function of cache size (Trace 1)
trace duration of about 4 hours. We characterize the filtered
request stream at the 1 second granularity.
Case 1: Deterministic Arrival Process
The first experiment deals with the simplest case: a deter-
ministic request arrival process. Exactly 60 requests arrive,
equally spaced, in each one second of the trace. This trivial
example simply provides a baseline for comparison.
Table 2 summarizes the statistical characteristics of the
filtered request arrival process. In these experiments, the
cache replacement policy is always LFU, while cache size
is varied from 1 MB to 1 GB. The corresponding cache hit
ratios are shown in the bottom row of Table 2.
Clearly, the presence of the cache reduces the mean ar-
rivalrate in the filteredrequeststream. Thelargerthe cache,
the greater this filtering effect. Note that in this (unrealistic)
case, the presence of the Web cache increases the variance
of the filtered request stream (since the input arrival pro-
cess is deterministic, while the output stream is not). The
variance of the filtered stream is similar at each cache size
considered, implying that the variance-to-mean ratio of the
filtered request stream increases with cache size.
Case 2: Poisson Arrival Process
The next experiment assumes that the input arrival process
is Poisson. That is, the inter-arrival times between requests
are exponentially distributed and independent. There is
some evidence that the Poisson arrival process character-
izes some aspects of Internet user behaviour [3, 21], though
it does not provide an adequate characterization of aggre-
gate Web traffic [3, 13].
Table 3 summarizes the statistical characteristics of the
filteredrequestarrivalprocess, foran LFU replacementpol-
icy, and cache sizes ranging from 1 MB to 1 GB. The cache
hit ratios are also shown in Table 3. Note that the cache
hit ratios are the same here as they were in Table 2, since
only the relative ordering of requests (not their arrival time)
matters to the Web caching simulator.
Again,thepresenceofthecachereducesthemeanarrival
rate in the filtered request stream. The larger the cache,
the greater this filtering effect. However, the impact of the
Web cache on the variance of the filtered request stream is
less pronounced. The variance-to-mean ratio of the filtered
request stream tends to increase with cache size, since the
mean rate drops significantly, while the variance decreases
slowly. For small cache sizes, the filtered request stream
is reasonably well-characterized as a Poisson process; for
large cache sizes it is not.
Case 3: Self-Similar Arrival Process
Recent research in network traffic measurement has chal-
lenged the Poisson assumptions in traditional network traf-
fic models [1, 13, 17, 21]. Leland et al. [17] showed that
Ethernettrafficisburstyacrossmanytimescales,andcanbe
described statistically as self-similar. The term self-similar
means that the statistical characterizationof the traffic is es-
sentially invariantwith time scale; the same statistical prop-
erties are observed at time scales of milliseconds, seconds,
minutes, hours, and more.
Our next experiment considers a self-similar request ar-
rival process.Several models for self-similar stochastic
processes exist, including Fractional Gaussian Noise and
Fractional-ARIMA processes. In our study, we use the syn-
Traff traffic modeling toolkit developed in prior work [6].
It uses a three-step modeling approach based on Fractional-
ARIMA processes to generate monofractal traffic. Using
this toolkit, we generate time series processes that are dis-
tributionallyself-similar. TheHurstparameteris H = 0.70.
Table 4 summarizes the statistical characteristics of the
filtered request arrival process. As observed previously, the
mean arrival rate decreases as the cache size is increased.
The variance of the filtered request stream also decreases,
but not as quickly as the mean. More importantly, further
analysis shows that the output stream maintains its self-
similar properties (see Section 5.1 for fuller evidence of
this). As observed earlier, the variance-to-mean ratio of the
filtered request stream tends to increase with cache size.