Performance models of a firm's proxy cache server

Ž .Decision Support Systems 29 2000 47–57www.elsevier.comrlocaterdsw

Performance models of a firm’s proxy cache server

Indranil Bose 1, Hsing Kenneth Cheng)

Department of Decision and Information Sciences, Warrington College of Business Administration, P.O. Box 117169,The UniÕersity of Florida, GainesÕille, FL 32611-7169, USA

Accepted 14 February 2000

Abstract

Ž .We examine the impact of installing a proxy cache server PCS on overall response time to Web requests. We analyzehow various factors affect the performance of that server. Our research specifically identifies a ‘‘crossover probability’’, theminimum cache ‘‘hit rate’’ probability at which installing a PCS becomes beneficial. We find that this probability decreasesas the arrival rate of Web requests or the average file size increases. In particular, the benefits of installing a PCS are morepronounced when the firm’s users exhibit heavy Web accesses. We also find a ‘‘diminishing rate of return’’ phenomenon interms of enhancing the PCS’s performance. The managerial implication is that it may not pay to choose an overpowerfulPCS as the marginal reduction in the overall response time becomes unjustified. Moreover, the ‘‘bottleneck’’ effect of thefirm’s network bandwidth is investigated and demonstrated. q 2000 Elsevier Science B.V. All rights reserved.

Keywords: Electronic commerce; Proxy cache server; World Wide Web

1. Introduction

The last several years have witnessed an explo-sive growth of the Internet. The number of peoplearound the world connected to the Internet grewfrom 40 million in 1996 to 100 million in 1997. Thenumber of Internet domain names increased from627,000 in 1996 to 1.5 million in 1997, and traffic

w xon the Internet doubled every 100 days 11 . Theexplosive use of the Internet and the World WideWeb has caused congested networks and overloaded

) Corresponding author. Tel.: q1-352-392-7068; fax: q1-352-392-5438.

Ž .E-mail addresses: [email protected] I. Bose ,Ž [email protected] H.K. Cheng .

1 Tel.: q1-352-392-0648; fax: q1-352-392-5438.

servers. As a result, the average waiting time forWeb page delivery is estimated to be as high as 15 to

w x45 s 7 . Adding more network bandwidth is consid-ered an expensive and ineffective solution to theproblem of long delays of Web page delivery.

It is commonly held that the majority of WorldWide Web accesses are redundant. An ‘‘80–20’’rule best describes such a phenomenon, with 80% ofrequested Web pages coming from 20% of the extantWeb sites. Corporate users exhibit more redundantpatterns since people doing similar tasks tend toaccess similar Web resources. ‘‘Caching,’’ i.e., stor-ing, these frequently accessed Web pages closer tothe requesting users can greatly speed up Web pagedelivery and impose less cost in bandwidth.

Ž .In general, caching can be implemented at 1Ž .individual browser software, 2 the originating Web

Ž . Ž .sites the sites delivering the requested pages , 3

0167-9236r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0167-9236 00 00062-2

( )I. Bose, H.K. ChengrDecision Support Systems 29 2000 47–5748

Ž . Ž .the Internet Service Providers ISP , and 4 theŽ .boundary between a local area network LAN and

the Internet. Browser caches are inefficient sincethey cache for only one user. The caching at the‘‘point of origin’’ Web sites can improve perfor-mance markedly for the originating Web servers byoff-loading requests from the outside world, althoughthe requested files are still subject to delivery throughthe Internet. ISPs such as America Online, cachenumerous Web pages to satisfy their members’ re-quests more efficiently. For example, instead offetching the same weather pages from the WeatherChannel at each member’s request, these pages arecached at the ISP’s server and delivered directly tothe members.

It has been suggested that, given the current stateof technology, the greatest improvement in responsetime for corporations will come from installing a

Ž .proxy cache server PCS at the boundary betweenw xthe corporate LAN and the Internet 5 . The primary

benefits include lower bandwidth requirements andfaster response times. Corporations can accommo-date more users with a given Internet connectioncapacity since the PCS can satisfy redundant re-quests from different users. Delivering duplicate re-quests directly from the PCS at LAN speed alsoimproves the response time. This type of server isthe primary focus of our paper.

Caching plays a vital role in improving responsetime to Web requests. Thus, it has become an in-creasingly important research area. Prior research hasfocused on analyzing or developing various cache

w xreplacement algorithms 1,3,9,14,15,17 , among oth-w xers. For example, Ref. 15 discusses a caching algo-

rithm for cache replacement and maintenance ofw xconsistency for cached documents, while Ref. 1

shows that the cache replacement problem is similarto a knapsack problem and suggests a greedy heuris-tic for solving the problem.

Our research looks at a more fundamental prob-lem: notably, the impact of installing a PCS onoverall response time to Web requests. In particular,we study the conditions under which installing aPCS becomes beneficial. We also analyze how vari-ous factors affect the performance of a firm’s PCS.These factors include the arrival rates of requests, theprobability of desired content already residing on the

Ž .PCS the cache ‘‘hit rate’’ probability , the average

file sizes of Web requests, the speed of the PCS, andthe firm’s network bandwidth.

Our model focuses on the performance impact ofinstalling a PCS on the overall response time tousers’ requests. We do not intend to analyze the prosand cons of various cache replacement algorithms,nor are we concerned with the freshness of thecached content issue. To minimize these concerns, acommon practice is for the PCS to have a reasonablylarge storage and to refresh the cached content dur-

Ž .ing off-peak hours e.g., nights .We specifically identify a ‘‘crossover proba-

bility’’, the minimum cache ‘‘hit rate’’ probability atwhich it is beneficial to install a PCS. We find thatthis probability decreases as the arrival rate of Webrequests or the average file size increases. In particu-lar, the benefits of installing a PCS are more pro-nounced when the firm’s users exhibit heavy Webaccesses. We also find a ‘‘diminishing rate of return’’phenomenon in terms of enhancing the PCS’s perfor-mance, so that it may not pay to choose an overpow-erful PCS, as the marginal gain in reducing theoverall response time becomes unjustified. More-over, we investigate and demonstrate the ‘‘bot-tleneck’’ effect of the firm’s network.

This paper is structured as follows. In Section 2,we propose a queuing network model to study thedynamics of installing a firm’s PCS. Overall re-sponse time formulas are developed for both the casewith and without a PCS. Several insights from themodel are offered in this section. Section 3 reportsnumerical experiments conducted to examine theresponse time behavior of the firm’s PCS with re-spect to various parameters of the model. Section 4provides concluding remarks and potential exten-sions of this research.

2. The model

Consider the case where members of a firm needto access the World Wide Web to accomplish theirtasks. In doing so, they are likely to repeatedlyfrequent the same Web sites. For example, the pur-chasing personnel may look up the same pricingcatalogues of a few major suppliers’ Web sites.Retrieving the same content repeatedly in this caseclogs up both the firm’s and the suppliers’ useful

( )I. Bose, H.K. ChengrDecision Support Systems 29 2000 47–57 49

bandwidth resources, and causes an unnecessary in-crease of workload for the suppliers’ Web servers. Apopular practice to improve the response time is toinstall a PCS that stores repeatedly retrieved files.

With a PCS, a user’s Web requests will first berouted to the firm’s PCS. If the requested files arealready stored in the PCS, the requested Web pagesor files will be directly delivered to the user from thePCS. When the requested files cannot be found inthe PCS, it initiates the process of fetching thedesired files from the remote Web site. These newfiles will be stored in the firm’s PCS, while a copywill be sent to the requesting user.

The benefits of a PCS depend on several factors.The most prominent of these factors are the likeli-

Žhood of desired files already stored in the PCS the.‘‘hit rate’’ , the speed of the PCS, the bandwidth of

the firm’s Internet connection, the speed of the re-mote Web server, and the remote Web site’s networkbandwidth.

To discern the effect of the aforementioned fac-tors on the PCS’s performance, we use a network ofqueues to model the dynamics of how the users’requests are handled in the presence of a PCS overthe World Wide Web. As seen in Fig. 1, requests forWeb pages or files arrive at the PCS at a Poissonrate of l per unit of time. Let F denote the averagesize of requested files. The probability that the PCS

Fig. 1. The performance model of a PCS.

can fulfill a request is p. Thus, p is the probabilitythat desired files already reside on the PCS. With

Ž .probability 1yp , the PCS needs to fetch the re-quested files from the remote Web site.

We define l and l such that:1 2

lsl ql , where l spl and l s 1yp l.Ž .1 2 1 2

1Ž .

The l traffic, depicted by a solid line in Fig. 1,1

delivers the readily available content from the PCSto the requesting user. The dashed line in Fig. 1represents the l traffic that fetches the desired files2

from the remote Web server and returns to the PCS.The l traffic first goes through a one-time initial-2

ization. This initialization captures the time of all therequired handshakings to establish a Transmission

Ž .Control Protocol TCP connection between thefirm’s PCS and the remote Web site. We use theparameter I to characterize this one-time initializa-s

tion. The remote Web server then retrieves the re-quested files and delivers them to the firm’s PCS. Acopy of the files is, in turn, downloaded to therequesting user.

The remote Web server performance is character-Ž . Ž .ized by 1 the size of its output buffer in bytes , B ,s

Ž . Ž . Ž .2 the static server time in seconds , Y , and 3 thesŽ .dynamic server rate in bytes per second , R . Thes

second parameter of the remote Web server, Y ,s

models the fixed overhead irrespective of the size ofthe requested files. The dynamic server rate, R , iss

closely related to the conventional measures of aserver’s power, e.g., millions of instructions per

Ž .second MIPS . In Section 3, numerical experimentsare conducted using realistic parameter values re-

w xported in Ref. 12 . Likewise, the firm’s PCS ischaracterized by B , Y , and R where the sub-xc xc xc

script ‘‘xc’’ stands for ‘‘proxy cache.’’ After oneoutput buffer’s worth of data is retrieved from theremote Web server, it is delivered to the PCS throughthe Web server’s Internet connection. The latter istermed the server network bandwidth in Fig. 1.

It is not unusual for the size of the requested file,F, to exceed the remote Web server’s output buffersize, B . In this case, it may take several loops ofs

retrieving and delivering smaller files to completethe PCS’s request. This looping phenomenon is in-

Ž .herent in the Hyper Text Transfer Protocol HTTP


where retrieval of the home page is followed byretrieval of embedded inline images. To model thislooping, let q be the branching probability that arequest from the PCS can be fulfilled at the first try;

� Ž .4 Ž .or qsmin 1, B rF . Consequently, a 1yq pro-s

portion of the requests will loop back to the remoteWeb server for further processing. In equilibrium,the traffic coming out of the remote Web servertoward the PCS after branching should equal theoriginal incoming traffic, l . Hence, ql

X equals l2 2 2

in Fig. 1 where lX is the traffic leaving server2

network bandwidth before branching. Section 5 liststhe notation used in the model.

The queuing network of Fig. 1 is assumed to be aJackson network. In essence, such a network behaves

w xas if all nodes are independent MrMr1 queues 8 .It then follows that the overall response time forcompleting users’ requests in the presence of a PCSis given by Eq. 2:

° ¶1 1 F~ •T s qp qxc 1 1 Ncyl yl1¢ ßF BI xcxc Y qxcB Rxc xc

°1 1~q 1yp qŽ . 1 1yl yl rq2 2¢ F BI ss Y qsB Rs s

¶F 1 F •q q q . 2Ž .1N Ns cyl2 ßF Bxc

Y qxcB Rxc xc

The first term in Eq. 2 is the expected look-uptime required to see if the desired files are availablefrom the PCS. With probability p, the content isalready stored. The second term in Eq. 2 describesthe expected time for the content to be delivered to

the requesting user. The third term in Eq. 2 identifiesthe expected time required from the time the PCSinitiates the fetching of desired files and the remoteWeb server transfers the files to the PCS, to the timethe PCS delivers a copy to the requesting user. FromFig. 1 and Eq. 2, the arrival rate to the remote Webserver is l

X , which equals l rq, due to the looping2 2

nature of processing at the remote Web server.Without a PCS, our model reduces to a special

w xcase reported in Ref. 16 where the overall responsetime is described by Eq. 3:

1 1 F FTs q q q .1 1 N Ns cyl ylrq

F BI ss Y qsB Rs s

3Ž .

A quick inspection of Eqs. 2 and 3 shows thatboth contain the term FrN . This implies that thec

client network bandwidth should not affect the deci-sion of whether to install the PCS to improve theoverall response time. The client network bandwidthis irrelevant in deciding whether to install the PCS,since improving the client network bandwidth en-hances the performance equally with or without it.

The upper limits on the arrival rates of users’requests, l , and the average file sizes, F , canmax max

be derived by prohibiting negative terms in Eq. 2 asfollows:

1 1 qB Rs sl smin , , ,max ½ I I F R Y qRŽ .s xc s s s

qB Rxc xc4Ž .5F R Y qRŽ .xc xc xc

and

qB Rs sF smin ,max ½ l R Y qRŽ .s s s

qB Rxc xc. 5Ž .5l R Y qRŽ .xc xc xc

The implication of Eqs. 4 and 5 is that when arrivalrates or file sizes exceed the limits, the result will bean intolerably long response time for the users.


3. Numerical explorations

Several numerical experiments are undertaken toexamine the performance behavior of the PCS withrespect to various parameter values. Parameter val-ues of our numerical experiments are summarized inTable 1. These experiments seek to determine theconditions making a PCS beneficial. Our resultsprovide guidelines to network managers on when toincorporate proxy caches for Web servers.

The arrival rate of users’ request, l, is variedfrom 10 to 90 requestsrs. Some literature, e.g., Ref.w x13 , experimented with only up to 10 requestsrs,while we consider a broader range of the arrival ratesas long as they fall within the range specified in Eq.4. The average size of requested files, F, varies

w xwidely from one Web site to another. Slothouber 16visited 1000 Web pages at random using the ‘‘ran-dom link’’ feature from several search engines andfound the average file size to be 5275 bytes. Hence,we experiment with values of F below and above5275 bytes, varying from 1250 to 8750 bytes. This

w xrange of values is consistent with Ref. 2 where 94%of the requested files was reported as less than 50kbytes.

The size of the Web server’s output buffer, B ,sw xequals 2000 bytes as in Ref. 16 . The one-time

initialization time of the remote Web server, I ,s

equals 0.004 s. The static server time of the remoteWeb server, Y , is 0.000016 s and the dynamic servers

rate, R , is set at 1.25 Mbytesrs. These values ares

chosen to conform to the performance characteristicsw xof Web servers in Ref. 12 .

Table 1Parameter values in numerical experiments

Parameter Experimented value

l 10–90 requestsrsF 1250–8750 bytesB 2000 bytess

I 0.004 ss

Y 0.000016 ss

R 1.25 Mbytesrss

a s B rB 0.1–1.0xc s

b s R rR sY r Y 0.1–1.0xc s xc s

g s I r I 0.1–1.0xc s

p 0.1–0.9

Table 2Available choices of network bandwidth N and Nc s

Ž .Type of connection Bandwidth kbps

ISDN 1 64ISDN 2 128T1 1,544T3 45,000Ethernet 10,000Fast Ethernet 100,000OC-3 154,400OC-12 622,000

In order to discern the effect of the PCS’s speed,we specifically make its parameter values dependenton those of the remote Web server as follows. We letasB rB , bsR rR sY rY , and gs I rI .xc s xc s xc s xc s

In the first experiments, a , b , g are set to 1.0,which implies that the remote Web server and thePCS have identical performance characteristics. Inthe last set of experiments, we vary a , b , g sepa-rately from 0.1 to 1.0 to investigate the effect of thePCS’s speed on the overall response time to users’Web requests. The probability that requested files arereadily available from the PCS is varied from 0.1 to0.9. The empirical statistics of p ranges from 21.3–

w x w x56.6% in Ref. 4 to 30–60% in Ref. 10 . Theavailable choices of values for the client networkbandwidth, N , and the server network bandwidth,c

w x Ž .N , are from Ref. 12 see Table 2 .s

In our experiments, we tacitly assume that theclient-side network is slower than the server-sidenetwork and set the network bandwidth parametersat N s128 kbps and N s1544 kbps.c s

3.1. Effect of the cache ‘‘hit rate’’ probability, p

Several numerical experiments are conducted toexamine the effect of the cache ‘‘hit rate’’ probabil-ity on overall response time, where the arrival rate l

is set to 20 requestsrs and F set to 5000 bytes. Theprobability p is varied from 0.0 to 1.0 in incrementsof 0.1. The overall response time without a cacheserver is independent of p, as observed from Eq. 3.Hence, Ts0.3478 s for all values of p. The overallresponse time with a PCS, T , decreases as pxc

increases, as seen in Fig. 2.


Fig. 2. Overall response time with respect to cache ‘‘hit rate’’Ž .probability ls20 requestsrs and Fs5000 bytes .

There is a crossover between the graphs represent-ing T and T . This crossover point gives us thexc

corresponding ‘‘crossover probability’’ defined asp). This crossover probability is significant in decid-ing whether to install a PCS. For any cache hit rategreater than this crossover probability, p)p) , thebenefits are realized from installing a PCS since theoverall response time to users’ Web requests will bereduced.

3.2. Effect of the arriÕal rate, l

The effect of a heavy arrival of Web requests onthe overall response time is shown in Fig. 3, where

ŽFig. 3. Overall response time in case of heavy arrival ls90.requestsrs and Fs5000 bytes .

the arrival rate is increased to 90 requestsrs with allother parameters held fixed.

Fig. 3 shows that for higher arrival rates, theresponse times suffer for both the cases, with andwithout a PCS. The ‘‘crossover probability,’’ p) ,however, decreases as the arrival rate, l, increases.Figs. 2 and 3 show that p) s0.238 when the arrivalrate is 20 requestsrs, and p) is reduced to 0.030when the arrival rate is increased to 90 requestsrs. APCS is more beneficial in the case of heavy traffic.

To reveal the relationship between the ‘‘crossoverprobability,’’ p) , and the arrival rate, we vary therates from 10 to 90 requestsrs in increments of 10requestsrs, and plot the corresponding crossoverprobability in Fig. 4. As expected, the crossoverprobability decreases as the arrival rate increases.Fig. 4 shows that crossover probability is a strictlydecreasing and a strictly concave function of thearrival rate. This implies that the benefits of in-stalling a PCS are more pronounced for heavier Webusage.

3.3. Effect of the aÕerage size of requested files, F

In Fig. 5, we plot the overall response times, Txc

and T , with respect to the cache ‘‘hit rate’’ probabil-ity when the average file size is large. The arrivalrate is 20 requestsrs and the average requested filesize equals 8750 bytes. The crossover probability,p) , is found at 0.148, implying that the overall

Fig. 4. The effect of arrival rate on crossover probability p)

Ž .Fs5000 bytes .


Fig. 5. Overall response time when average file size is largeŽ .ls20 requestsrs and Fs8750 bytes .

response time with a PCS will be smaller when theprobability that the requested files are stored in thePCS exceeds 0.148.

Fig. 6 shows the effect of the average file size onthe crossover probability where the arrival rate isheld the same at 20 requestsrs. The crossover proba-bility in Fig. 6 decreases as the average file sizeincreases, indicating that the advantage of having aproxy cache is more evident when the file size islarger. This result is rather intuitive since the reduc-tion of response time is more significant for largerfiles with a PCS. Therefore, a smaller crossover

Fig. 6. The effect of file size on the crossover probability p)

Ž .ls20 requestsrs .

Fig. 7. Effect of proxy cache server’s buffer size on overallŽ .response time ls20 requestsrs and Fs5000 bytes .

probability is needed to realize the benefit of in-stalling one.

The curve in Fig. 6 is convex and then becomesslightly concave for file size larger than 6800 bytes.The reduction of the crossover probability is moreprominent in the region of 1250–3750 bytes in Fig.6. When the average file size exceeds 3750 bytes,the ‘‘marginal’’ reduction in the crossover probabil-ity plateaus. Fig. 6 exhibits an inflection point whenfile size is around 6800 bytes.

3.4. Effect of the serÕer parameters

In the previous experiments, we tacitly assumethe PCS to be identical to the remote Web server,

Fig. 8. Effect of proxy cache server’s speed on overall responseŽ .time ls20 requestsrs and Fs5000 bytes .


Table 3The bottleneck effect of N on T in Eq. 6c xc

N Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 Term 7 Tc xc

64 kbps 0.0043 0.0021 0.6250 0.0021 0.0022 0.0130 0.0021 0.6500128 kbps 0.0043 0.0021 0.3125 0.0021 0.0022 0.0130 0.0021 0.33831.544 Mbps 0.0043 0.0021 0.0259 0.0021 0.0022 0.0130 0.0021 0.0517

and let B sB , R sR , Y sY , and I s I .xc s xc s xc s xc s

Identical servers are assumed to isolate and study theeffect of the arrival rate of requests, the average filesize, and the cache ‘‘hit rate’’ probability on theoverall response time in the presence and absence ofa PCS. It is not necessarily true, however, that thePCS is identical to the remote Web server. In thissection, we study the effect of the PCS’s parameterson the overall response time behavior. We assumethat asB rB , bsR rR sY rY , and gsxc s xc s xc s

I rI . In Fig. 7, we show the behavior of T withxc s xc

respect to a , the output buffer size ratio between thePCS and the remote Web server, while keepingbsgs1. The arrival rate is fixed at ls20 re-questsrs and the file size is kept at Fs5000 bytes.As we increase this output buffer ratio, the averageresponse time decreases. Ceteris paribus, increasingthe output buffer size of the PCS reduces the deliv-ery time of requested files.

In Fig. 8, we plot the behavior of T with respectxc

to, b , the speed ratio between the PCS and theremote Web server, keeping asgs1. As in Fig. 7,the arrival rate and the average file size remain thesame. We observe the same pattern of behavior as inFig. 7. As the speed of the PCS increases, the servicetime decreases. This leads to a reduction in theoverall response time.

The ‘‘marginal’’ decrease in the overall responsetime in the region of a)0.5 and b)0.5 becomesminimal in Figs. 7 and 8, respectively, exhibiting a‘‘diminishing rate of return’’ phenomenon. From amanagerial perspective, it may not pay to choose anoverpowerful PCS, as the marginal reduction in theoverall response time cannot be justified. This turn-ing point occurs roughly around the point where thePCS is half as powerful as the remote Web server.

We experiment with the effect of the PCS’s look-up time, I . The reduction of the overall responsexc

time, T , exhibits a linear behavior with respect toxc

the reduction of I , a straightforward result as im-xc

plied by the first term in Eq. 2.

3.5. Effect of the firm’s network bandwidth

In our experiments, the remote Web server’s net-work bandwidth is equivalent to a T1 line, N s1.544s

Mbps, while the firm’s network bandwidth is thesame as an ISDN line, N s128 kbps. Since the firmc

usually has little control on the remote Web server’snetwork bandwidth, we do not investigate the effectof N on the overall response time. Instead, we shows

the effect of the firm’s network bandwidth, N , onc

the overall response time. Again, N affects T andc xc

T in the same way. Hence, changes in the firm’snetwork bandwidth, N , will not positively or nega-c

tively affect the ‘‘relative’’ performance of the PCSas compared to the case without it. To see the‘‘bottleneck’’ effect of the firm’s network band-width, which tends to be the slowest component inboth Eqs. 2 and 3, we rearrange Eqs. 2 and 3 asfollows:Overall response time with a PCS, T :xc

I p FxcT s q qxc B R1yl I Nxc xcxc cyl1FY R qFBŽ .xc xc xc

1yp I 1ypŽ . Ž .sq q B R1yl I s s2 s yl rq2w xFY R qFBs s s

1yp F pŽ .q q ,B RN xc xcs yl2FY R qFBŽ .xc xc xc

6Ž .


Table 4The bottleneck effect of N on T in Eq. 7c

N Term 1 Term 2 Term 3 Term 4 Tc

64 kbps 0.0043 0.0051 0.0259 0.6250 0.6603128 kbps 0.0043 0.0051 0.0259 0.3125 0.34781.54 Mbps 0.0043 0.0051 0.0259 0.0259 0.0612

and overall response time without a PCS, T :

I 1sTs q B R1yl I s ss ylrq

FY R qFBŽ .s s s

F Fq q . 7Ž .

N Ns c

Tables 2 and 3 show the breakdown of all compo-nents of T in Eq. 6 and T in Eq. 7 when N isxc c

varied. Both tables demonstrate that any increase inN will decrease the overall response time to a greatc

extent, either with or without a PCS. In these experi-ments, the arrival rate of users’ requests is ls20requestsrs, the average file size equals Fs5000bytes, the ‘‘cache hit rate’’ probability p is set at0.5, and the remote Web server has the bandwidth ofa T1 line.

In both Tables 3 and 4, the bottleneck effect ofthe firm’s network bandwidth is evidenced by Nc

being the dominant terms in both tables. In fact,increasing N from 64 to 128 kbps reduces T byc xc

47.33% and T by 47.95%. Although the firm’snetwork bandwidth does not impact the decision ofwhether to install a PCS, Tables 2 and 3 indicate thatimproving it has the significant benefit of shorteningthe overall response time to users’ Web requests.

4. Concluding remarks and future research

Coincident with the World Wide Web’s taking offin recent years, the role of a PCS in improvingresponse time to Web requests has become an activeresearch area. Prior research has focused on analyz-ing or developing various cache replacement algo-rithms. We look at a more fundamental problem byexamining the impact of installing a PCS on overall

response time to Web requests. Using an analyticalqueuing model, we examine various performanceissues related to a firm’s PCS. Several factors areidentified that influence the behavior of the PCS.These factors include the arrival rate of users’ Webrequests, the average size of requested files, the‘‘cache hit rate’’ probability, the bandwidth of theLAN, and several server-specific parameters.

The major findings show that the response timedecreases as cache ‘‘hit rate’’ probability increases,for various arrival rates and different file sizes. Withhigher arrival rates or larger file sizes, the responsetime increases for both the cache and the non-cachecases, and the benefit of the PCS becomes moreprominent.

We identified a ‘‘crossover probability’’ that rep-resents the minimum cache ‘‘hit rate’’ probabilityafter which installing a PCS becomes beneficial.This probability decreases with increases in the ar-rival rate of Web requests or the requested file size.The benefits of installing a PCS were seen to bemore pronounced for heavier Web usage. Further,the marginal reduction of the crossover probabilitylevels off for larger files.

The response time decreases when the PCS has abigger output buffer, or a faster server rate. There is,however, a ‘‘diminishing rate of return’’ phe-nomenon to enhance the PCS performance. From themanager’s standpoint, it may not pay to choose anoverpowerful PCS, as the marginal reduction in theoverall response time cannot be justified.

We have not been concerned with the pros andcons of different cache replacement algorithms, norwith the freshness of the cached content. A commonpractice to diminish these issues is for the PCS tohave a reasonably large storage and to refresh the

Ž .cached content during off-peak hours e.g., nights .The queuing model used is a static model that pro-vides a snapshot of randomly fluctuating arrival pat-terns. For those types of arrivals, a transient analysiswould be more appropriate, but this is beyond thescope of this research.

There are several potentially fruitful extensions tothis work. The model assumes that the requestedfiles are, on the average, of the same size. In reality,

Ž .multimedia files audio, video and image files areŽlarger in size compared to non-multimedia files plain

.text and pure HTML . One extension would consider


two classes of files, large files and small files. Usingsimilar numerical techniques, the behavior of thePCS for handling a mixture of files of various sizescan be explored. The desired model should considerassigning higher priority to multimedia traffic. In thepresence of multimedia traffic, the variance as wellas the mean of response times should be examined.Also to be investigated is whether the PCS becomesespecially beneficial for improving the response timeas the proportion of multimedia traffic increases.

Recent literature on modeling Internet traffic re-ported that the Web traffic is usually bursty and assuch, there is some debate on how good Markovian

w xmodels are in analyzing this kind of traffic 6 . Itwould be useful to understand the behavior of thePCS given bursty arrivals that are modeled as MarkovModulated Poisson Processes. We have consideredthe case of a single PCS with a single remote Webserver, which could be extended to the case ofseveral PCSs in a serial or parallel mode. Furtherextensions would incorporate multiple proxy cachesand study the interactions and influences betweenthem, or explore the effect of ‘‘mirror’’ remote Webservers.

5. Model parameters

Žl arrival rate of requests for Web pages in.number of requests per second

ŽF the average file size of users’ requests in.bytes

ŽB the size of Web server’s output buffer ins.bytes

I total time required for the one-time initial-sŽization at the remote Web server in sec-

.ondsŽY the static server time of the Web server ins

.secondsŽR dynamic server rate of the Web server ins

.bytes per secondŽ .B the size of PCS’s output buffer in bytesxc

Ž .I the lookup time of the PCS in secondsxcŽY the static server time of the PCS in sec-xc

.ondsŽR dynamic server rate of the PCS in bytesxc

.per second

p the probability that the desired content isalready stored at the PCS

q the branching probability that the remoteWeb server can fulfill a request from theproxy cache at the first try

N server network bandwidth, the speed of thesŽserver’s connection to the Internet in bits

.per secondN client network bandwidth, the averagec

speed the client browser software receivesŽa buffer’s worth of data in bits per sec-

.ond

Acknowledgements

The authors gratefully acknowledge comments andsuggestions of Professors Ira Horowitz and GaryKoehler and two anonymous reviewers. Any remain-ing error belongs to the authors.

References

w x1 C. Aggarwal, J.L. Wolf, P.S. Yu, Caching on the WorldWide Web, IEEE Transactions on Knowledge and Data

Ž .Engineering 11 1999 94–107.w x2 V.A.F. Almeida, J.M. de Almeida, C.S. Murta, Performance

analysis of a WWW server, in: Proceedings of the 22ndInternational Conference for the Resource Management andPerformance Evaluation of Enterprise Computing Systems,San Diego, USA, December 8–13, 1996.

w x3 M.A. Arlitt, C.L. Williamson, Internet Web servers: work-load characterization and performance implications,

Ž . Ž .IEEErACM Transactions on Networking 5 5 1997 631–645, October.

w x4 M. Baentsch, L. Baum, G. Molter, S. Rothkugel, P. Sturm,Enhancing the Web’s infrastructure: from caching to replica-

Ž .tion, IEEE Internet Computing 1997 18–27, MarchrApril.w x5 S.J. Caughey, D.B. Ingham, M.C. Little, Flexible open

caching for the Web, Computer Networks and ISDN SystemsŽ .29 1997 1007–1017.

w x6 M.E. Crovella, A. Bestavros, Self-similarity in World WideWeb traffic: evidence and possible causes, IEEErACM

Ž . Ž .Transactions on Networking 5 6 1997 835–846, Decem-ber.

w x7 M. Ferelli, Like politics, all web caching should be local,Ž .Computer Technology Review 1998 1–19, April.

w x8 D. Gross, C.M. Harris, in: Fundamentals of Queuing Theory,2nd edn., Wiley, 1985.

w x9 M. Kurcewicz, W. Sylwestrzak, A. Wierzbicki, A filtering


algorithm for Web caches, Computer Networks and ISDNŽ .Systems 1998 2203–2209, November 25.

w x10 A. Luotonen, Web Proxy Servers, Prentice-Hall, 1998.w x11 L. Margherio, et al., The emerging digital economy, U.S.

ŽDepartment of Commerce Report, 1998 http:rrwww.ecom-.merce.gov .

w x12 D.A. Menasce, V.A.F. Almeida, Capacity Planning for WebPerformance: Metric, Models, and Methods, Prentice-Hall,1998.

w x13 P. Rodriguez, E.W. Biersack, Continuous multicast push ofŽ .Web documents over the Internet, IEEE Network 1998

18–31, MarchrApril.w x14 P. Scheuermann, J. Shim, R. Vingralek, A case for delay-

conscious caching of Web documents, Computer NetworksŽ .and ISDN Systems 29 1997 997–1005.

w x15 J. Shim, P. Scheuermann, R. Vingralek, Proxy cache algo-rithms: design, implementation and performance, IEEE

Ž .Transactions on Knowledge and Data Engineering 11 1999549–561.

w x16 L.P. Slothouber, A model of Web server performance, in: 5thInternational World Wide Web Conference, Paris, France,May, 1996.

w x17 R.P. Wooster, M. Abrams, Proxy caching that estimates pageload delays, Computer Networks and ISDN Systems 29Ž .1997 977–986.

Dr. Indranil Bose received his PhD from Krannert GraduateSchool of Management, Purdue University in 1997. He has re-search interests in telecommunications design and policy issues,data mining and artificial intelligence, electronic commerce, ap-plied operations research, human–computer interaction andtelemedicine. His teaching interests are in telecommunications,database management, systems analysis and design, and globalmanagement of information systems. He has had works publishedin Computers and Operations Research, and Ergonomics.

Dr. Hsing Kenneth Cheng received his PhD from William E.Simon Graduate School of Business Administration, University ofRochester in 1992. Professor Cheng teaches information technol-ogy strategy and electronic commerce. His research interestsinvolve electronic commerce, economics of information systems,and computer clustering technology. His works have appeared inComputers and Operations Research, Decision Support Systems,European Journal of Operational Research, IEICE Transactions,Journal of Business Ethics, Journal of Management InformationSystems, and Socio-Economic Planning Sciences. He also con-tributed book chapters on ‘‘Hacking, Computer Viruses, andSoftware Piracy: The Implications of Modern Computer Fraud forCorporations’’ and ‘‘The Critical Role of Information Technologyfor Employee Success in the Coming Decade.’’

Documents

Performance models of a firm's proxy cache server