Understandng te Performance of ooeratve We acng Systems Xaosong u Facuty of omuter Scence, Daouse Unversty xaosong@cs.da.ca A. Nur Zncr-eywood Facuty of omuter Scence, Daouse Unversty zncr@cs.da.ca Astract We cacng as een recognzed as an effectve sceme to aevate te servce ottenec and reduce te networ traffc, terey mnmzng te user access atency on te Internet. o maxmze te erformance of cacng, cace cooeraton systems suc as erarcca, Dstruted and yrd are emoyed. In ts wor, we frst derve an anaytca mode to cacuate te erformance arameters for te aforementoned tree cacng systems. We ten test tese systems on a we cace smuator. Resuts sow tat te yrd system s very comettve n terms of te t rato and te andwdt usage comared to te dstruted system and erarcca system, resectvey. On te oter and, te yrd system gves te otma resuts n terms of atency and te numer of os.. Introducton Wt te exosve growt of te Word Wde We wc can e consdered as a arge dstruted nformaton system, te we ecomes te domnant acaton on te Internet. Atoug te nternet acone caacty ncreases sgnfcanty eac year, te demand for andwdt st outstrs te suy as more and more nformaton servces are moved onto te We. Actuay, some of today s Internet users are sufferng two major roems: congeston and server overoadng. One osse way to aevate tese roems s We acng. In fact, we cacng s not a new tecnue snce rowser cacng and roxy cacng ave een used wdey. Researcers wor to comne te snge roxy cace nto a cooeratve cacng system to mrove te Internet erformance furter. erarcca [], dstruted [2, 3] and yrd [4] systems are some exames of testate-of-te-art cooeratve cacng mecansms. In erarcca cacng, tere are tree eves of caces: nsttutona, regona and natona eves [5]. We can treat a regona cace as te arent of some nsttutona caces and te natona cace as te arent of some regona caces. A cent can e drecty connected to any one of tese caces, wc ten ecomes te defaut cace for te cent. Wen a reuest s not satsfed y te defaut cace, t s redrected to te arent cace and te arent cace can n turn forward ts unsatsfed reuests to ts arent cace. If te document s not found at any cace eve, te natona cace contacts te orgna server drecty. Wen te document s found, eter at a cace or at te orgna server, t traves down te erarcy, and eac of te ntermedate caces aong ts at maes te decson weter a coy of te document soud e caced ocay or not, ased on te cace content udate agortm used. In dstruted cacng, tere are no ntermedate caces oter tan te nsttutona caces, wc cooerate to serve eac oters msses. In order to decde from wc nsttutona cace to retreve a mss document, nsttutona caces need oter mecansms to sare te documents tey contan. Some of tese mecansms are Inter ace Protoco IP [6], ace Array Routng Protoco [7], Summary ace [8] and ace Dgest [9]. On te oter and, wt yrd cacng, caces may cooerate wt oter caces at te same eve or at a ger eve usng dstruted cacng so tat te document s fetced from a arent/negor cace tat as te owest round tr tme (R). In ts wor, we frst deveo an anaytca mode to anayze and comare te erformance of te tree cacng systems. We try to mae our assumtons and arameters as reasonae as osse usng te current terature. en, we derve modes to cacuate te t rato, te average numer of os, and te atency exerenced y te cents. Furtermore, to confrm te mode s reasonae, we carry out severa smuatons ased on te networ used y te anaytca mode. In te foowng, secton 2 ntroduces te structure of te anaytca mode and deduces te formuae to cacuate te arameters used to evauate te erformance of te tree cacng systems. e resuts of trace-drven smuatons are ten gven n secton 3 to anayze te reaty of ts anaytca mode. Fnay, concusons are drawn and future wor s dscussed n secton 4. 2. e anaytca mode As Fg- sows, we frst mode te underyng networ system tooogy as a fu O-ary tree. In ts
mode, assume O reresents te noda outdegree of te tree, e te numer of os etween two negor eve networs (assumng te dstance of two negor routers s one o), z s te numer of ns etween te natona networ and te orgna source server, and s te eve of te tree suc tat 0 +z, were = 0 s te nsttutona networ and = +z s te orgna source. Let D I, D R and D N e te transmsson rates of te ns at te nsttutona, regona, and natona networs and D e te transmsson rate of te ns from te natona networ to te source. Moreover, t s assumed tat te nsttutona caces are assocated wt te nsttutona networ, te regona cace wt te regona networs and te natona cace wt te natona networs. s n return rovdes a system to deveo te tree aforementoned cooeratve cacng systems. Fg-: ooogy of te networ 2.. Mode descrton Denote N as te tota numer of dfferent documents reuested and P N () as te condtona roaty gven te arrva of a reuest made for document [0]. Assumng a te documents are raned n order of ter ouarty were document s te t most ouar document, P N () can e defned as P N () = W/ a were _ s a constant tat determnes ow sewed te Zf dstruton s and ts range s 0 < a. W s gven y - W = ˆ Á Ê N. Let S e te average document sze. As Ë = a [0] sows, te document sze as no strong correaton wt ts ouarty. Wt ts n mnd, we can denote te cace sze as te numer of documents caced. us, et ndcate te cace sze as te numer of documents stored, were Œ(, r, n) and, r, n are nsttutona, regona and natona caces, resectvey. Snce te we age contents are aways modfed over some tme, te caced ages ecome nvad f te od versons are stored. o ts end, reresents te average avaae tme for a caced document. 2.2. t rato anayss o mae te t rato as g as osse, we need to ee te most ouar ages n te cace. s can e fufed wt te LFU (Least Freuenty Used) reacement agortm. ere LFU s used ut t s easy to erform dervatons. Let e te t rato ganed at cace over a ts reuests. For a gven cace, te most ouar documents are caced. If a reuest s for a document n and ts nterva s ess tan, t s a t. erefore, = ( P ( ) P ) () = N were P s te roaty tat tere s a reuest for document wtn at cace. o cacuate P, et t as te tme nto te nterva [0, ] at wc a reuest occurs, and P ( t) s te roaty tat tere s a reuest for document durng te nterva [0, t] at cace. en P = Ú D D 0 ( ) P t dt -, were P ( t) = -e t were, s te average reuest rate for document at cace and, = (W/ a )[]. us, = ( / N) -a - D = a -D W / ( - e e next ssue s ow to sove. Assumng tat te art of arrva rate from te cents drecty connected to t s, we ten determne tat te aggregate reuest arrva rates at every networ eve are, c ) d (2) and for te erarcca, dstruted, and yrd systems, resectvey. For te erarcca system, te reuest rate at te eves were caces are ocated s te sum of and te art ftered y te t rato at te ower caces. At te oter eves, t s just te art ftered y te t rato at te ower caces. us te aggregate reuest arrva rate generated y te erarcca system at a n etween te eves and + s gven y O _ (- = ) 0 < c = O (-) r (- = r ) < n (- = n ) < +z were r and n are te reuest rate at te regona and natona eves resectvey. As for te dstruted system, te aggregate reuest arrva rate at a n etween eves and + ncudes two arts. e frst art s ftered y te documents aready t n any nsttutona cace eongng to te sutree rooted at eve,. e oter art s generated y reuests from te nsttutona caces out of te sutree and satsfed y te nsttutona caces n te sutree. erefore, te reuest rate etween eves and + n dstruted system s gven y 2
d = Fnay, for te yrd system, we confgure te sng caces nto grous so tat te caces can vst ter grou memers as n te dstruted system. Out of te grous, a cace can vst te ger-eve cace as te erarcca system. erefore, te reuest rate for yrd system s very smar to te erarcca system excet te ns just aove te cace eves. For te ns aove te cace eves, te reuest rate s smar to te dstruted system. us, te reuest rate etween eves and + n te yrd system s gven y (+ = )(O-2)/O = 0 O (- = ) < After deducng te formuae for cacuatng te t rato at a snge cace, we now focus on ow to cacuate te t rato over a cooeratve cacng system. For erarcca and yrd system, te reuests from dfferent eves are wt dfferent t ratos snce some can vst more caces tan te oters. Let and e te average t rato aceved at eve for te reuests from cace for te erarcca and yrd system resectvey:,œ(, r, n) were, r and n s te nsttutona, regona and natona caces n te networ system, resectvey. cacuated wt euaton (2). Let and can e and e te average t rato for reuests from cace for te erarcca and te yrd system resectvey. us, s te sum of were euas, r and n = resectvey. We can sove n te same way. Fnay, te average t rato for te erarcca and te yrd system, and resectvey, s te wegted average of t ratos for reuests from nsttutona, regona and natona caces. us, =(O =(O = +O = + = )/(O +O +) r = +O = + = )/(O +O +) On te oter and, te t rato over te dstruted system can e cacuated y modfyng euaton (2), snce caces n te dstruted system are ony at te nsttutona eve and tey can vst a oter caces, f te reuest s mssed ocay. us, a caces ecome an ntegrated arge cace and te t rato for te dstruted system D ecomes: D -a = ( O / N) - O 2 -DO I W - e 2 a / ( ) DO 2.3. os O ((- ) + ( =n )) 0 < O (- =n ) r = < +z r (+ =r )(O-2)/O = O - r (- =r ) < < n (- =n ) < +z n n I e numer of os s defned as te exected numer of ns traversed to retreve a document. For reuests from one eve, te average numer of os s te sum of te roducts of os from a cace to a cent and te roaty of te reuest accessng tat cace. Let B () and B () e te average os of te erarcca and te yrd system for te reuests from eve, Œ (0,, ), resectvey. e euatons for B () and B () can e found n []. Let B and B e te wegted average of os for reuests from dfferent eves for te erarcca and te yrd systems. B and B can ten e cacuated as te foowng: B =( O B (=0)+ O B (=)+ B (=))/(O +O +) B =( O B (=0)+ O B (=)+ B (=))/(O +O +) Snce reuests on te dstruted system can ony e generated at te nsttutona eve, average os, B D, can terefore e cacuated drecty as te foowng: B D = D /O D ( O -) + (2 + ) +(- D )(+z+) 2 -+ O = 2.4. Latency anayss Latency s referred as te tme for a reuest to e satsfed. It deends on: te numer of os, transmsson deay and ueue deay, were te ueue deay deends on te reuest rate and te rocessng caacty. For te atter two, te M/M/ ueung mode s used to do te anayss. e numer of os deends on te numer of networ ns from te cent to te cace and te roaty tat te cace may contan te vad coy of ts document. e atter s te t rato at tat cace. If we use P connectons and d as te er-o roagaton deay, te connecton tme of er-o s 4d due to te tree-way andsae. erefore, te connecton tme for te tree systems s te roduct of 4d and te average os for eac system. Let ()] e te transmsson deay of a n from eve to te eve - were Œ(c, d, ) and c, d and reresent te erarcca, te dstruted and te yrd systems, resectvey. We negect te tme of transmttng te reuest snce te sze of te reuest tsef s very sma. e M/M/ ueung teory [2] gves W =. us, to cacuate te transmsson m - deay, /m e te average document sze; S, e te n andwdt and s te acet arrva rate. en, te transmsson deay of a n from eve to te eve - ecomes: ()] = S D - S For te erarcca and te yrd system, to cacuate te average transmsson deay over te networ, 3
we frst need to cacuate te transmsson deay for te reuests from te same eve. Let ]() e te transmsson tme of te erarcca (=c), and te yrd systems (=) for te reuests from eve, Π(0,, ), resectvey. Let L e te networ eve. We defne a genera formua for cacuatng te mean transmsson deay of te reuests from eve as: ]() = (( P( L >= ) ( )]) = 0,, + P(L =+z) (L = +z)] P(L >= ) s te roaty tat a reuest as to move u ger tan or eua to te eve n order to get a coy of te reured document. P(L =+z) s te roaty tat a reuest as to move to te source server n order to get a coy of te reured document. Snce we ave deduced te formuae for t rato at cace for reuests from eve and n secton 2.2, P(L =+z) s te mss rato of te reuests from eve and P(L >= ) s te mss rato at eve L for reuests from eve. e over a average transmsson deay ], for te erarcca and te yrd system s terefore te wegted average of te transmsson deay of reuests from dfferent eves. ] = O ]( = 0) + O ]( = ) O + O + O + O + + E [ ]( = ) were _(c, ) O + O + For te dstruted system, snce a reuests are from te nsttutona eve, ts transmsson deay can e gven as te deay from te eve n te erarcca system wt te foowng euaton ]= ( P( L >= ) ( )] +P(L =+z) (L=+z)] = 0 + (( P( L <= ') ( ' )]) were = d - ' = 0 owever, comared wt te erarcca and te yrd systems, te dstruted system as one addtona art - ' = 0 (( P( L D <= ') ( ')]), ecause reuests ave to trave down to a cooeratve nsttutona cace, and terefore, resonses ave an addtona (movng-u) transmsson deay. 2.5. Vsuazaton of te anaytca mode o uanttatvey comare and contrast te erformance of te tree cacng systems, we use MALAB to ot out te fgures for t rato, os, traffc and atency of te tree cacng systems ased on te aforementoned euatons and te arameters n tae-. e resuts are sown n []. We are not ntended to sow tem ere ecause of te sace mtaton. 3. Smuaton resuts o anayze te reaty of te anaytc mode, we deveo a we cace system smuator. Because of age mtatons, detas of te smuator can e found n []. e data set s te catured og fe from te roxy of Facuty of omuter Scence, Daouse Unversty. We extract te successfu two mon get reuests as records of our data set. For eac record, we extract te URL and te document sze. e URL ncudes te at and document name so tat te document can e unuey dentfed. e data set s used on te tooogy gven n Fg- and te erformances of te tree cacng systems are comared accordng to t ratos, te numer of os, traffc generated on te networs and te atency. ae-: Parameters used for te mode and te smuaton Parameter name vaue Noda outdegree of te tree (O) 3 os etween negor caces () 2 os from te root to te source (z) 0 [3] Bandwdt at nsttuton eve (D I ) M/sec Bandwdt at regona eve (D R ) 5 M/sec Bandwdt at natona eve (D N ) 0 M/sec Average roagaton deay er o 0.004 sec Bandwdt to te source (D) 0 M/sec Average roagaton deay er o 0.004 sec Average document sze (S) 0KB[4] Reuest rate from te cents ( _ ) 2 re/sec ota document numer mon Document udate tme ( ) Sew factor of Zf dstruton 0.64 [0] Average roagaton deay er o 0.004 sec 3.. t rato As sown n Fg-2, te vaue of t ratos at dfferent cace szes ncrease ogartmcay or as a sma ower as a functon of cace sze. Wt te ncrease of te cace sze from 0.5 to 0 ercent, te t rato ncrease from 0.8 to 0.9 for te dstruted system, 0.46 to 0.7 for te erarcca system and 0.57 to 0.8 for te yrd system. Smar to te anaytca mode, smuaton resuts sow tat te dstruted system as te gest t rato wereas te erarcca system as te owest. 3.2. os 4
e average numer of os to retreve te reured documents s sown n Fg-3. Agan, te resuts are comate wt te anaytca mode. Wt te ncrease of cace sze from 0.5 to 0 ercent, te average numer of os decrease from 9.5 to 9 for te dstruted system, 9 to 5.2 for te erarcca system and 8 to 5.3 for te yrd system. e major dfference etween resuts from te smuaton and te anaytca mode s wen te cace sze s around 0.5 ercent, te average numer of os wt te erarcca system s very cose to and may exceed te dstruted system. We tn ts dfference s caused y te sma cace sze. te n to te source. Agan, smuaton resuts are smar to te anaytca mode. 3.4. Latency Fg-5 sows te average atency for te tree cacng systems. omared wt te anaytca mode, smuaton resuts for te dstruted system are a tte ger, esecay wen te data set s sma. For te erarcca and te yrd system, smuaton resuts are aso a tte ger wen te cace sze s sma. owever, wt te ncrease of te cace sze, smuaton resuts are more and more cose to te anaytca resuts and wen te cace sze s 0 ercent, resuts are amost dentca. Among te tree systems, smuaton resuts, smar to te anaytca resuts, aso sow tat te dstruted system as te gest atency wereas te yrd system as te owest. Fg-2: e t rato of te tree cace systems Fg-4: Average traffc on te tree cace systems Fg-3: e average numer of os to satsfy reuests 3.3. raffc As sown n Fg-4, traffc on te n to te source s muc ger tan te oter ns for te erarcca and te yrd systems. s confrms tat ts n s te ottenec. For te dstruted system, te traffc on te ns at te natona eve can e ger tan te traffc on Fg-5: Latency of te tree cacng systems 5
4. oncuson As t can e seen n secton 3, te smuaton and anaytca mode gve smar trends n terms of erformance factors: t ratos, numer of os, traffc generated and atency. Based on te resuts otaned ot from te anaytca mode and smuatons, te t rato of te dstruted system s very g even wen te sze of a cacng sever s very sma. s eneft soud e attruted to ts mecansm,.e. no redundant coes and a caces wor as a woe. e t rato of te erarcca system s ow f te sze of te cace server s sma. As te sze of a cace ncreases, te t rato aso ncreases ucy. e t rato of te yrd system s moderate among te tree systems. Atoug te ncreases n t ratos of te tree systems are dfferent, tey a sow a ogartmca functon or a functon wt a sma ower to te cace sze. On te oter and, atoug te t rato wt te dstruted system s g, ts are unformy dstruted over a te caces on te networ. In oter words, caced documents are usuay far from cents and tus, te average numer of os to satsfy te cents reuests are greater tan tose of te erarcca and te yrd systems excet wen te cace sze s very sma. It soud aso e noted tat te yrd system gves te est osse resuts among te tree systems snce t can aways ee te average os at a reatvey ow eve. As for traffc, te dstruted system generates more traffc at te ower networ eves. owever, as dscussed aove, ecause of ts g t rato, te dstruted system coud e wt muc ower traffc to te source server tan te erarcca and te yrd systems. In contrast, we fnd te yrd system s st very comettve. o most WWW servce users, te most mortant erformance ndcator s to e ae to retreve te reured document as ucy as osse. From ts vew ont, te yrd system as te est resut among te tree systems snce t can ee te atency aways ower tan te oter two. References [] A. anuntod et a., A erarcca nternet oject cace, n Proc. 996 USENIX ecnca onf., San Dego, A, Jan. 996 [2] D. Povey and J. arrson, A dstruted Internet cace, n Proc. 20t Austraan omuter Scence onf., Sydney, Austraa, Fe. 997. [3] R. ewar, M. Dan,. M. Dan,. Vn, and J. Kay, Beyond erarces: Desgn consderatons for dstruted cacng on te Internet, n Proc. IDS 99 onf., Austn, X, May 999. [4] M. Ranovc, J. ase, and S. Gadde, Not a ts are created eua: cooeratve roxy cacng over a wdearea networ, omuter Networs and ISDN Systems 30, 22-23,. 2253-2259, Nov. 998. [5] P. Rodrguez,. Sanner and W. Bersac, Anayss of We acng Arctectures: erarcca and Dstruted acng, n Proc. of te 4 t Internatona WWW acng Worso, 999 [6] D. Wesses and K. affy, IP and te Sud We ace, IEEE journa on seected areas n communcatona, Vo. 6, No. 3, Ar 998 [7] V. Vao and K. W. Ross, ace array routng rotoco v.0, Internet Draft <draft-vnod-car-v- 03.txt>. [8] L. Fan, P. ao, J. Ameda, and A. Z. Broder, Summary ace: A Scaae Wde-Area We ace Sarng Protoco, IEEE/AM ransactons on Networng, Vo. 8, No. 3, June 2000. [9] A. Roussov and D. Wesses, ace Dgest, n Proceedngs of 3rd Internatona WWW onference, Santa ara, Ar 997. [0] L. Bresau, P. ao, L. Fan, G. Ps and S. Sener, We aceng and Zf-e Dstrutons: Evdence and mcatons, n Proc. of te IEEE onference on omuter ommuncatons (INFOOM 99), May 999 [] X. u, Understandng te Performance of te ooeratve We acng Systems wt Anayss Modes and Smuatons, MS tess, Facuty of omuter Scence, Daouse Unversty, afax, NS, anada, tt://www.cs.da.ca/~xaosong. [2] OPNE tutora manua: M/M/ Queue utora, tt://we.ns.navy.m/~mceacen/ec3850/comuter/c omtut.df, retreved n June 2003 [3] Assessng average o count of a wde area Internet acet, tt://www.nanr.net/na/learn/wngsan.tm, retreved n Jun 2003 [4] We statstcs: sze, te average age, tt://www.centedes.com/statstcs_researc/we _statstcs.tm, retreved May, 2003 6