An Efficient Load Balancing Algorithm for P2P Systems
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- Francis Walton
- 8 years ago
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1 648 JOURNA OF OMMUNIATIONS VO 6 NO 8 NOVEMBER An Effcn oad Balancng Algorm for PP Sym Kald Ragab ompur Scnc Dp ollg of ompur Scnc and Informaon Tcnology ofuf Saud Araba abdulawab@fudua Abrac Pr-o-Pr (PP nwor ar condrd o b mo mporan dvlopmn for conn drbuon and arng nfrarucur T qualy of rvc provdd by maory of PP ym quond oad balancng among pr crcal and a y callng T papr propo a load balancng algorm bad on ocac analy I addr ou-of-da problm a a rul of nod a cang durng load movmn among nod Ind Trm Pr-o-Pr Ovrlay Nwor load balancng I INTRODUTION In rcn yar dvlopmn of drbud ym pcally nrn a bn nfluncd avly by Pr-o-Pr (PP paradgm PP a cla of applcaon a a advanag of rourc g orag cycl conn uman prnc avalabl a dg of Inrn [] PP ym offr an alrnav o uc radonal cln-rvr ym for vral applcaon doman Ty av mrgd a an nrng oluon for conn drbuon arng and locang rourc ovr Inrn In PP ym vry nod (pr of ym ac a bo cln and rvr (rvan and provd par of ovrall rourc/nformaon avalabl from ym Eac nod ofn a dffrn rourc capabl (g procor orag and bandwd [] Tu rqurd a ac nod a a load proporonal o rourc capabl On accoun of dynamm naur of PP ym dffcul o nur a load unformly drbud acro ym In parcular papr condr a PP ym of M nod n wc nod on/lav and daa ny nrd/dld connuouly Smlarly o [3] [4] [5] papr aum nod and daa ny av bn agnd dnfr a con randomly Tu r a Θ(log M mbalanc facor n numbr of daa n ord a a nod Addonally mbalanc facor bcom mor wor f PP applcaon aoca manc w daa ny ID nc ID wll Manucrp rcvd Fbruary 5 ; rvd May 5 ; accpd July 5 T auor on lav olday from An Sam Unvry aro Egyp no b unformly drbud onqunly mporan o dgn mcanm a balanc ym load Tr ar wo dnc rag o drbu ym worload [6] Fr load balancng algorm a rv o qualz worload among nod Scond load arng algorm wc mply amp o aur a no nod dl wl ob a or nod ar wang for rvc oad balancng cnqu n PP ym ould b calabl and cop w larg z Ty ould plac or r-plac ard daa n opmally among nod wl mananng an ffcn ovrlay roung abl o rdrc qur o rg nod T communcaon dlay among pr gnfcanly alr pcd prformanc of load balancng cm Du o uc dlay nformaon a a parcular pr a abou or pr a any m dad and may no accuraly rprn currn a of or pr For am raon a load n o a rcpn pr arrv a a dlayd nan In man m owvr load a of rcpn pr may av condrably cangd from wa wa nown o ranmng pr a m of load ranfr T papr propo a ocac dynamc load balancng algorm a acl ou-of-da problm T rmandr of papr organzd a follow Scon wo nroduc a urvy for load balancng algorm Scon r po propod ocac load balancng modl and algorm Evaluaon of propod a bn dcud n con four Scon fv draw a concluon of papr II OAD BAANING SURVEY oad balancng problm of mappng and rmappng worload n drbud ym A oad Balancng Dgn oad balancng dgn drmn ow nod communca and mgra load for purpo of load balancng I mov worload from avly loadd nod (ndr o lgly loadd nod (rcvr o mprov ym ovrall prformanc [5] oad balancng dgn nclud four componn a can b clafd a follow [6] [7] Tranfr polcy: I dcd wr a nod n a uabl a o parcpa n a load ranfr; r AADEMY PUBISER do:434/cm
2 JOURNA OF OMMUNIATIONS VO 6 NO 8 NOVEMBER 649 rcvr or ndr ocaon polcy: Onc ranfr polcy dcd a a nod a rcvr or ndr T locaon polcy a rponbly o fnd a uabl ndr or rcvr Slcon polcy: Onc ranfr polcy dcd a a nod a ndr lcon polcy pcf wc load ould b ranfrrd I ould a no accoun vral facor uc a load ranfr co and lf m of proc a ould b largr an load ranfr m Informaon polcy: I dcd wn and ow o collc ym a nformaon oad balancng dgn ar cagorzd no ac and dynamc W a ac load balancng cm load ar card from ndr o rcvr roug drmnc pl Sac cm ar mpl o mplmn and ay o acv w lg ovrad [3] Ty prform prfcly n omognou ym wr all nod ar almo am and all load ar am a wll On or and dynamc load balancng cm ma dcon bad on currn au nformaon [5] Accordngly ranfr polcy a cran nod dcd o b a ndr or rcvr lcon polcy lc load o b ranfrrd T dynamc load balancng cm prform ffcnly wn nod av rognou load and rourc T ypcal arccur of dynamc load balancng cm can b clafd no cnralzd drbud and opologcal In a cnralzd cm a cnral rvr coordnaor rcv load rpor from or nod wl ovrloadd nod rqu coordnaor o fnd undrloadd nod [7] In drbud arccur ac nod a a global or paral vw of ym au onqunly ranfr polcy a ac nod can locally dcd o ranfr a load r ou from (ndr-nad or no (rcvr-nad [8] Tn locaon polcy a ac nod prob a lmd numbr of nod o fnd a uabl rcvr or ndr P Krugr [9] propod ymmrcally-nad adapv locaon polcy a u nformaon gard durng prvou arc n ordr o p rac of rcn a of ac nod n ym I fnd a uabl rcvr wn a avly-loadd nod w o nd a load ou and fnd a uabl ndr wn a lglyloadd nod w o rcv a load Fnally n a ym w larg numbr of nod a opologcal cm ould b ud [] I paron nod no group T load balanc prformd n ac group fr n a global load balanc among group wll b prformd owvr nod n rarccal arccur [] ar organzd no a r Innr nod gar au nformaon of ub-r Tn load balancng prformd lav o roo of r B PP oad Balancng oad balancng a crcal u for ffcn opraon of PP ym Rcnly aracd muc anon n rarc communy pcally n drbud ad abl (DT bad PP ym Nampac balancng rugglng o balanc load acro nod by nurng a ac nod rponbl for a balancd nampac T vald only undr aumpon of unform worload and unform nod capacy Orw r a Θ(log M mbalanc facor n numbr of obc ord a a nod To mga mbalanc wo cagor nod placmn and obc-placmn load balancng cnqu wr propod In nod placmn cnqu nod can b placd or rplacd n locaon w avy load For ampl a nod n Mrcury load balancng mcanm [7] abl o dc a lgly loadd rang and mov r f ovrloadd In obc placmn cnqu obc ar placd a lgly loadd nod r wn y ar nrd no ym [] or roug dynamc load balancng cm bad on vrual rvr (VS concp [8] wo plc dfnon and u for load balanc wa propod by Godfry al [9] and Rao al [] In [8] a vrual rvr rprn a pr n DT; a orag of daa m In addon roung a plac a vrual rvr lvl rar an a pycal nod lvl Eac pycal nod a a pool of VS a n n fgur oad balancng could b acvd by mgrang VS from avly loadd pycal nod o lgly loadd pycal nod On man advanag of ung VS for balancng load a approac do no rqur any cang o undrlyng DT In fac ranfr of a vrual rvr can b mplmnd mply a a pr lavng and pr onng ym In [] Rao al propod r mpl and ac load balancng cm: on-oon on-o-many and many-o-many Godfry al combn bo on-o-many and many-o-many cm and u m n dffrn cnaro [9] lurd VS cm prnd n [] a opmzd bac VS framwor o rduc ovrad nvolvd n VS framwor owvr VS canno b movd and rfor cm canno rpond o dynamc cang n nwor condon T papr focu on dgn and analy of PP load balancng algorm bad on ocac analy [3 4] and bad on VS concp [8] allng: PP oad Balancng oad balancng cnqu n PP ym ar facng callng comng from caracrc of ym Fr z of PP ym larg a man a calabl load balancng cnqu rqurd Scond dmlar o radonal ym nod of a PP ym ar no rplca and rqu canno b cud n any nod If nod av dad naccura nformaon abou a of or nod du o random communcaon dlay bwn nod n could rul n unncary prodc cang of load among m For ampl an ovrloadd nod rmov AADEMY PUBISER
![oad balancng dgn ar cagorzd no ac and dynamc W a ac load balancng cm load ar card from ndr o rcvr roug drmnc pl Sac cm ar mpl o mplmn and ay o acv w lg ovrad [3] Ty prform prfcly n omognou ym wr all](/docs-images/53/11861143/images/page_2.jpg "nod ar almo am and all load ar am a wll On or and dynamc load balancng cm ma dcon bad on currn au nformaon [5] Accordngly ranfr polcy a cran nod dcd o b a ndr or rcvr lcon polcy lc load o b ranfrrd T")
3 65 JOURNA OF OMMUNIATIONS VO 6 NO 8 NOVEMBER om of vrual rvr owvr uc mpl dlon wll cau problm of load rang for rmovd vrual rvr may ma or nod ovrloadd onqunly papr propo a ocac PP load balancng algorm a appromaly drmn mnmum amoun of m o cang nod a from ovrloadd o undrloadd and vc-vra omparng a m w rqurd m o mgra vrual rvr nabl u o com o a carful dcon Accordngly propod algorm undoubdly avod load rang To b of auor nowldg r no any load balancng algorm for PP ym bad upon followng ocac analy III OAD SARING AGORITM A Modl T papr condr a PP ym conng of M pycal nod (pr dnod by P M Eac pr can b modld a a quung ym uc a M/M/ M/D/ c Eac pycal nod P a a capacy a corrpond o mamum amoun of load a can proc pr un of m Nod cra vrual rvr (VS wc on PP nwor Trfor can own mulpl nonconguou poron of DT dnfr pac Eac vrual rvr parcpa n DT a a ngl nry (g roung abl Morovr ac vrual rvr or daa m wo ID fall no rponbl rgon of DT dnfr pac A n n fg a nod P mg av n VS v v v n ; wr n VSz Eac v a load l ; (for n T load of pr P n a un of m l +l + +l n T ulzaon of a nod P / From prpcv of load balancng a vrual rvr rprn cran amoun of load (g load gnrad by rvng rqu of daa m wo ID fall no rponbl rgon [5] To avod flucuaon n worload nod ould opra blow r capacy If a nod fnd lf rcvng mor load an uppr arg load U ( ( / >U condr lf ovrloadd A nod P alo a load l an condrd o b undrloadd An ovrloadd nod no abl o or obc gvn o rou pac or carry ou compuaon dpndng on applcaon Dfnon A nod P n on of followng a a follow Undrload d f Q < S Normal f Q U Ovrloadd f U < Q larly a pac Q con of non-ngav ngr ub-dvdd no r don rgon [ [U] and (U corrpondng o undrloadd normal and ovrloadd a rpcvly oad rang a condon wn load balancng algorm ngagd n movng vrual rvr bac and for bwn nod Fgur Nod load pcfcaon A PP ym dfnd o b balancd f um of load of a pycal nod P mallr an or qual o arg load of nod for vry nod P M n ym Wn ym mbalancd goal of a load balancng algorm o mov VS from ovrloadd nod o undrloadd on w mnmum load ranfr ovrad T amoun of ovrload o b ranfrrd from ovrloadd nod P ; M a random varabl dnod by A gvn by Q U f Q > U A( p ma( Q U } Orw Smlarly amoun of undrload a can b accpd a undrloadd pr P ; M a random varabl dnod by B gvn by Q f Q < B ( p ma( Q } Orw Dfnon {Q( ; } b a aonary ocac proc w a pac conng of non-ngav ngr S and S b wo dnc non-ngav numbr T Fr Paag Tm (FPT bwn a S and S dnod by FPT(S S gvn by nf { ; Q( S Q( S } f S S FPT ( S S f S S I a random varabl wc maur mnmum amoun of m ndd o rac a S from a S W no a bcau am ocac proc Q( aonary ranlang abov vn by a fd amoun of m a no ffc upon probably drbuon of FPT(S S In fac a fr paag m from a S o a S can b dvdd no wo par namly fr ranon ou of a S (ay S followd by fr paag from S o S Aum a <; nc cang of a av un magnud n a br and da of load n FPT FPT + FPT < < ; + + -u FPT FPT ( Smlarly f > FPT FPT + < + > ( A aonary ocac proc a propry a on drbuon don no dpnd on m orgn T ocac proc {Q(; I} calld aonary f I and + I ( any pov ngr n {Q( Q( } and {Q( + Q( +} av am on drbuon [] AADEMY PUBISER
4 JOURNA OF OMMUNIATIONS VO 6 NO 8 NOVEMBER 65 ( P{FPT } and condrng a ummand n bo quaon ( and ( ar ndpndn Tu f w apply aplac ranformr for + ( ( n w can ow a: ( + ; < ( Upward (3 ( + ; > ( Downward (4 larly drbuon of fr paag m of un downward ndpndn of arng a wl drbuon of fr paag m of un upward dpnd upon arng a B oad Sarng Edg T am of con o udy FPT of ranon from normal a o ovrloadd ovrloadd o normal undrloadd o normal c For ac ranfr par FPT wll b compud o prdca fuur bavor of ranfr par bfor load ranfr ( vrual rvr mgraon dcon an Dfnon 3 [Q( R(] b a ranfr par w Q(X and R(Y wr X>U and Y< T oad Sarng Edg SE bwn Q and R a random varabl E(XY wc dfnd a follow: E(XY mn {FPT(XU FPT(Y} Wr FPT(XU fr paag m o mov from a X o a U and FPT(Y fr paag m o mov from a Y o a SE prod of m wn wc ovrloadd nod mu compl ranfrrng load o undrloadd nod bfor ovrloadd nod dnf a unncary o ranfr load or undrloadd nod bcom nlgbl o rcv a ranfrrd load Aum load ranfr m dnod by I m ndd o pacag and nd load ( la loadd vrual rvr a wll rla ovrload o n R Tu load ranfr mu b nad only f SE > Snc SE a random varabl w nd o formula ranfr crron n rm of probabl Aum probably a SE cd P{E(XY > } Trfor load ranfr mu b nad f P{E(XY > } larg T condraon ld o formulaon of a cla of rul o calld Quanl rul T quanl of a probably drbuon funcon dfnd a follow: Dfnon 4 F( b probably drbuon funcon of a non-ngav random varabl X << T - quanl of F a non-ngav ral numbr q afyng F ( q P{ X q } From dfnon 4 -quanl rul for load ranfr wa nroducd Dfnon 5 Gvn a ranfr par [Q( R(] and a load ranfr m Alo for << l q b -quanl of probably drbuon of SE bwn Q( and R( Tn load ranfr nad only f q > T propod algorm n papr u a -quanl rul bfor ranfrrng load and nur a P{E(XY } In gnral can b an 9 or larg T probably drbuon of random valu SE gvn a follow P ( ; X Y P{ E ( X Y } for Tu probably drbuon funcon of load arng dg SE bwn par Q( and R( gvn by P ( ; X Y [ F ( ; X U ] [ G ( ; Y ] Wr F(; XU and G(; Y ar probably drbuon of fr paag m from X o U and from Y o n quu {Q(} {R(} rpcvly Eac nod modld a M/M/ quu n wc proc arrv accordng o a Poon proc w man arrval ra n procd w ponnal rvc m [3 4] and w man rvc ra µ mma Aum conan br ra and da ra µµ µ n probably drbuon funcon + ( ( FPT + m a lap bfor cumulav numbr of da fr cd cumulav numbr of br wn X(+ Alo valu of + ( do no dpnd on X( [3 4] mma T aplac-sl ranform of probably drbuon funcon of fr paag m from a o a n an M/M/ quu + ( + 4µ (5 Aum a fr paag m FPT can b prd a FPT + f X ( + FPT S + FPT f X ( Wr S m of fr ranon Aum a ( P{FPT } a wll FPT can b upward or downward afr fr ranon S Ung orm 4-7 [3 4] ( can b prd a follow + µ + ( d+ µ ( ( d ( Tang aplac-sl ranform on bo d of quaon ( and u convoluon propry n followng quaon can b oband: + ( + Tu AADEMY PUBISER
![normal undrloadd o normal c For ac ranfr par FPT wll b compud o prdca fuur bavor of ranfr par bfor load ranfr ( vrual rvr mgraon dcon an Dfnon 3 [Q( R(] b a ranfr par w Q(X and R(Y wr X>U and Y< T](/docs-images/53/11861143/images/page_4.jpg "oad Sarng Edg SE bwn Q and R a random varabl E(XY wc dfnd a follow: E(XY mn {FPT(XU FPT(Y} Wr FPT(XU fr paag m o mov from a X o a U and FPT(Y fr paag m o mov from a Y o a SE prod of m wn wc ovrloadd")
5 65 JOURNA OF OMMUNIATIONS VO 6 NO 8 NOVEMBER S and ( + From lmma µµ and from quaon (4 + ; > Tu ( from quaon ( w oban followng quadrac quaon [ ( ] ( + ( (v Equaon (v a wo oluon w condr oluon wc af a ( + ( + 4µ for ral ( ; nc K + ( + [ ] 4µ orollary T dny funcon of fr paag m from a o a n an M/M/ quu / +µ µ / ( I µ (6 o For > m; wr I Modfd Bl funcon of ordr If quaon (5 bona fd aplac ranform aplac ranform of ( [3 and 4] From aplac ranform { c f ( } f ( + c ; ( c and w ( + ; So w can wr quaon (5 a w w 4µ [3 4] ( w Wl aplac ranformaon + + a { I ( a/ } [3] n w can ay a a numraor aplac ranform of / µ / I ( µ / ; u aplac ranform of quaon (5 So w av nc o ( µ ( µ / o ( I ( µ / µ / +µ ( I ; > mma 3 (Downward T probably drbuon of fr paag m form a o a n an M/M/ quu : n µ ( ; µ Γ ( n + n + n ( (7 Wr Γ ncompl Gama funcon Aum a modfd Bl funcon of ordr I ( n ( / 4 n ; n!( n +! S µ Tu I ( µ µ n n ( µ ; n!( n +! By ubu no quaon (6 w can compu dny funcon a follow: o ( µ n + n ( o ( µ ; n n!( n +! From dfnon of probably drbuon funcon w av and ( ( d ( d ( n + n Tu ( µ ( µ d + n n!( n! If w cang nfn um and ngral w g n ( µ + n ( d ; Γ( d n n!( n +! nc n µ ( ; µ Γ ( n + n + n ( mma 4 T probably dny funcon of fr paag m of M/M/ quu from a o a ( + ( r + no rvc µ and For ( + mplcy nc ; + nc FPT By compung nvr of aplac ranformaon w g: ( mma 5 (Upward T probably drbuon funcon of fr paag m of M/M/ quu from a o a ; < ( + (8 wr ( r r ; ar dnc roo of polynomal of dgr dfnd rcurvly a: D ( D ( ; D ( + D ( ( + D ( µ D ( ; alo for D ( ( + r D ( r In lmma 4 w av prov a + aplac ranformaon of probably drbuon of fr paag m of FPT Aum a + S + + µ µ µ + + AADEMY PUBISER
![ranform of ( [3 and 4] From aplac ranform { c f ( } f ( + c ; ( c and w ( + ; So w can wr quaon (5 a w w 4µ [3 4] ( w Wl aplac ranformaon + + a { I ( a/ } [3] n w can ay a a numraor aplac ranform of](/docs-images/53/11861143/images/page_5.jpg "/ µ / I ( µ / ; u aplac ranform of quaon (5 So w av nc o ( µ ( µ / o ( I ( µ / µ / +µ ( I ; > mma 3 (Downward T probably drbuon of fr paag m form a o a n an M/M/ quu : n µ ( ; µ Γ ( n + n + n ( (7 Wr")
6 JOURNA OF OMMUNIATIONS VO 6 NO 8 NOVEMBER ( + + Bu + + ( nc FPT + K+ + ( + ( nc ( + ( + + [ µ ( ( ] Ung mamacal nducon w can prov a quaon ( afd for all I can b rwrn a rao of wo funcon N ( and D ( T funcon can b dfnd a follow: ( ( M ( µ Tu N ( > ; [ ( ] M ( ; Wr D ( a polynomal of dgr ; Tu quaon ( can b rwrn a follow: N( + µ Bu for gnral ranon from a o a : Tu w can oban aplac ranform of dny of upward ranon from a o a by canclng common rm from D ( dnomnaor and numraor from abov quaon From dfnon T [ ]( u T ( d ( D ( D ( I a rlaon funcon n wc numraor polynomal a dgr I wl dnomnaor polynomal a dgr (+ and ( < Tu w can pand no a fn um of paral fracon a follow: If for all and > n zro canno b a roo of ; and can b wrn n followng form: D ( ( + r ( + r ( + r wr r for all o ar roo of D ( nc can b wrn a + follow: ( + r Wr ; and ( + r r ( ( + ( + r Accordngly w can nvr aplac Tranform of abov quaon Bu ac rm n rg and d n form Wr α ar conan ( + α α Eac rm a nvr aplac ranformaon nc ( + ( r α Torm [Q( R(] b a ranfr par a con of M/M/ quu m b amoun of ovrload and n amoun of undrload Tn probably drbuon funcon of oad Sarng Edg (SE ( µ ( n m r P ( ; m n m µ Γ + m wr r ; ar roo of polynomal dfnd rcurvly a ; ; + ( + µ ; ; Alo for n ( + r r ( n + m T ranfr par a probably drbuon funcon P ( ; of SE; > U < wc dfnd by P ( ; [ F ( ; U ]]*[ G ( ; ] wr m amoun of ovrload (m -U and n amoun of undrload (n - n P ( ; m n [ F ( ; m] ]*[ G ( ; n ] for an M/M/ quu ca F(m and G( -n av bn drvd from 3 and 5 rpcvly nc n m r µ P ( ; m n m µ Γ( n + m + m Du o nfn numbr of rm n probably drbuon ( ; m n of SE n M/M/ followng P lmma wll drv a formula for SE a fn numbr of rm a follow mma 6 For a ranfr par [Q( R(] w an amoun of ovrload m and an amoun of undrload n Man oad Sarng Edg MSE(m n n MSE ( m n F ( r m r wr r r r ar conan dfnd n prvou orm Alo m + ( + 4µ Fm Snc P ( ; m n [ F( ; m] ] [ G( ; n ] w oban AADEMY PUBISER
7 654 JOURNA OF OMMUNIATIONS VO 6 NO 8 NOVEMBER MSE ( m n From lmma 5 w g n MSE ( m n P ( ; m n d [ F ( ; m] ] [ G( ; n ]d Bu aplac ranform T [ α q ]( r T [ q ]( + α [ F ( ; m ]d T [ q]( q( S S α r n d and n MSE ( m n F ( r m r onqunly a bn obrvd a for quung modl n wc ob arrval and procng ra ar ndpndn of quu z uc a M/M/ quu T drbuon of SE dpnd only on amoun of undrload and ovrload T followng algorm wll u numrc valu of gvn man load arng dg formula a bad upon followng m n µ µ q paramr Algorm T con nroduc propod load balancng algorm bad upon abov analy Prodcally vry T cond ac ovrloadd pr ranfr cd load o undrlaodd pr ( ndrnad algorm T algorm mpo a -quanl rul for ranfrrng load For ac par ( µ a corrpondng -quanl ould b drmnd wl mu b an 9 or larg T algorm own n followng cnaro: T ovrloadd nod S cra a uabl doman (group D from ngbor nod o pr S Eac nod blong o D af D {S ; P(FPT > 9 and } Wr rqurd communcaon dlay o nd a mag form nod S o S plu rqurd m o rply w load ranfr of cran vrual rvr from S o S Alo FPT fr paag m of nod S o ranfr from ovrloadd a o normal or undrloadd a D an ordrd w rpc o communcaon I mplmnd a an ordr lnd l Tu S nd a broadca mag o all nod blongng o doamn D Nod S mu rcv a rply from all nod blongng o D wn FPT m 3 Nod S lc an undrlaodd nod S D wr man load arng dg MSE bwn S and S f q > n ranfr load (vrual rvr from S o S Wr par and µ ar gvn m ndd o ranfr load l an or qual o A(S 9 or larg 4 Rpa p 3 for ac undrloadd nod S blongng o D wnvr FPT prod don run ou y oad_balanc(s T {// Evry prod T cond S cc load // ump abov uppr load U // I ould do followng ra(d S ; // cra doman of ngbor Wl ( q > do } {// rpa followng wn a prod IV EVAUATION T papr mplmn an vn-bad mulaon o valua propod load balancng algorm I u vral paramr a follow: dfaul numbr of vrual rvr pr nod ( numbr of nod (496 ym ulzaon (8 Obc arrval ra (Poon w man arrval m c avrag numbr of obc ( mllon and prodc load balancng prod (T6 cond T mulaon valua followng mrc oad Movmn Rao (MR dfnd a oal movmn co ncurrd du o load balancng dvdd by oal co of movng all obc n ym a onc In ca valu of MR nfr a balancr conum abou % of bandwd o nr obc T nod arrval ra modld by a Poon proc and lfm of a nod drawn from an ponnal drbuon T mulaon ran w wo nr-arrval m and 6 cond f ady-a numbr of nod n ym o 496 nod Fg plo MR mrc a a funcon of ym ulzaon o udy load movd by propod load balancng algorm a a fracon of load movd by undrlyng DT du o nod arrval and dparur Fg dmonra a load movd by propod load balancng algorm gnfcanly mallr an load movd by undrlyng DT pcally for mall ym ulzaon In addon fg ow a MR w nod nr-arrval m c largr an w nod nr-arrval m 6 c Fg 3 vrf prcpon a ncrang numbr of vrual rvr dcra condrably fracon of load movd by undrlyng DT Fg 4 dmonra a ncrang q Slc S D ; // lc from ordr D D D \ {S } If ( q > n ranfr_load(s S ; } ranfr_load (S S { If!(Ovrloadd n rurn; //Sndr-nad If (S VSz > n oo v S VS uc a: a Tranfr v o S wll no ovrlaod S b v la loadd vrual rvr a wll rla ovrload Falng a l v b mo loadd VS Rurn vrual rvr ragnmn } AADEMY PUBISER
8 JOURNA OF OMMUNIATIONS VO 6 NO 8 NOVEMBER 655 numbr of vrual rvr pr nod a load balanc a g ym ulzaon and gran ffcn load movmn du o low bandwd lo Fg 5 plo 9-quanl of load arng dg (SE w ym ulzaon wn ovrload 5 a ourc nod and undrload a dnaon nod I dmonra a 9-quanl of SE nd o b mallr a ym ulzaon ncra A n from fg 5 9quanl of SE 994m u load can b ranfrrd only f <994m In addon ncrang numbr of vrual rvr rduc gnfcanly 9quanl a lp n avodng load rang V ONUSION Fgur 4 Bandwd lo v ym ulzaon w dffrn numbr of vrual rvr pr nod oad balancng among pr crcal and a y callng n pr-o-pr ym T papr b a ocac analy a avod load rang and acl ou-of-da problm du o pr a cang durng load movmn (vrual rvr mgraon Tn propo a load balancng algorm bad on a ocac analy An ffcn mulaon a bn carrd ou a dmonra ffcvn of propod load balancng algorm Fgur 5 9-quanl of SE v ym ulzaon w dffrn numbr of vrual rvr pr nod REFERENES Fgur MR v ym ulzaon w wo nod arrval m Fgur 3 MR v numbr of vrual rvr w wo nod arrval m AADEMY PUBISER [] Sry Modrn PP Dfnon p://www opnppcom/pub/a/pp///4/rywappml [] S Sarou al A Maurmn udy of Pr-o-Pr arng ym Proc Mulmda ompung and Nworng onf (MMN [3] I Soca al ord: A calabl pr-o-pr looup rvc for Inrn Applcaon AM SIGOMM Augu pp 49-6 [4] Anony Rowron and Pr Drucl Pary: Scalabl drbud obc locaon and roung for larg-cal Pr-o-Pr ym n Proc Mddlwar [5] S Ranaamy al A Scalabl onn- Addrabl Nwor n Proc AM SIGOMM alforna USA [6] Dr I al Adapv load arng n omognou drbud ym IEEE Tran on Sof Eng Vol No 5 Sp 986 [7] A R Baramb al Mrcury: upporng calabl mul-arbu rang qur In Proc of onf on Applcaon Tcnolog Arccur and Proocol For ompur ommuncaon AM Nw Yor4 [8] Fran Dab al Wd-ara cooprav orag w FS Proc 8 AM Symp Oprang Sym Prncpl (SOSP pp -5 Oc [9] Godfry al oad balancng n dynamc rucurd PP ym Proc IEEE INFOOM 4 [] J Byr Smpl load balancng for drbud a abl Proc Of nd In Worop on Pr-o-pr ym (IPTPS 3 Fb 3
9 656 JOURNA OF OMMUNIATIONS VO 6 NO 8 NOVEMBER [] A Rao al oad balancng n rucurd PP ym Proc Of nd In Worop on Pr-o-pr ym (IPTPS 3 Fb 3 [] PBGodfry and I Soca rogny and oad balanc n drbud a abl Proc IEEE INFOOM 5 [3] J ao Kamda A dcompoon algorm for opmal ac load balancng n Tr rarcy nwor confguraon IEEE Tran On Paralll and Drbud Sym Vol 5 No5 994 [4] T aavan and JG Kul A aonomy of cdulng n gnral-purpo drbud compung ym IEEE Tran on Sofwar Engnrng vol 4 no pp 4-54 Fb 988 [5] N G Svarar al oad drbung for locally drbud ym ompur vol5 no pp33-44 Dc 99 [6] Gocn A Drbud Oprang Sym: T logcal dgn Addon-Wly 99 [7] S Zou A Trac-Drvn Smulaon Sudy of Dynamc oad Balancng IEEE Tranacon on Sofwar Engnrng vol 4 no 9 pp Sp 988 [8] D Eagr al A comparon of rcvr-nad and ndr-nad adapv load arng SIGMETRIS Prformanc Evaluaon Rvw 3 Aug 985 [9] P Krugr and N G Svarar Adapv locaon polc for global cdul IEEE Sof Eng Vol Jun 994 [] S Zou al Uopa: a load arng facly for larg rognou drbud compur ym Sofwar- Pracc and Eprnc Dc 993 pp [] S P Dandamud and K o A rarccal oad Sarng Polcy for Drbud Sym n Proc of 5 In Worop on Modlng Analy and Smulaon of ompur and Tlcommuncaon Sym MASOTS IEEE S Wangon D 997 [] yman Danl P Socac modl n opraon rarc vol I MGraw-ll Inc 98 [3] a obay Modlng and Analy: An Inroducon o ym prformanc valuaon modology Addon-Wdly 978 [4] a obay al Sym modlng and analy: foundaon of ym prformanc valuaon Prnc all 9 [5] Zu Y and u Y Effcn Promy-awar oad Balancng for DT-bad PP Sym IEEE Tran On Paralll and Drbud Sym Vol 6 No 4 5 Kald Ragab an aan profor a Dparmn of ompur Scnc ollg of ompur and Informaon Tcnology Kng Faal Unvry Saud Araba Morovr on lav aan profor of ompur Scnc a Dparmn of Mamac ompur Scnc dvon An Sam Unvry ond Dparmn of ompur Scnc Toyo Unvry n 5 a podocoral poon wa born n 968 and rcvd BSc MSc dgr n ompur Scnc from An Sam Unvry aro Egyp n rpcvly and PD dgr n ompur Scnc from Toyo Inu of Tcnology n 4 a word n An Sam Unvry aro Egyp n a aan lcurr a word a rarc cn n ompur Scnc Dp Tcncal Unvry of mnz Grmany n 999- rarc nr nclud auonomou dcnralzd ym Pr-o-Pr Sym Ovrlay Nwor oad Balancng Wb-rvc and applcaon-lvl mulca AADEMY PUBISER
![gnral-purpo drbud compung ym IEEE Tran on Sofwar Engnrng vol 4 no pp 4-54 Fb 988 [5] N G Svarar al oad drbung for locally drbud ym ompur vol5 no pp33-44 Dc 99 [6] Gocn A Drbud Oprang Sym: T logcal](/docs-images/53/11861143/images/page_9.jpg "dgn Addon-Wly 99 [7] S Zou A Trac-Drvn Smulaon Sudy of Dynamc oad Balancng IEEE Tranacon on Sofwar Engnrng vol 4 no 9 pp 37-34 Sp 988 [8] D Eagr al A comparon of rcvr-nad and ndr-nad adapv load arng")
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