An Efficient IP Based Approach for Multicast Routing Optimisation in Multi-homing Environments

Transcription

1 An Effcen IP Based Appoach fo Mulcas Roung Opmsaon n Mul-homng Envonmens N. Wang, G. Pavlou Unvesy of uey Guldfod, uey, U.K. {N.Wang, G.Pavlou}@suey.ac.uk Absac- In hs pape we addess he opmsaon poblem of jon na- and ne-doman mulcas oung n mul-homng envonmens, a opc ha has no eceved much aenon unl now. Insead of focusng on he adonal ene ee based mulcas oung opmsaon, we consde plan IP based appoaches n whch oung s conolled hough opmsed mul-opology-awae IGP/BGP confguaons. The benef s ha no dedcaed MPL unnellng s equed fo mulcas affc delvey acoss mulple domans. In hs pape we popose a se of heusc algohms fo he fomulaed mul-objecve opmsaon poblem consdeng boh na- and ne-doman opeaon. Though ou smulaon expemens, we show ha he poposed schemes acheve sgnfcan mpovemen n he elevan pefomance compaed o convenonal appoaches. also makes unnecessay o compue a ene ee acoss mulple domans. If we assume ha A3 ams a mnmsng endo-end laency nsead of consevng bandwdh esouces, hen he shoes A-pah oung shown n Fgue (b s obvously a bee soluon. Fom hs example, we can see ha hee s no ncenve fo ndvdual newok povdes o jonly compue a global ene ee acoss mulple domans as hs mgh no mee he own equemens. -access oue -coe oue - bode oue s A s A I. INTRODUCTION Today, Inene Newok Povdes (INPs who offe mulcas sevces ae facng he challengng ask of effcenly delveng mulcas affc boh whn and acoss he newoks. Tadonally, mulcas oung opmsaon has been fomulaed as he well-known ene ee poblem, wh he majo objecve o delve mulcas affc wh leas cos, e.g., by consumng mnmum bandwdh esouces. Neveheless, we ague ha hs poblem fomulaon can be only appled o he na-doman scenao, as compung a global ene ee fo ne-doman mulcas affc s geneally nehe necessay no vable n pacce. Fs, compung such a dsbuon ee eques he knowledge of boh he oue-level newok opology and goup membeshp acoss mulple domans. Unfounaely, ndvdual INPs do no nomally elease elevan nfomaon o he pees who ae poenal busness vals, due o pvacy easons. Moeove, a global ene ee does no always bng benefs o all he nvolved domans. In Fg. (a a global opmal ee n ems of hop couns (shown n hck lnes s shown acoss hee domans, wh he souce s esdng n A and hee eceves dsbued n A2 and A3. We noce ha, alhough he mulcas ee consumes mnmum bandwdh esouces (9 newok lnks n oal, no all sub-ees whn ndvdual domans ae opmal n ems of bandwdh consevaon. Fo example, n Fg. (b ha shows a global sub-opmal ee, he sub-ee n A2 uses only 3 newok lnks ohe han 4 n s counepa consung he global opmal ee. On he ohe hand, he heeogeney n he objecves of opmsng mulcas oung A2 A3 A2 (a (b Fgue Ine-doman mulcas ee consucon In hs pape, we focus on mulcas oung acoss mulple domans, no necessaly o compue a global ene ee, bu o opmse mulcas oung fo ndvdual INPs affc engneeng (TE objecves. In hs pape, we consde wo ypcal objecves: ( na-doman bandwdh consevaon and (2 load balancng acoss ne-doman lnks connecng wh adjacen domans. The fs objecve nhes he adonal popey of ene ees, and he second one s based on he ecen obsevaon ha a sgnfcan popoon of Inene congeson comes fom he ho spos on ne-doman lnks beween INPs [3]. Ths s because many INPs end o ovepovson he coe newoks, whle bandwdh esouces on ne-doman lnks ae ahe scace. Mul-homng, whch s vey popula n oday s Inene, offes INPs hghe obusness and moe powe fo load balancng. By akng one sngle goup as an example, Fg. 2 llusaes how mul-homed doman R can pefom mulcas affc opmsaon hough boh ne- and na-doman oung. In he fgue, he goup souce s s locaed n he emoe doman whose aggegaed IP addess pefx s denfed by P. Accodng o A3

2 doman R, P can be eached hough some of s adjacen domans (namely N N, specfcally va mulcas-awae bode oues (M-ABRs b o b k. In hs case, he affc opmsaon fo doman R s wo fold: ( To decde whch M- ABR o ac as he bes ngess pon fo he mulcas affc comng fom s, and (2 how o confgue na-doman oung o opmally delve he affc fom ha ngess M-ABR o ndvdual eceves. In hs pape, we consde small o medum szed INPs and also assume ha all mulcas eceves ae sac local hoss whose locaons ae aleady known. A ypcal example of hs case s sub domans. In ou fuue wok we wll consde scenaos whee mulcas ee leaves no only nclude local goup membes, bu also M-ABRs ha lead o emoe eceves (e.g., doman N. In hs case, he sevce ageemen beween INPs may povde nfomaon on emoe eceves. N s Doman (Ps b Doman R Fgue 2 Mulcas opmsaon n a mul-homng envonmen A salen novely of ou poposed scheme s ha, soluons based on dec mulcas pah selecon heuscs ae abandoned, as hey need explc oung funconales, e.g., usng MPL. Whle MPL s a poweful echnology fo ceang ovelay unnels o suppo any specfc oung saegy, s also expensve and suffes poenally fom scalably poblem n ems of LP sae manenance. In hs pape, we adop plan IP oung poocols fo enfocng opmal mulcas oung whou seng up dedcaed pon-o-mulpon (P2MP LPs. pecfcally, mul-opology exensons o IGPs (M-IGP [9,0] and mul-poocol BGP (M-BGP [2] ae manpulaed fo nfluencng na- and ne-doman mulcas pah selecons especvely. These poocol exensons allow us o decouple he mulcas pah selecon fom he defaul uncas oung. Dealed descpon on hs appoach wll be povded n secon III. The advanage of hs plan IP based soluon s obvous: he hgh expense and complexy n seng up P2MP LPs acoss mulple domans can be avoded. Hence, we egad he poposed scheme as an effcen and scalable soluon o ackle ne-doman mulcas oung opmsaon. bk N II. BACKGROUND We sa fom uncas oung opmsaon. In he leaue, opmsng IGP lnk weghs [6,4,9] has been deemed as a scalable and effcen alenave o MPL based appoaches fo offlne na-doman affc engneeng. Ths ype of plan IP based TE paadgm s also applcable o he ne-doman case, whee BGP oung abues ae manpulaed fo opmal nedoman affc dsbuon. ome of hese BGP abues ae used o conol oubound affc (.e., how uncas flows ae delveed ou of he local doman owads emoe desnaons, such as he Local_Pefeence (local_pef abue [3,6], whle some ohes can be appled fo nfluencng nbound affc, such as he A_PATH abue and he Mul_Ex_Dscmnao (MED abue [4,]. The objecves of hese nbound/oubound uncas TE schemes cove a vey wde ange, fom busness aspecs (e.g. mnmse oveall moneay cos [6], o newok pefomance aspecs (e.g., bandwdh consevaon [3] and load balancng [,6]. Neveheless, none of he exsng IP based affc opmsaon woks have consdeed mulcas flows whn he newok. Despe dffeen poblem fomulaons fo mulcas oung opmsaon, mos common soluons ae o apply dec pah selecon heuscs o consuc he sac mulcas ee sep by sep [8,3,5,20]. The mos dsnc dsadvanage of hs saegy s ha, as he poposed oung algohms canno be easly mplemened n IP oues, MPL unnels ae needed o enfoce pah selecons. Insped fom he IP based uncas affc engneeng appoach n [6], we poposed an na-doman mulcas TE scheme by opmsng M-IGP lnk weghs [8]. In hs case, opmal na-doman mulcas ees ae epesened no shoes pah ees ha can be auomacally handled by legacy IP oues. III. OVERVIEW OF THE OPTIMIATION FRAMEWORK Befoe fomulang he jon offlne na- and ne-doman mulcas affc opmsaon poblem, we fs povde a bef evew on he cuen mulcas oung semancs, akng ouce pecfc Mulcas (M [] as a ypcal example. In M, PIM- M [5] s esponsble fo consucng a mulcas ee acoss he Inene, fom ndvdual goup membes o he sngle souce fo each goup. As Desgnaed Roues (DRs fo eceves aleady oban he IP addess of he goup souce, hey ae able o send PIM-M jon equess decly owads he emoe souce. Tadonally, pah selecons of PIM-M jon equess follow he undelyng uncas oung able ha s populaed by he convenonal IGP/BGP oung poocols. The adven of mulopology exensons o hese poocols, such as M-II [9], MT- OPF [0] and M-BGP [2], has made possble o decouple mulcas oung fom s uncas counepa. As a esul, dedcaed mulcas oung opmsaon can be acheved hough manpulang he oung mecs such as IGP lnk weghs and BGP oue abues, specfcally whn he oung plane fo mulcas affc.

3 A. Mul-Topology Roung The mul-opology exensons o I-I and OPF povde he ognal poocols wh addonal ably of vewng he wegh of each lnk fo dffeen logcal IP opologes ndependenly. Take MT-OPF as an example, he feld of Mul Topology Idenfe (MT-ID wh value n MT-OPF s dedcaed o he mulcas oung plane. Wh hs mul-opology capably, newok povdes ae able o pefom dedcaed M-IGP lnk wegh opmsaon n he mulcas oung plane, whou woyng abou he unwaned pah changes fo he uncas affc due o he adjusmen of shaed lnk weghs. ame as he convenonal II/OPF poocols, he ognal BGP only povdes a unque oung plane acoss he Inene. Tha means, gven any IP pefx (ndcaed n he feld of Newok Laye Reachably Infomaon, NLRI, only one sngle oue s advesed fo all ypes of flows, ncludng IPv4/6, uncas/mulcas flows. In M-BGP, exensons o NLRI ae made fo advesng nconguen oues fo dffeen ypes of affc. These new abues ae known as MP_REACH_NLRI and MP_UNREACH_NLRI. As specfed n [2], he Addess Famly Infomaon (AFI and ub Addess Famly Infomaon (AFI caed n each M-BGP advesemen jonly denfy he oung plane fo dffeen ypes of flows. Fo example, an M-BGP updae message wh AFI = and AFI = 2 ndcaes ha hs advesemen s only cayng IPv4 mulcas oues. In hs case, exsng ne-doman uncas TE echnologes by weakng BGP oue abues [6] can be appled o mulcas as well, povded ha he oue abues ae confgued n he logcal newok opology fo mulcas affc. B. An Inegaed Infasucue Fg. 3 llusaes he negaed IPv4 mulcas affc opmsaon based on he M-IGP and M-BGP poocols. Whn each esouce opmsaon cycle, e.g., on weekly o monhly bass, M-IGP lnk weghs and M-BGP oue abues (e.g., local_pef ae compued/manpulaed offlne accodng o he gven opmsaon objecves. Theeafe, he esulng M-IGP lnk weghs and M-BGP oue abues ae confgued n he IPv4 mulcas oung plane especvely, usng pope MT-ID and AFI/AFI values. The IP oues wll hen populae he mulcas oung able (M-RIB fo each souce pefx. Once a PIM-M jon eques s eceved, each oue decdes, accodng o s M-RIB, he nex hop neghbou o send he packe ou of he local doman owads he emoe goup souce. In hs scenao, he PIM-M jon eques follows an engneeed ougong pah decded by he M-BGP abue (e.g., local_pef and MT-OPF lnk weghs. As a esul, he mulcas affc no only s njeced no he local doman va he desed M-ABR (fom whee he ognal PIM-M jon eques packe s delveed ousde he local doman, bu also avels along he opmal na-doman pahs ha confom o he opmsaon equemen. In addon, he mulcas fowadng nfomaon base (M-FIB s dynamcally updaed fo he ncomng neface (f and ougong neface (of ls of each goup. M-IGP lnk wegh opmsaon MT-OPF MT-ID = M-RIB M-FIB IPv4 M-BGP M-BGP mulcas oue abue AFI = plane PIM-M weakng AFI = 2 Opmsaon IP oue Fgue 3 IPv4 mulcas affc opmsaon wh M-IGP/M-BGP IV. PROBLEM FORMULATION As we have menoned pevously, opmsaon of na-doman mulcas oung s ofen fomulaed no he ene ee poblem fo bandwdh consevaon puposes. In a mul-homng envonmen, bandwdh consumpon can be also nfluenced by he poson of he ngess M-ABR. As we consde plan IP based soluons, he opmsaon poblem s ackled jonly hough M-IGP lnk wegh unng and M-ABR ngess pon selecons. Le s ake Fg. 4 as an example. We assume ha he pefx conanng he souce s fo he mulcas goup can be eached va boh M-ABRs b and. If b s seleced as he ngess pon, wh convenonal na-doman hop-coun based shoes pah oung, he esulng ee uses 6 newok lnks (Fg. 4(a. If s seleced, wh pope M-IGP lnk wegh seng we ae able o conseve 50% of na-doman bandwdh esouces, as only 3 newok lnks ae used (shown n Fg. 4(b. Fom hs example we can see ha he ask of M-ABR selecon s o fnd he opmal oo of he mulcas ee whn he doman, whle M- IGP lnk wegh unng s esponsble fo explong he bes nadoman pahs fom he oo o ndvdual eceves. Apa fom bandwdh consevaon, we also consde ohe objecves such as load balancng acoss ne-doman lnks, and hs uns he ask of negaed mulcas oung no a mul-objecve opmsaon poblem. b Towads s (a b 2 Towads s 2 2 Fgue 4 M-IGP lnk wegh unng and M-ABR selecon (b

4 A newok s epesened hough a deced gaph G =< V, E > whee V and E denoe he node se and he na-doman lnk se especvely. The node se V s fuhe caegosed no Access oue se VA, Bode oue (M-ABR se VB and Coe oue se VC. The nodes n VA ae only aached wh sac end hoss (eceves, whle hose n VB connec ohe domans (nomally povde domans hough ne-doman lnks. Fo smplcy, we assume ha each M-ABR b VB s aached wh only one nedoman lnk whose bandwdh capacy s C b. All he nodes n V ae logcally conneced n full mesh wh nenal M-BGP (-M- BGP sessons. We consde a se of dsjoned uncas addess pefxes P = { P,..., P k } n he Inene, each of whch can be eachable va a dsnc subse of VB. We also assume mulcas goup sessons m,..., m. The sngle souce of each mulcas goup s (0<< s ncluded n one of he addess pefxes P j (0<j<k unde consdeaon. Each goup m s assocaed wh a eceve se whch means ha R VA as well as he bandwdh demand D, D uns of bandwdh s consumed on each lnk T spannng s and R. of he mulcas ee Gven he newok and mulcas goup nfomaon, he jon opmsaon ask s o ( fo each pefx P j (0<j<k, o selec he bes M-ABR b j as he ngess pon, and ( o assgn a pope M-IGP wegh w uv fo each na-doman lnk ( u, v E, based on whch shoes pah oung s pefomed fo compung all mulcas ees. As we have menoned befoe, he opmsaon objecve of he ask above s o consuc a mulcas ee T fo each goup m wh he pupose of ( na-doman bandwdh consevaon,.e. na mnmse l = = ( u, v E D x uv f ( u, v T whee xuv = 0 ohewse and ( ne-doman load balancng,.e., D yb ne = mnmse max( ub = fo each b VB (3 Cb whee f b s seleced as he ngess of m (.e. oo of T y = b 0 ohewse (4 I s woh emphassng ha, f he souces of mulple goups belong o he same pefx (a specal case s ha mulple goups ( (2 shae he same souce, all hese goups should selec he same M- ABR as he common ngess pon. In ohe wods, he bnay vaable of y n (3 and (4 should have he same value fo all b goups whose souces belong o he same pefx. The eason fo hs s because M-BGP oue abues ae only assocaed wh aggegaed uncas addess pefxes whou consdeng mulcas goup nfomaon. Hence, M-ABR ngess selecon s based on pefxes ohe han goup specfc. V. PROPOED ALGORITHM The opmsaon poblem fomulaed above s NP-had, as s a combnaon of hee ohe NP-had poblems: namely ene ee [8,5], shoes pah epesenably [9] and he Genealsed Assgnmen Poblem (GAP [3]. In hs secon we popose a se of effcen schemes fo solvng he poblem, whch can be fuhe classfed no ngle Ingess elecon (I and Mulple Ingess elecon (MI algohms. A. ngle Ingess elecon (I We fs noduce he mos saghfowad algohm named ngle ngess selecon wh Hop-Coun na-doman oung (ngle-hc. In hs appoach, na-doman oung s based on he mec of hop-couns, whch means ha he M-IGP wegh s se o fo all na-doman lnks. On he ohe hand, M-ABR ngess selecon s based on a geedy seach algohm solely fo he pupose of consevng bandwdh esouces (objecve (. Tha s, o selec a sngle M-ABR fo each pefx ha esuls n he leas na-doman bandwdh consumpon l na wh he consan of bandwdh capacy of ne-doman lnks. pecfcally, we so ndvdual pefxes n descendng ode accodng o he sum of he bandwdh demand fom he goups whose souce s n ha pefx. Afe ha, we assgn sequenally hese pefxes o a specfc M-ABR (wh suffcen esdual bandwdh on he ne-doman lnk wh leas na-doman bandwdh consumpon. Nex we consde jon na- and ne-doman oung by akng no accoun M-IGP lnk wegh opmsaon. In ode o oban he opmal value of each lnk wegh as well as he bes ngess canddae fo each pefx, we noduce a Genec Algohm (GA based appoach he ngle-ga algohm. Genec Algohms can be descbed as follows. Fs, a sees of andom soluons ae obaned as he nal geneaon of chomosomes n he populaon. Theeafe, mpoved offspngs evolve eavely fom he paens by calculang he fness. Chomosomes wh hghe fness have hghe pobables of beng nheed by he nex geneaon. In each eaon, a new geneaon of chomosomes s ceaed hough he pocess of paen selecon and epoducon. Ths s specfcally acheved hough genec opeaos such as cossove and muaon on genes consung each chomosome. Afe a pedefned numbe of geneaons, o when fness pefomance has conveged, he chomosome wh he bes fness s seleced as he fnal soluon.

5 Pocedue ngle-ga-fness Begn e he M-IGP wegh of each na-doman lnk n he newok accodng o he chomosome Fo each pefx P j Aggegae goup bandwdh demand accodng o P j,.e. = D = ne fo s Pj End fo o he pefx ls P n descendng ode accodng o Fo each pefx Pj n he odeed ls P ne (0<j<k Assgn an M-ABR b VB eachable o Pj such ha ( Ina-doman bandwdh consumpon l na j s mnmsed fo he goups whose souce s Pj and (2 M-ABR b has suffcen esdual bandwdh fo he aggegaed demand ne Updae ne-doman lnk ulsaon on b,.e., ne ne ne u = u + AD / C b b b b End fo k na na l = l j /* um up oal na-doman bandwdh j= consumpon fo all pefxes */ ω fness = l na + α max( u ne End Fgue 5 Algohm fo compung fness (ngle-ga Ou saegy s o le GA seach fo opmal M-IGP lnk weghs dung he evoluon pocess of he populaon. In hs case, he genes n each chomosome ae he M-IGP weghs fo ndvdual na-doman lnks. In addon, we desgn a smple heusc fo M-ABR ngess selecon fo each chomosome,.e., a dedcaed se of lnk weghs. Ths algohm s smla o ngle-hc, excep ha na-doman oung s based on he undelyng M-IGP weghs obaned fom each chomosome. The mos mpoan ssue n GA based soluons s how o desgn he fness so as o dve he whole populaon owads he opmal esul. In he poposed ngle-ga appoach, he fness eflecs boh objecves of na-doman bandwdh consevaon and ne-doman load balancng. To acheve hs, we defne he fness of each chomosome as follows: fness = f ( l na, max( u ne = l na ω + α max( u ne whee ω s a consan and α s a uneable paamee fo conollng he ade-off beween he wo objecves, namely na ne mnmsng l and mnmsng max( u. If we use he noaon n he poblem fomulaon, he fness s: ω fness = D xuv + α max (( D yb / Cb = ( u, v E b VB = Wh hs defnon, chomosomes wh hghe fness,.e., lowe oveall na-doman bandwdh consumpon and lowe maxmum ne-doman lnk ulsaon, have hghe possbles o suvve n he nex geneaon. Fg. 5 povdes descpon of compung fness n he ngle-ga appoach, ncludng he embedded heusc of M-ABR ngess oue selecon. The me complexy of he ngle-ga algohm s O ( E ++klogk+k V B : e he wegh of each lnk akes O( E. The ask of aggegang goup bandwdh can be done hough vsng ndvdual goups wh he complexy of O(, and song of he souce pefx ls akes O(klogk. Fnally, he ngess pon selecon has complexy of O(k V B. B. Mulple Ingess elecon (MI In he uncas scenao, Ho Poao Roung (HPR s vey popula fo delveng ne-doman affc owads a specfc emoe pefx va mulple egess pons. In HPR, f mulple oues ae avalable fo a gven pefx whose oue abues wh hghe poes (e.g., local_pef, A_PATH ae equally good, each oue wll hen selec s own closes ABR (decded by he IGP lnk wegh o delve he uncas affc ou of he local doman. The benef of HPR fo uncas affc s wo folded. Fs, helps o mnmse na-doman bandwdh consumpon, and second, he delay of affc delvey can be also educed as each flow s sen ou fom he local doman as quckly as possble. In conas o s populay n uncas oung, HPR s seldom consdeed n mulcas affc delvey. Apa fom he lack of mulcas deploymen n pacce, hee exs wo majo heoecal easons fo hs. Fs, HPR s always able o acheve mnmum na-doman bandwdh consumpon fo uncas oung (hopcoun based f he capacy consan on ne-doman lnks s gnoed [3]. Howeve, hs s no he case fo mulcas oung, whee s possble o consume sll lowe bandwdh esouces by makng mulple eceves shae a common na-doman pah han allowng hem o fnd he own closes ngess pons (see Fg. 6. The second ssue s bandwdh consumpon on ne-doman lnks. In uncas oung, he oal bandwdh esouces consumed on ne-doman lnks s no nfluenced by egess oue selecons ncludng HPR. Agan, mulcas oung does no obey hs ule: Fo each pacula goup, he oveall bandwdh consumpon on ne-doman lnks s popoonal o he numbe of ngess pons seleced n HPR. Ths means ha, usng HPR fo na-doman bandwdh consevaon mgh esul n undesed hgh ulsaon on ne-doman lnks.

6 b Towads s 2 (a I b Towads s 2 (b HPR Fgue 6 Ineffcency n usng HPR n mulcas oung In hs secon, we exploe he feasbly of applyng conolled HPR fo mulcas oung opmsaon. Ou MI saegy s ha, addonal ngess pons ae seleced only f hey ae able o acheve sgnfcan na-doman bandwdh consevaon compaed o I. One appoach o enablng MI n pacce s as follows. Fo all M-ABRs ha can each he souce pefx, fs o se hghe (bu equal values of local_pef fo he M-ABRs seleced by he opmsaon pocedue, and (2 o confgue equally good abues (befoe eachng he abue of M-IGP lnk wegh fo hese seleced M-ABRs, such ha each -M-BGP speake can decde s neaes ngess pon accodng o M-IGP lnk weghs only fom hese seleced M-ABRs. As a esul, HPR can be only pefomed among he M-ABRs wh hghe local_pef. Agan, we emphasse ha, HPR can be only adoped on pe pefx bass, and s no possble fo ndvdual goups o selec he own ngess pons. We exend ngle-ga no a new algohm named Conolled GA-based HPR (C-HPR-GA. Fs of all, we assume ha he selecon of he pmay ngess oue b fo pefx P j whn each chomosome n he ngle-ga algohm esuls n oveall na-doman bandwdh consumpon of na l j ({ b}. Afe ha, we consde he scenao of addng anohe poenal ngess b' VB \{b}. We y all M-ABRs ha can each P j, excep b self, and fnd he one, namely b, ha (jonly wh b esuls n leas na-doman bandwdh consumpon and also has suffcen bandwdh on s nedoman lnk. If he new oveall na-doman bandwdh na consumpon l j ({ b} { b' } na s below λ l j ({ b}, whee 0<λ< (λ s se o 0.5 n ou algohm, hen b wll be seleced as he seconday ngess fo P j. We epea hs pocedue unl a pe-defned maxmum numbe of ngesses fo each pefx, namely B m, s eached. Fg. 7 shows he dealed algohm fo MI dung he compung of fness fo each chomosome. The me complexy of he C-HPR-GA algohm s 2 O( E ++klogk+k V B, assumng ha he maxmum value of B m s V B. Pocedue C-HPR-GA-fness Begn e he M-IGP wegh of each na-doman lnk n he newok accodng o he chomosome Fo each pefx P j Aggegae goup bandwdh demand accodng o P j,.e., = D = ne fo s Pj End fo o he pefx ls P n descendng ode accodng o Fo each pefx Pj n he odeed ls P Assgn an M-ABR b VB eachable o Pj such ha na ( Ina-doman bandwdh consumpon l j ({ b} s mnmsed fo he goups whose souce s P and j (2 M-ABR b has suffcen esdual bandwdh fo he aggegaed demand ne Updae ne-doman lnk ulsaon on b,.e., ne ne ne u = u + AD / C b b b b B j = {b} ne (0<j<k B j = /* Fnd addonal ngesses fo P j */ Whle B j < Bm Fnd b ' VB \ B j eachable o Pj such ha ( Ina-doman bandwdh consumpon na l j ( B j { b'} s mnmsed and (2 M-ABR b ' has suffcen esdual bandwdh fo he aggegaed demand ne f na na l j ( B j + { b'} < λ l j ( B j B j = B j {b'} B j = B j + Updae ne-doman lnk ulsaon on b ',.e., ne ne ne u b' = ub' + ADb' / Cb' end f End whle End fo k na na l = l j ( B j /* um up oal na-doman bandwdh j= consumpon fo all pefxes*/ ω fness = l na + α max( u ne End Fgue 7 Algohm fo compung fness (C-HPR-GA

7 VI. PERFORMANCE ANALYI In ou smulaon expemens, we used he GEANT [7] newok opology ha conans 23 nodes and 76 undeconal lnks (wo lnks wh oppose decons beween any pa of adjacen nodes. The scaled bandwdh capacy of each lnk s se o 0 4 uns. We consde 00 mulcas goups whose souces ae dsbued andomly n 50 emoe pefxes. We epea hs andom dsbuon fo en mes fo each nsance of es confguaon, and hose pefxes ha do no conan any souce fo hese 00 goups ae no consdeed. We assume ha each emoe pefx can be eached va maxmum 50% of he M-ABRs of he newok. In ode o oban he bes GA pefomance, we es dffeen values fo manpulang he chomosomes n each geneaon, and we se he pobably of cossove and muaon o 0.3 and 0.00 especvely. The numbe of chomosomes ncluded n each geneaon s se o 00. The maxmum geneaon fo each nsance of GA calculaon s 500. Apa fom he GEANT newok opology, we also used andom opologes ceaed by GT-ITM fo esng ou poposed algohms, and we found ha he pefomances ae vey smla among hese opologes. Apa fom he GA based schemes, we also mplemened hee ohe appoaches fo compason puposes, namely, ngle ngess selecon wh hop coun based na-doman oung (ngle-hc, unconolled HPR wh hop coun based na-doman oung (U- HPR-HC, and conolled HPR wh hop coun based nadoman oung (C-HPR_HC. In ode o evaluae na-doman bandwdh consevaon capables, we use he pefomance of ngle-hc as he baselne, and defne Bandwdh Consevaon Rao (BC-ao fo he es algohms. pecfcally, he BC-ao of a specfc algohm s he ao of s na-doman bandwdh consumpon ove ha of he ngle-hc algohm. The maxmum bandwdh demand fo ndvdual mulcas goups Max D s used as he x-axs n he followng fgues. The ange of Max D fo each es s fom 200 o 200 uns. BC-ao 00% 90% 80% 70% 60% 50% U-HPR-HC C-HPR-HC ngle-ga C-HPR-GA Max D Fgue 8 BC-ao vs. Max D (α =0 3 Max lnk ulsaon 250% 200% 50% 00% 50% 0% ngle-hc U-HPR-HC C-HPR-HC ngle-ga C-HPR-GA Max D Fgue 9 Maxmum ne-doman lnk ulsaon vs. Max D (α =0 3 Fg. 8 and Fg. 9 llusae oughly equal-spl effos on he wo objecves by seng he value of α o 0 3. Fom Fg. 8 we can see ha all he poposed algohms oupefom ngle-hc n ems of na-doman bandwdh consevaon. pecfcally, unconolled HPR s able o acheve he BC-ao of 78%, whch means up o 28.2% of he bandwdh esouces whn he newok can be saved. By lmng he oal numbe of ngess oues, he C-HPR-GA algohm has hghe BC-ao (87%, meanng ha s able o conseve 4.9% of na-doman bandwdh compaed o ngle-hc. On he ohe hand, by usng conolled HPR wh hop coun na-doman oung, and opmsng M-IGP lnk weghs wh sngle ngess selecon, C-HPR-HC and ngle-ga have he BC-ao of 9% and 94% especvely. Fg. 9 shows he maxmum lnk ulsaon acoss ne-doman lnks. As we expeced, unconolled HPR has much hghe ulsaon on nedoman lnks han all he ohe algohms, whch ndcaes ha nomally s no a pope soluon n pacce. Anohe noable esul s ha, boh ngle-ga and C-HPR-GA acheve he bes pefomance n load balancng acoss ne-doman lnks. Moeove, C-HPR-GA does no exhb much hghe ulsaon on ne-doman lnks. Ths s because we have ghly conolled maxmum ne-doman lnk ulsaon n he fness calculaon funcon. BC-ao 0% 00% 90% 80% 70% 60% 50% ngle-ga C-HPR-GA Max D Fgue 0 BC-ao vs. Max D (α =0 4

8 Max lnk ulsaon 60% 50% 40% 30% 20% 0% 0% ngle-ga C-HPR-GA Max D Fgue Maxmum ne-doman lnk ulsaon vs. Max D (α =0 4 Fg. 0 and Fg. show he pefomance of he GA-based algohms when moe effos ae pu owads load balancng acoss ne-doman lnks. We acheve hs by nceasng he value of α fom 0 3 o 0 4. Fom now on we don nclude ohe algohms because hey ae no capable of unng effos beween he wo objecves hough α. Fom Fg. 0 we noce ha nehe C-HPR-GA no ngle-ga have any gan on na-doman bandwdh consumpon. Howeve, Fg. shows ha he wo algohms ae able o fuhe decease maxmum ne-doman lnk ulsaon (by 7% compaed o Fg. 9. mla o he pevous scenao, he gap beween he wo GA-based schemes n ne-doman load balancng s vey small n Fg. 0. VII. UMMARY In hs pape, we nvesgaed offlne opmsaon on jon naand ne-doman mulcas oung n mul-homng envonmens. Fs of all, we demonsaed why adonal ene ee based poblem fomulaons do no geneally apply o he ne-doman case. Followng ha, we poposed a genec opmsaon famewok usng plan IP based oung paadgms. pecfcally, lnk weghs of M-IGP and oue abues of M- BGP ae jonly manpulaed fo opmsed na-doman bandwdh consumpon and load balancng acoss ne-doman lnks. mulaon esuls have shown ha he poposed soluon s able o acheve sgnfcanly bee pefomance han convenonal oung confguaons. Especally, f HPR s popely conolled, na-doman bandwdh can be fuhe conseved whou any expense of nceasng ne-doman lnk ulsaon. Ths IP based appoach acheves hgh smplcy and scalably n he conol plane, as hee s no need fo seng up dedcaed P2MP MPL unnels acoss mulple domans. As hs wok s he vey fs sep owads ne-doman mulcas affc opmsaon, hee sll exs many ssues ha need o be consdeed. Fs, BGP has been ofen blamed fo causng poenally Inene oung nsably and slow convegence poblems. When M-BGP, whch s an ncemenal exenson o BGP, s used fo ne-doman mulcas oung, s no supsng ha hese poblems do occu n he mulcas oung plane. Hence, ou nex sep s o nvesgae sable nedoman mulcas oung opmsaon, akng no accoun some exsng eseach woks on boh uncas and mulcas oung sably, e.g., [2,7]. Fnally, oung obusness n case of boh na- and ne-doman lnk falues s ye anohe opc o be addessed n ou fuue eseach. REFERENCE []. Bhaachayya, An Ovevew of ouce pecfc Mulcas (M, RFC 3569, Jul [2] T. Baes e al, Mulpoocol Exensons fo BGP-4, RFC 2858 [3] T. C. Bessoud e al, Opmal Confguaon fo BGP Roue elecon, IEEE INFOCOM, [4] R.K.C. Chang and M. Lo, Inbound Taffc Engneeng fo Mulhomed As Usng A Pah Pependng, IEEE Newok Magazne, Mach/Apl 2005 [5] B. Fenne e al, Poocol Independen Mulcas - pase Mode (PIM-M: Poocol pecfcaon (Revsed, Inene daf, dafef-pm-sm-v2-new-.x, Oc. 2004, wok n pogess [6] B. Foz e al, "Inene Taffc Engneeng by Opmsng OPF Weghs", IEEE INFOCOM, 2000, pp [7] The GEANT newok opology, avalable onlne a: hp:// [8] L. Kou e al, A Fas Algohm fo ene Tees, Jounal of Aca Infomaca, 5, pp. 4-45, 98 [9] T. Pzygenda e al, M-II: Mul Topology (MT Roung n I- I, Inene Daf, daf-ef-ss-wg-mul-opology-09.x, Mach. 2005, wok n pogess [0] P. Psenak e al, Mul-Topology (MT Roung n OPF Inene Daf, daf-ef-ospf-m-04.x Ap [] B. Quon e al, A pefomance evaluaon of BGP-based affc engneeng, Inenaonal Jounal of Newok Managemen, 5(3, May-June [2] P. Rajvadya, K. Almeoh, Mulcas Roung Insables, IEEE Inene Compung, Vol. 8, Issue 5, 2004, pp [3] G. N. Rouskas e al, Mulcas Roung wh End-o-end Delay and Delay Vaaon Consans, IEEE JAC Vol. 5, No. 3, pp , Ap. 997 [4] A. dhaan e al, Achevng Nea-Opmal Taffc Engneeng oluons fo Cuen OPF/I-I Newoks, IEEE INFOCOM, pp , Ap [5] H. Takahash, A. Masuyama, An Appoxmae oluon fo he ene Poblem n Gaphs, Mah. Japonca 6, pp [6]. Uhlg and O. Bonavenue, Desgnng BGP-based oubound affc engneeng echnques fo sub Aes, ACM IGCOMM Compue Communcaons Revew, Ocobe [7] H. Wang e al, able Roue elecon fo Inedoman Taffc Engneeng, IEEE Newok Magazne, Decembe, 2005 [8] N. Wang, G. Pavlou, Bandwdh Consaned IP Mulcas Taffc Engneeng whou MPL Ovelay, IEEE/IFIP MMN, 2004 [9] Y. Wang e al, Inene Taffc Engneeng whou Full Mesh Ovelayng, Poc. IEEE INFOCOM, Vol., pp , 200 [20] Q. Zhu e al, A ouce Based Algohm fo Delay-consaned Mnmum-cos Mulcasng, Poc. on IEEE INFOCOM, Vol., pp , 995