THE well established 80/20 rule for client-server versus

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1 IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT, ACCEPTED FOR PUBLICATION 1 Optml Fuctolty Plcemet for Multply Servce Provder Archtectures Ios Pppgotou, Studet Member, IEEE, Mtths Fler, Member, IEEE, d Mchel Devetsots, Fellow, IEEE Abstrct The prolferto of multply servces s cretg desg dlemms for servce provders, relted to where cert ey etworg fuctolty should be plced. For exmple, servce provders eed to ow whether to dstrbute more etwor tellgece closer to the subscrber or cluster t cetrl locto. I vew of ths, we qutfy the cost dffereces mog servce provder rchtectures, detfed bsed o the fuctolty dstrbuto (cetrlzed vs. dstrbuted, clustered vs. uclustered d sgle vs. mult edge). For ths purpose, we formulte modulr mxed-teger progrmmg model bsed o set of close-to-rel-cse sceros. Gve the complexty of such problems, we propose methodologes tht c reduce the umber of loctos. Our results dcte tht dstrbutg the IP tellgece d the vdeo replcto s preferble. Moreover, deployg edge systems wth fster bcple hs lttle beeft the ggregto etwor, d provders should rther vest fster terfces. Idex Terms Aggregto etwors, metro Etheret, Etheret bsed DSL, edge systems, trple ply. I. INTRODUCTION THE well estblshed 80/20 rule for clet-server versus locl trffc hs drve etwor desgers to ddress problems wth pure L2 swtches ctg s hubs, d L3 routers performg the routg towrds dfferet pths. However, the rse of o demd vdeo stremg (e.g., Netflx, Hulu), Peerto-Peer (P2P) televso over the teret (e.g., TVUPlyer, PPLve, QQLve, PPStrem), d the dvet of moble trffc hs trggered umber of ctos from brodbd provders who re tryg to cheve flexblty, sclblty d effcecy [21]. Accordg to severl studes, the ul globl trffc wll be doublg volume every two yers, whle qurter of ths s proected to be vdeo trffc [2], [3]. Curret 4G moble servce provder rchtectures re bdwdth costred, d the cost to buld out ew etwors to crese the vlble bdwdth s prohbtvely expesve. Therefore, t s of vtl mportce for the Iteret Servce Provders (ISPs) to egeer ther frstructure to meet these chlleges. I ths pper, we focus o swerg the questo Muscrpt receved Mrch 5, 2011; revsed November 28, 2011, d Mrch 15 d My 29, The ssocte edtor coordtg the revew of ths pper d pprovg t for publcto ws A. Vslos. I. Pppgotou d M. Devetsots re wth the Deprtmet of Electrcl d Computer Egeerg, North Crol Stte Uversty, Rlegh NC, USA (e-ml: {ppp, mdevets}@csu.edu). M. Fler s wth the Edge Router Busess Ut of Csco Systems, Ottw, Cd (e-ml: mfler@csco.com). Ths wor ws supported prt by the Isttute for Next Geerto IT Systems, Reserch Grt 09-06, d by the Csco Uversty Reserch Progrm, Gft # (3696). Dgtl Obect Idetfer /TNSM /12/$31.00 c 2012 IEEE of where to plce cert fuctoltes the ggregto etwor. We model ths through Networ Desg Problem (NDP) tht the SP my use to cheve the mxmum effcecy wth the mmum deploymet cptl cost. I the pst, NDPs hve bee used to ddress the problem of cost optmzto whe developg ew frstructures. Noetheless, most ISPs lredy possess ccess frstructure. I order to ddress ths ssue, we propose optmzto formulto tht uses the curret frstructure ( terms of desg), but defes the optml dstrbuto of fuctoltes sted. Aother mportt spect s tht devces used the Etheret ggregto, d edge prt of the etwor, re ot ymore purely lyer 2 swtches ( the NDP lterture they re sometmes clled ggregtors [26]) d lyer 3 routers. Most of the vedors hve egeered multpurpose edge systems tht corporte dfferet fuctoltes d etwor tellgece modulr sub-systems e.g., hghed bcples whch multple terfce d fuctolty le crds re dded. Therefore, desg problems for such rchtectures eed to be revsted. Cosderg the bove chlleges, ths pper we clssfy the ggregto rchtectures bsed o the locto of the fuctoltes d etwor tellgece, d the proceed to buld modulr optmzto model tht s ble to cheve the mmum deploymet cost. Our cotrbuto s summrzed s follows: We defe the possble ggregto rchtectures d group them to three m ctegores: 1. Cetrlzed Sgle-Edge; 2. Cetrlzed Mult-Edge; d 3. Dstrbuted Sgle-Edge. O top of these ctegores, other subctegory s dded, whether to cluster the edge systems or eep the fuctoltes sgle box. We develop etwor desg model tht goes beyod the well vestgted locto d dmesog problems. Our modelg pproch s ppled to both desg ggregto rchtecture, s well s upgrdg the curret frstructure. We propose models bsed o edge systems, rther th etwor elemets. Edge systems my support dfferet types of fuctoltes ether o ther ow, or s ttched sub-systems (le crds). We formulte costrts tht ccout for physcl chrcterstcs (le crd cpcty, port cpcty), bdwdth (devce d port bdwdth), d lyer 2 versus lyer 3 fuctoltes (such s swtchg d routg, VLAN/IP termto cpcty, or busess fuctos).

2 2 IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT, ACCEPTED FOR PUBLICATION We propose two ovel heurstcs for sclg dow the problem d for decresg the executo tme of the problem. We evlute our model wth two close-to-rel-cse sceros d wth multple trffc profles. We show tht, wth the curret treds, the SPs wll eed to re-egeer ther ggregto frstructure. The pper s structured s follows: I the ext secto, we provde overvew of the curret stte of the rt NDPs d ggregto desg methodologes. I secto III, we defe d expl the rchtectures ccordg to the dstrbuto of the edge systems. I secto IV, we descrbe the proposed modelg methodology d ssumptos. Gve the plurlty of symbols d ottos, ll of them re summrzed the tbles of secto IV. I secto V, we expl the modelg pproch for the trffc flows d Secto VI we deploy the cost optmzto model. I secto VII, we expl the heurstcs tht hve bee used to scle-dow the problem, d secto VIII we showcse evluto of two mult-servce sceros over metro re etwors bsed o rchtecturl vlues from EU ISPs d ctul system vlues from vedors. Secto IX, cludes the dscusso d further remrs, d we coclude wth the fl secto. II. BACKGROUND WORK Durg the Iteret er the extesve eed for bdwdth becme crucl ssue for Iteret SPs. Ths led the reserch commuty to focus o Networ Desg Problems tht requre dvced optmzto techques to be solved. These problems c be dvded to two m ctegores: Loctog problems, whch re pure topologcl desg problems d where the demd volumes re ot te to cosderto; Dmesog problems, whch corporte the demd volumes. Both clsses of problems hve bee extesvely lyzed [20], [26], [27], [28]. A sub-ctegory of the dmesog problems, re the twolevel herrchcl etwor problems [10], [15]. I [7], the uthors vestgte herrchcl etwor problem for fst movg users. These problems ssume set of cddte loctos, cpbltes of cocetrtors d routers, d determe the optml locto plcemet. However, more d more vedors re developg etwor systems tht support o the sme bcple (or chsss) multple fuctoltes (le crds or bldes). Moreover, the hgh demd for vdeo trffc ffects the wy IPTV fuctoltes re dstrbuted Next Geerto Networs [17]. Hece, o the bss of dmesog problem, our proposed pproch s dfferet from prevous wor the followg pots: () We propose modelg pproch were mcro-optmzto s requred ech locto to determe the pproprte tellgece. (b) The proposed modelg pproch my be ppled to etwor desgs s well s etwor upgrdes. For exmple, etwor rchtect c use the model to determe the cost of dstrbutg the fuctolty closer to the subscrber. (c) The proposed desg s ot lmted to sgle herrchcl desg (e.g. IP termto fuctolty c be plced before or fter the swtch). (d) Ech servce my hve dfferet chrcterstcs. For exmple vdeo trffc for IPTV s usully multcst [13]; P2P pplctos ted to geerte multple flows, some of whch re geogrphclly cocetrted or dstrbuted over log dstces [5]; Iteret trffc s usully bsed o clet-server behvor [22]. I [29], the uthors hve solved Networ Utlty Mxmzto (NUM) problem for trple ply servces. The uthors propose three utlty fuctos for ech offered servce. However, NUM problems ddress the ssue of fress d requre the pror owledge of the utlty fucto, whch my cses s hrd to compute. I our wor, we propose three dfferet flows, whch hve drectol chrcterstcs d re qutfble by performg Deep Pcet Ispecto (DPI) or flow specto d clssfcto [6]. I [32], the uthors cosdered ADSL ccess etwor cosstg of subscrbers, Dgtl Subscrber Le Access Multplexers (DSLAMs), metro Etheret swtches d Brodbd Remote Access Aggregto Server (BRAS), d hve developed lytcl expressos for dmesog the ccess etwor the upstrem drecto. Moreover, [11], the uthors performed cost vestgto of trsport rchtectures bsed oly o demd d physcl lyer cpbltes. I our wor, we use Etheret bsed ext geerto ggregto etwor whch the BRAS hs bee replced by multpurpose Brodbd Networ Gtewys (BNGs), Mult-Servce Edge Routers (MSEs) d Vdeo BNGs [4], [12]. We lso propose multple rchtectures bsed o the dstrbuto d clusterg of the edge fuctoltes. Our pproch s bsed o the TR-101 brodbd forum s report [1], whch stdrdzes the Etheret bsed ggregto desg. I [24] we preseted comprso of cetrlzed vs dstrbuted uclustered topologes, through two optmzto problems. I ths pper, we combe the problems to sgle cost optmzto model d exted the bove wor to clude most of the possble ISP rchtectures. Flly, we evlute our methodology wth rchtecture desgs provded by three mor Europe servce provders. III. ARCHITECTURAL COMPARISON Sce ech edge system (BNG, MSE, Vdeo BNG) my support dfferetl d modulr fuctoltes, vrous topologes my be mplemeted eve whe the edge router s bcple rems the sme. For exmple BNG (to sgle chsss) tht corportes both IP termto d vdeo fuctoltes. Aother pproch tht s followed by some vedors s to dd severl L3 fuctoltes o L2 devces (e.g., IP termto) [4]. We propose the followg rchtecturl combtos for ISP ggregto etwor: Cetrlzed or Dstrbuted bsed o the tellgece; Sgle or Mult edge bsed o the servces per locto; Clustered d Uclustered bsed o the fuctoltes. A. Networ Elemets Aggregto Networ L2 Aggregto devces: re hgh cpcty L2 ggregto swtches used s secod level of ggregto, d perform low cost VLAN polcy eforcemet. They usully support Ggbt Etheret ports d multple flterg polces per VLAN. They re the smplest ggregto devces.

3 PAPAPANAGIOTOU et l.: OPTIMAL FUNCTIONALITY PLACEMENT FOR MULTIPLAY SERVICE PROVIDER ARCHITECTURES 3 Level 1 Access DSLAM Level 2 L2 Aggregto Multcst Replcto Pot Level 3 L3 Edge CDN Locl Trffc (P2P) flow Hgh Speed Iteret flow IPTV Multcst flow Busess flow Level 1 Access Level 2 L2 Aggregto Multcst Replcto Pot Level 3 L3 Edge CDN Locl Trffc (P2P) flow Hgh Speed Iteret flow IPTV Multcst flow Busess flow IPTV server Iteret IPTV server Iteret Busess Resdetl BWA Swtch 1... Swtch J L2 Cloud BNG (Sgle Box) L3/MPLS Cloud P-Router Resdetl Busess Wreless BWA Swtch 1... Swtch J L2 Cloud Vdeo Router P-Router BNG MSE L3/MPLS Cloud Fg. 1. Cetrlzed sgle edge overly rchtecture. Fg. 2. Cetrlzed mult edge overly rchtecture. BNG: Brodbd Networ Gtewys re IP devces termtg the lyer 2 ccess d route over IP/MPLS wth support of full set of MPLS d IP routg protocols, cludg multcst routg (PIM-SM/IGMP [8]). They eforce sophstcted IP QoS per servce d per-cotet/source dfferetto. They usully termte PPP sessos or IP tuels d c support up to hudred of thousds of subscrbers d Gbps cpctes. Edge routers, ccordg to [1], c support ddtol fuctoltes relted to Authetcto, Authorzto d Accoutg (AAA) d re dymc devces tht mly focus o resdetl customers. Moreover severl ext geerto BNGs hve the cpblty to support moble bldes to provde moble termto fuctoltes. MSE: Mult-Servce Edge Routers re resposble for routg busess trffc, whch s usully dedcted bdwdth. There s o eed to uthetcte the busess users s these re lesed les, hece MSEs support less tellgece. Vdeo BNG: Vdeo Brodbd Networ Gtewys re dedcted routers tht hve bee troduced to hdle the cresg demd for vdeo trffc (e.g. IPTV, Netflx etc.). A vdeo BNG does ot mplemet subscrber mgemet fuctos (e.g., PPP termto, per user QoS), sce these fuctos re lely to be performed by the other etwor elemets. I fct the vdeo BNG my be the pot of serto of IPTV flow d/or the replcto pot (L3 Multcst). B. Cetrlzed Sgle-Edge Archtecture Ths type of desg ws very mportt the erly evoluto of ggregto etwors. I ths type of rchtecture, the L2 Metro Etheret ggregtes the trffc from multple ccess pots d delvers the Vrtul Locl Are Networ (VLAN) to the IP Edge etwor, s show o Fg. 1. Some of the chrcterstcs of ths rchtecture re: 1) ll types of trffc re bchuled to the BNGs d the to sgle P- Router locto, whch s coected to the ISP bcboe (P- Router s prt of the bcboe d sometmes clled PoP); 2) Subscrber termto fuctolty, multcst replcto d IP QoS polces re executed the BNG deeper the etwor; 3) Multcst trffc for brodcst vdeo s trsmtted from the edge router over L2 multcst VLANs to ll customer premses (Wreless BS, DSLAM). C. Cetrlzed Mult-Edge Archtecture I the mult-edge rchtecture there re dfferet types of edge routers (BNG, Vdeo BNG d MSE) tht hdle seprte clsses of subscrber d dfferet types of trffc, s show Fg. 2. Resdetl subscrbers re usully termted the BNG, wheres the Busess VLANs or lesed les re routed through the MSE. Some provders, order to eforce specfc QoS polces o ther vdeo chels (IPTV), mplemet seprte Vdeo BNG [1]. Therefore, the Cetrlzed Mult-Edge rchtecture beefts from cumbecy, sce t s eser to evolve from the exstg rchtecture. D. Dstrbuted Sgle-Edge Desg A dstrbuted IP Edge pproch s beg cosdered by my SPs s ltertve rchtecture to stsfy the bdwdth requremets for future pplctos. As show Fg. 3, the edge etwor s comprsed by both L2/L3 routers. Vdeo d HSI re bchuled over seprte VLANs to the Edge Routers, where servces d ccess to the IP etwor s cotrolled. The sclblty s cresed, sce the mout of stte formto the BNG s decresed (less subscrbers re termted per BNG) d IP QoS polces re eforced closer to the lst mle. IP multcst routg s used cross the L2/L3 Crrer Etheret etwor for delvery of brodcst vdeo servces. I the sgle edge cse, ll servces flow through sgle devce dstrbuted closer to the subscrber. Furthermore, bsed o the llocto of subscrbers the foremetoed rchtectures c be further dvded to: Clustered: Alloctg the subscrbers to prtculr servce over my systems locted the sme PoP. Uclustered: Alloctg ll subscrbers for prtculr servce to oe system. Wth the curret cetrlzed desg, the cresg demd of vdeo chels over IP etwors leds to uvodble bdwdth problem the ggregto etwors. Dstrbutg the replcto fuctoltes multple ggregto levels my result less cogesto of trffc bdwdth d VLANs, sce sgle ucst flow s requred from the CDN to the dstrbuted Vdeo BNG. Moreover, the evoluto of P2P IPTV sets ew stdrds o how users terct. Dstrbutg the IP tellgece c del more effectvely wth trffc flows tht

4 4 IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT, ACCEPTED FOR PUBLICATION Busess Resdetl Fg. 3. Level 1 Access DSLAM BWA Level 2 L2 Aggregto Multcst Replcto Pot L2 Cloud BNG 1... BNG J Level 3 L3 Edge CDN IPTV server Swtch Dstrbuted sgle edge overly rchtecture. L3/MPLS Cloud Locl Trffc (P2P) flow Hgh Speed Iteret flow IPTV Multcst flow Busess flow P-Router Iteret ted to be locl, sce trffc s termted d routed closer to the subscrbers. I ddto, severl wreless provders re lredy fcg ssues o how to bchul the cresg demd of moble trffc. For ths reso our wor focuses o determg whch rchtecture s the optml oe. Flly, the dstrbuted mult-edge rchtecture hs bee bdoed due to the cresg complexty of dstrbutg multple type of boxes over the ggregto etwor. Hece, we exclude t from the potetl solutos. Geerl Agg. Swtch Edge Systems TABLE I MODELING INPUT PARAMETERS Descrpto Symbol Access Locto =[1,..., A] 1st Level Aggregto Loctos =[1,..., I] 2d Level Aggregto Loctos =[1,..., J] Core Loctos =[1,..., K] Number of subscrbers SUB Subscrbers per Resdetl Locto res Subscrbers per Busess Locto bus DSLAM subscrber cpcty S Number of IPTV Chels from CDN Ch % of cocurret subscrbers wtchg IPTV w Cpcty of Port c = {1G, 10G} Cost ($) co L2 Bdwdth (Gbps) C L2 VLAN cpcty vl Number of slots for Ports P L2,c Cost ($) of swtchg ports co L2,c Cost ($) for Type t co L3 t Bdwdth (Gbps) for Type t C t IP Termto Cpcty for Type t sub L3 t Number of slots for Ports for Type t Cost ($) of routg ports P L3,c t co L3,c frstructure (multple ggregto etwors). I other words, solvg the problem for the whole ISP etwor would requre rug the model multple tmes for ech ggregto etwor wth dfferet put prmeters (e.g., subscrbers, levels of ggregto). IV. METHODOLOGY AND ASSUMPTIONS A. Overvew The m obectve of our wor s to crete sgle modulr d portble model tht s ble to provde the cost optml soluto mog dfferet rchtecturl cddtes. We model ths through mxed teger progrmmg model. We dvde the vrbles qulttve (0-1) d qutttve. The qulttve vrbles re used to select the pproprte rchtecturl pproch (Cetrlzed vs Dstrbuted), wheres the qutttve to determe the umber of systems per locto. The model s o ler mxed teger; the o-lerty ppers the costrts. Such problems c be chllegg d drg veture, becuse they combe ll dffcultes of ther subclsses: the combtorl ture of teger progrms (MIP) d the dffculty solvg o-covex oler progrms (NLP). Hece, we hve trsformed the problem to ler oe the expese of extr costrts. I ddto, we decresed the serch spce by defg upper bouds for the umber of elemets d terfces. By usg these heurstcs the optmzto problem ws solvble fte mout of tme. I ths model, we ssume tree topology (bprtte) wth multple ggregto levels. I fct, most of the ISPs usully mplemet smll d medum ggregto stes d severl core stes. The umber of loctos vres bsed o the sze of the ISP. Smll loctos my vry from 10-10,000, the medum loctos from 10-1,000 d the core locto from Every core ste my support dfferet ds of res (rurl or o-rurl) wth vrous customer dstrbutos. Thus, we re modelg sgle three-level ggregto etwor. The results c the be extrpolted to clude the whole ISP ggregto B. Deftos O the frst level there my exst A ccess loctos. I ech ccess locto =[1,..., A], the L2 ccess devces re ble to hdle fte umber of subscrbers. O the remg levels the model s gog to defe how to dstrbute the hgher lyer fuctoltes d how to hdle dfferet ds of servce flows. 1) Archtecture: The frst ggregto level s comprsed of I loctos ( =[1,..., I]), the secod level of J loctos ( =[1,..., J]) d the lst level of K =1sgle locto (sgle core ste sce we re modelg oe ggregto re). The core ste corportes the P-Router whch s resposble to route the o locl trffc to the bcboe or trffc from Ter-2/3 SPs (LAC/LNS fuctolty). However, t ws ot cluded s vrble the model s t does ot ply y role o the fuctolty dstrbuto. The serto pot of the vdeo trffc from the CDN s ssumed to be the core locto. From the results, we otced tht f the serto pot ws the Vdeo BNG, the soluto would hve very smll vrto. 2) Ls: I order to model the ls betwee ech ggregto level, we hve used boole costts u 1, for every ggregto level {,, }. Ifu 1, =1,thelower level locto 1 s coected wth hgher level locto. However, t my be the cse tht the problem detfes tht less ggregto levels re eeded. Thus, smlr mer u 1,+1 represets the coecto wth ls betwee two dfferet lyers. 3) Prmeters: Tble I summrzes the prmeters of the model. Our model s bsed o etwor tht hs t most three ggregto levels. Our pproch s ble to determe, whether ll three re eeded or the ISP my decde to mplemet fewer

5 PAPAPANAGIOTOU et l.: OPTIMAL FUNCTIONALITY PLACEMENT FOR MULTIPLAY SERVICE PROVIDER ARCHITECTURES 5 TABLE II TYPES OF EDGE FUNCTIONALITIESt Type Fuctolty Edge Desg Combtos A All Sgle Edge Noe B HSI d Vdeo Sgle/Mult Edge oly type E C HSI d Busess Sgle/Mult Edge oly type F D HSI Sgle/Mult Edge type E,F E Busess (MSE) Mult Edge type D,F or type B F Vdeo Mult Edge type D,E or type C levels. I the sme tble, we lso preset the propertes of ech of the devces. Note tht edge systems hve the subscrpt t, whch correspods to dfferet types. I regrds to the port umber, we me the followg smplfcto: Edge system bcples cot fte mout of slots. I ech slot, le crds re dded tht hve fte umber of ports. Hece, sted of hvg so my vrbles, we hve decded to ssocte the umber of ports per devce s the oe to vry Pt L3. Ech port s lso ssocted wth cost co L3,c. 4) Edge System Fuctolty: We lso ssume sx dfferet types of edge routers t T = {A, B, C, D, E, F }, bsed o the fuctolty, the chrcterstcs d the servces tht they support. We defe the followg edge system fuctoltes: Hgh Speed Iteret (HSI): T 1 = {A, B, C, D} T becuse they requre IP termto; Busess: T 2 = {A, C, E} T for busess subscrbers; sce they lese VLANs they do ot requre y termto. Vdeo replcto (Multcst): T 3 = {A, B, F } T. Tble II summrzes the types, the fuctoltes, the edge desg tht they form, d the potetl combtos wth other edge systems t the sme locto. More specfclly, order to vod redudcy of fuctoltes d therefore uecessry cost, ot ll types of edge routers should be used () sgle locto d (b) y pth from ccess ode to P-router. For stce, f BNG (type A) s used locto, the t could perform everythg sgle box, thus o other BNG should be stlled the sme pth (or locto) towrds the P-Router. C. Vrbles The obectve fucto of the optmzto problems s, gve the pproprte loctos, correspodg ls d trffc demds, to optmlly llocte the etwor elemets d terfces, d detfy where to plce the routg fuctoltes. For ths, there re two dfferet types of vrbles, qulttve d qutttve 1 : 1) Qulttve Vrbles (0-1): s boole vrble tht specfes whch type of system should be used t locto. If the edge router of type t s chose t locto, the t s equl to 1; otherwse t s 0.,t s boole vrble tht specfes f swtch s gog to be plced t locto or ot. If t s, the t tes the vlue 1; otherwse t s 0. u L2 1 The vrbles re wthout ccet. Lower-cse u s used for qulttve vrbles tht te vlues 0 or 1, d upper-cse Y s used for qutttve vrbles tht re turl umbers s boole tht tes the vlue 1, f o devce s stlled t ll. Tht s,t =0, t T d ul2 =0. Evdetly,t + u L2 + u 0 =1. s boole vrble tht tes the vlue 1, f 1Ge terfces (le crds) re chose to be stlled t locto ; otherwse t s 0. s boole vrble tht tes the vlue 1, f 10Ge terfces (le crds) re chose to be stlled t locto ; otherwse t s 0. u 0 u 1G u 10G Thus f,t =0, the ether swtch or other type of edge system or othg s stlled. If,t =1for y t T,the the optml rchtecture s the cetrlzed oe (ccordg to the defto of the prevous secto). Wheres, f,t =1, for, the optml rchtecture s the dstrbuted. For the cetrlzed cse, f t = A, the the progrmmg model wll hve selected the sgle-edge rchtecture. 2) Qutttve Vrbles: As qutttve vrbles we defe those vrbles tht re turl umbers, N 0.Ithsset there c be: rel vrbles, those ssocted wth specfc chrcterstc d ffect the obectve fucto; dummy vrbles, those tht re used for other purposes d re ot prt of the obectve fucto. The ltter oes re used the loctos tht the provder does ot eed to ope or use. More specfclly: x,c,d d Y re the teger vrbles specfyg Y x,c,up,+1 1, the umber of terfces of cpcty c ttched to the etwor elemet of lyer x d locted locto. Those terfces re ttched to ls tht coect, ether the upl wth oe level hgher ( +1), or the dowl wth oe level lower ( 1). Y,t x s the teger vrble specfyg the umber of etwor elemets x t locto d of type t. If Y,t L3 > 1 the t mes tht the locto eeds ts routg fuctoltes to be clustered. Y 0 s the teger dummy vrble tht s used wheever ether routg or swtchg fuctolty s stlled locto. If ll the loctos re the sme level hve Y 0 > 0, the ths mes tht t s cost optml to hve less ggregto levels. s the teger dummy vrble tht s used to depct fctol umber of terfces, wheever o devce s determed to hve bee stlled t the +1 locto, Y+1 0 =0. Y 0,+1,d V. MODELING THE TRAFFIC FLOWS I our modelg pproch, we ssume tht the begg of the trffc s the frst ggregto pot, or else y ccess locto. Ths ws doe for severl resos: ) the umber of subscrbers my rge to mllos, mg the problem hrd to be solved wth tht mout of vrbles d costts; b) etwor rchtects usully use me (or some percetge) trffc demds over subscrbers of bgger geogrphcl re [3], [18]; c) ccordg to the VLAN polcy mplemeted, trffc subscrber VLANs re budled to bgger VLAN per servce from the ccess locto (e.g. DLSAM wred d odeb 4G wreless) utl the edge locto (BNG etheret ggregto or RNC 4G wreless); d) the servce provders do ot ted to corporte L3 type cpbltes d

6 6 IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT, ACCEPTED FOR PUBLICATION TABLE III VOLUMES OF TRAFFIC Trffc Volume per subscrber HSI trffc (Mbps) for resdetl customers HSI trffc (Mbps) for busess customers Bdrectol P2P (Locl trffc) Mbps IPTV Bdwdth (Mbps) of ech chel ch Iteret (No locl Trffc) flowg through the locto IPTV Trffc flowg through the locto from the CDN to the frst IP replcto pot P2P (Locl Trffc) flowg through the locto from oe level below from oe level bove to oe level below to oe level bove HSI res HSI bus P 2P ptv ch x HSI x IPTV x CDN x P 2P x P,d, 2P x P 2P,up, x P 2P,d,out x P 2P,up,out mgemet fuctoltes tht close to the subscrbers. For exmple HSI res (o tble III s clculted by tg to ccout the hrmoc me of the bdwdth cosumed per subscrber tht s served by the ccess locto. However, ISP my properly cofgure the per subscrber usge order to ssume worst cse (or some percetle) d possbly overprovso the etwor [19]. I the evluto, we re vestgtg vrety of etwor throughput d showcse the effect of the trffc demd to the optml soluto. The trffc clsses d servce types re geerlly vlble to the ISPs, sce BNGs corporte DPI or flow clssfcto fuctoltes [6]. For modelg resos, we hve grouped the trffc flows to three m clsses,.e. IPTV, Iteret (No Locl) d P2P (Locl). The trffc demds re show o Tble III. We ctegorze the trffc flows ccordg to the effect (utlzto, drecto etc.) tht they hve o ech ggregto level {,, }. Hece we defe three m ctegores of trffc clss: A. Iteret (o locl) Trffc Clss Iteret trffc clss s y type of resdetl or busess trffc tht wll flow through ll the levels of the ggregto etwor. It s usully clet-server type of trffc d ts mor porto s usully web trffc [18]. I terms of etwor optmzto, ths type of trffc stsfes the coservto theorem, uless redudcy elmto devces re cluded y level of the etwor [23]. The Iteret trffc per ggregto level s represeted by the followg equtos. x HSI = x HSI u, (xres = + x bus ) u, xhsi (1) x HSI = (x res + x bus ) The o locl trffc tht flows through ccess locto s bsed o the umber of subscrbers d the correspodg etwor usge per subscrber. Thus x res = res HSI res d x bus = bus HSI bus, dcte the budled trffc tht rrves ccess locto, for resdetl d busess subscrbers respectvely. The reso tht we use seprte volumes for ech type of subscrber s becuse the etwor usge s dfferet d ther coectos towrds the edge systems re dfferet. B. P2P (Locl) Trffc Clss P2P trffc clss cludes those pplctos tht exhbt loclty ther behvor. Those trffc flows re dstrbuted cross the ggregto etwor over severl drectos d my ether rem locl the sme geogrphcl re (e.g., P2P or busess ut tht hs locl server), or the sme routg dom, d deped o how peers re tercoected. I P2P systems the fles re splt smller chus d re dowloded from vrous sources. The system s therefore ttg vrous flows to vrous users. The P2P flow wll hve dfferet performce bsed o the plcemet of the routg fuctoltes. Let us ssume tht users the sme ccess locto re dowlodg P2P trffc wth cert throughput P 2P Mbps from sources tht re ether the sme edge etwor or outsde the ggregto re. Therefore, the totl P2P trffc tht flows through ccess locto s x P 2P = sub P 2P. The dstrbuto of fuctoltes s lso ffected by the overly P2P etwor. If the user s dowlodg fle from peers the sme frst ggregto level the we deote ths probblty wth p 1. Smlrly f the two peers coexst t the sme secod ggregto level locto, ther probblty s p 2, d p 3 for the thrd ggregto level locto. Sce the P2P fles re usully dvded chus, the bove probbltes c be regrded s equl to the porto of trffc tht s comg from users t the sme ggregto level. Prctclly those probbltes re relted to the drecto of the trffc, d c be clculted by the ISP through performg flow detfcto (such fuctolty c be foud both L2/L3 devces). Equvletly for the flow tht goes outsde of the etwor 1 3 l=1 p l. The questo ow s how ths probblty my ffect the cost of the rchtecture. The followg equtos show how the P2P trffc flows over the etwors. Effectvely the frst equtos budles the P2P trffc to VLAN tht wll be offered to the frst ggregto lyer. The exstece of router of type t t y level, sdefedbythevrble,t wll ffect the drecto of the flow. For exmple, f router tht performs IP termto (t T 1 ) s plced t the frst ggregto lyer (,t = 1), ll trffc tht would rem locl t the frst ggregto lyer would ot hve to flow through the rest of the lyers. Smlrly for the rest of lyers x P 2P x P 2P = [,tx P 2P + = {(1,t )(1 x P 2P = u,x P 2P (,t +,t 2 =1 p )+,t } u,x P 2P 3 p )] (2) =2 x P 2P C. Multcst Trffc Clss Multcst s requred order to me effcet use of etwor resources whe delverg brodcst cotet. Mly, the desred gol s to support multcst optmzto by cotrollg

7 PAPAPANAGIOTOU et l.: OPTIMAL FUNCTIONALITY PLACEMENT FOR MULTIPLAY SERVICE PROVIDER ARCHITECTURES 7 the floodg of Etheret multcst frmes. The IGMP/PIM- SM gets c loclly dust replcto flters o the devce, such tht pcets re replcted oly o those ports tht hve specfclly requested to be prt of the multcst group [8]. However, the locto of the multcst fuctolty (ether s IGMP soopg o L2 devces, or s IP multcst o L3 devces) s bsed o the VLAN rchtecture. I the followg, we ssume tht the VLAN polcy mplemeted by the ISP requres the replcto to hppe the edge system. A ucst IPTV trffc flow s ssumed to be tted from the CDN(s) d s replcted t the Edge Router, where multcst s mplemeted. The stremg bt rte s usully betwee ptvch SD =1Mbps for Stdrd Defto (SD) d ptvch HD =10Mbps for HD chels d the user s ssumed to choose ether the chel oe defto or the other [30]. Severl studes hve show tht the selecto of IPTV chels ch {1,..., Ch}, follows Zpf Lw dstrbuto p ch = α/ch, gve tht the chels re rrged by chel populrty [31] (α s costt). It s lso ssumed tht the percetge of resdetl users per ccess loctos (e.g., DSLAM, Wreless Bse stto) tht hve selected the IPTV servce s w. I order to clculte the requred bdwdth for the ucst trsmsso of IPTV chels, from the CDN to the frst replcto pot, the umber of requested chels, from the resdetl subscrber populto, eeds to be determed. The probblty tht t lest oe user s wtchg chel c, d belogs t the subtree formed by the locto, c be determed s 1 P {oe wtchg chel ch}(t) = 1 (1 p ch ) w res u,. Therefore, regrdg the ucst flow from the CDN to the frst IP replcto pot, the bdwdth c be defed by the followg equto x CDN = ptvhd ch + ptvsd ch 2 Ch 1 (1 p c ) w res u, c=1 (3) After the flow reches the Vdeo router ll flows re dstrbuted to the subscrbers through multcst. However, the dstrbuto of vdeo routg fuctolty plys role o the dstrbuto of IPTV flows over the etwor. Note tht f multcst routg fuctolty hs bee determed to exst tht locto, the the flow coservto theorem does ot hold (sce the vdeo router wll replcte the IPTV flow to the correspodg IPTV VLANs). For exmple, f sgle BNG s plced the frst ggregto level, the the multcst s gog to hppe closer to the subscrbers. Therefore the IPTV flow tht every ccess locto s demdg s = w res IPTV ch (percetge of users w from the populto of sub coected to ccess locto ), the the flows re gog to be dstrbuted the etwor s follows x IPTV x IPTV = u,x IPTV x IPTV, there re two possbltes. If type T 3 router s plced t y of the depedet frst ggregto levels (,t =1), the the bdwdth of the IPTV flows s equl to xiptv. If ths s ot the cse, the the bdwdth s equl to the eq. (1). The thrd equto tes to ccout the property t T 3 (,t + ul3,t + ul3,t ). Thus, f router tht cludes IPTV fuctolty s cluded t the cetrl locto, the the IPTV bdwdth s xiptv. Otherwse t mes tht IPTV cpble router hs bee plced ether the 1st or the 2d ggregto level d the bdwdth for the flow s x CDN ptvhd ch +ptvsd ch 2. From the bove, t s redly see tht f users ted to wtch smlr progrms, less bdwdth s used, decresg the frstructure cost. I ddto, tegrtg the multcst fuctolty (.e. t T 3 ), closer to the ccess etwor, decreses the bdwdth too. Therefore the totl mout of trffc tht rrves every ggregto locto s x = x IPTV + x P 2P + x HSI. VI. EDGE DESIGN MODEL The obectve fucto of the optmzto problem s to determe the optmum deploymet cost by optmlly dstrbutg the fuctoltes over the ggregto etwor m {,,}[ (co x,c Y x,c )+ co L3 t Y,t x + col2 Y L2 ] c x t (5) The bove obectve fucto cludes the cost of the terfces bsed o the cpcty c =[1G, 10G], tht wll be mplemeted ode of lyer x =[L2,L3] t locto, swellsthe cost of the etwor elemets tht wll be plced t the sme locto. A. Costrts 1) No Ler to Ler Trsformto: The problem hs two sets of vrbles per locto, Y,t L3 d,t. The multplcto of those vrbles results o ler problem. Hece, we try to trsform the model from o-ler to ler, by ddg some extr costrts log wth two bg costts BIGD (for the devces) d BIGI (for the terfces). For exmple, devces per locto my rge betwee , therefore BIGD c be s hgh s Ay vlue hgher th tht my result uecessry crese of the serch spce. I the ext secto, we provde heurstc to determe pproxmte upper boud. The extr costrts re expressed s follows: Y L2 Y L3,t BIGD BIGD (1,t), {,, } (6) {t T 1 =, } or {t T = } x IPTV = x IPTV u,[,t x CDN +(1,t )x IPTV ] (4) t T 3 t T 3 = x IPTV,t + xcdn t T 3 (1 t T 3,t ) For the frst defto of the bove equto, x IPTV s equl to the bdwdth tht ll IPTV VLANs geerte. For the The bove costrts specfy tht () the Y,t L3 must be bgger th bg costt, d (b) every locto there c be oly ggregto swtch or edge system. I terms of fuctoltes, the two sets defe tht for the frst d secod ggregto levels = {, }, oly IP termto fuctoltes c be dstrbuted (t T 1 ). The lst set effectvely excludes the mult-edge rchtecture from the possble

8 8 IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT, ACCEPTED FOR PUBLICATION solutos. We follow smlr pproch for the terfces. BIGI Y L2,c Y L3,c Y L3,c,t, {t T 1 =, }, {t T = } BIGI (1,t), {,, } (7) + Y L2,c BIGI u c, {,, } The frst costrt, of the bove set, defes tht edge system terfce wll be chose f t lest oe edge system s stlled tht locto. The secod costrt shows tht ggregto swtch t locto must ot be stlled f edge router s stlled t ths locto. The lst costrt dctes tht ether 1Ge or 10Ge terfce c be stlled t etwor devce. 2) Avodg redudcy of fuctolty: I order to vod the redudcy of fuctolty pth, oly cert combto of routers c be used per pth. The pth strts from the ccess ode d eds t the P-Router, d c be represeted by the multplcto of the followg bry costts u, u,. I tht pth, ech fuctolty must ot be repeted (whch s represeted by the sum of the bry vrbles the pth must ot be greter th oe) d cert fuctolty must ot be used. u,u,,t +,t +,t 1 u,u,( t={a,c} u,u,( t={a,b} u, u, u, u, (,t +,t )+,t) 1 t T 2 (,t +,t )+ t T 3,t) 1 u,u,,t +,t +,t (8) t={a,c} t={a,b} (,t + ul3,t )+ t T 2,t (,t + ul3,t )+ t T 3,t 3) Cpcty Costrts: The cpcty costrts defe the mout of trffc tht ether ggregto swtch or edge system c support. Ths s effectvely the bcple cpcty. For the cse of dstrbuted router,t =1selected t locto = {, }, the followg two costrts re defed,t(x CDN + x res + x bus + x P 2P ) Y,t L3 Ct L3, (9) = {, },t= {A, B},t(x IPTV + x res + x bus + x P 2P ) Y,t L3 Ct L3, (10) = {, },t= {C, D} Type A d B do hve multcst fuctolty, therefore they wll replcte the trffc. Hece, oly the flows tht correspod to the requested chels eed to be routed x CDN. Noetheless, f type C or D re selected to be dstrbuted, the the replcto of the chels s doe the core locto, d they wll eed to route the budled flows for the multcst trffc. Strtg from the top, type A router hdles ll trffc, therefore the throughput t cetrl must be less th the totl throughput of the routers of type A. Note tht type A hdles ll types of trffc, thus t serves ll the trffc x CDN + x bus + x res + x P 2P. Smlrly for the rest, wth the m dfferece tht oly subset of fuctolty re support per edge system.,a (xcdn + x bus + x res,b (xbus,c(x res + x res + x bus,d(x res + x P 2P ) Y,A L3 C A + x P 2P + x P 2P + x P 2P,Ex bus,f x CDN ) Y L3,B C B ) Y,CC L3 C ) Y L3,DC D (11) Y L3,EC E Y L3,F C F For the swtchg cpcty thgs re more complcted s the cpcty s ffected by the dstrbuto of the edge system fuctolty. For exmple, the closer the multcst fuctolty s to the subscrbers, the closest the replcto tes plce. Equto (VI-A3) dctes the swtchg cpcty costrts. The frst s relted to the loctos the frst ggregto level. Ths costrt dctes tht f edge = 1 the there s o eed to cre bout the swtchg cpcty. The secod costrt s relted to the loctos the secod ggregto level. If multcst replcto tes plce t lower level,a + ul3,b =1,the system s stlled,t oly sgle flow per chel eeds to be swtched x CDN. If t s tg plce t the core locto,,c + ul3,d =1 or t T 3,t =1(T 3 s the set of the routers tht support multcst), the seprte flow per subscrber for the IPTV eeds to be swtched. Flly, f router s plced t the secod ggregto level,t =1, the there s o eed to swtch y trffc. If swtch s plced core locto d lso MSE or Vdeo BNG s plced t the sme locto, the they wll route busess d IPTV trffc d therefore those two portos eed to be excluded from the swtchg cpcty x bus (1 t T 2,t )+xcdn (1 t T 3,t ). Those costrts c be foud the equlty set (VI-A3) t the top of the ext pge. 4) Subscrber Termto/VLAN Cpcty: The followg equltes determe the umber of VLANs per locto. A dstcto s mde betwee the resdetl d the busess VLANs. S res = S bus S res = S bus u, Sres,Sbus = = S res u, Sbus u,(1,t )S res u,(1 t={a,c} = = (1,t )S bus (13) (1,t)S res T 1 t={a,c},t)s bus For routers of type A, B, C d D whch my exst t y of the levels = {,, } the subscrber termto costts re smlr to the cpcty oes. They re expressed s follow,t S Y,t L3,whereS = S res + S bus for Type A/C, S = S res for B/D. S = sum BUS for Type E,

9 PAPAPANAGIOTOU et l.: OPTIMAL FUNCTIONALITY PLACEMENT FOR MULTIPLAY SERVICE PROVIDER ARCHITECTURES 9 (u, (,A + ul3,b )xcdn +(,C + ul3,d )xiptv (1,t )(xcdn + x res + x bus )+,t xiptv t T 3 + x P 2P (1,t )(xiptv +(x res + x bus )+x bus (1 t T 2 + x res + x bus + x P 2P ) Y L2 C gs + x P 2P )(1,t ) Y L2 C gs (12),t )+xcdn (1,t ) Y L2 t T 3 C gs d S = w RES for Type F. The ltter s expressed le tht s ll these must be termted t the Vdeo BNG, becuse oly porto w of subscrbers re wtchg chel d the totl umber of IPTV VLANs re determed by w res For VLANs tht eed to be swtched, the cse s bt more complcted. For the secod level of ggregto d f customer hs bee lredy bee termted the prevous level, the J 1 VLANs wll be requred to swtch trffc mog the sme level of swtches d oe more tht wll sed the trffc to the P-router. If however oly the resdetl subscrbers hve bee termted the prevous level (,B + ul3,d =1) the the busess VLANs wll stll rem (S bus + J). The costrts for the VLAN cpcty re metoed the ext pge, equlty (14) 5) L d Iterfce Costrts: Ech ccess locto sssumedtohven devces d ech locto hs both upl d dowl terfces. The mmum umber of dowl terfces from the frst ggregto level s equl to the umber of ccess devces tht re coected to ths locto,.e. u, N. I every of the frst d secod level ggregto loctos ether router or swtch or othg s plced. Therefore, two of the Y L3,c,d 1, re gog to be zero. u,( Y L3,t Y,t L3 u, N c + Y L2 ) Y 0,d, + c + Y L2 + Y 0,d, c, Y L2,c,d 1, (Y L3,c,d, Y L3,c,d, Y L3,c,d, d Y 0,d, + Y L2,c,d, ) + Y L2,c,d, + Y L2,c,d, (15) elemet. The costrts re expressed s follows. u, Y L2,c,d, + u, Y L2,c,up, Y L2 P L2,c u,y L3,c,d, + u,y L3,c,up, Y,t L3 P L3,c,t u, Y L2,c,d, + Y L2,c,up Y L2 P L2,c (16) u,y L2,c,d, + Y L2,c,up t T Y L3,t P L3,c,t As we c see bove, the frst costrt mes sure tht there s t lest oe l betwee the ccess ode d the frst ggregto level. However f the soluto determes tht o devce s gog to be stlled, the d d Y 0 =1. 6) Iterfce Cpcty Costrts: The terfce cpcty costrts re the most complcted, sce they must be determed wthout y owledge of the plcemet of the devces. I every devce there re gog to be terfces tht coect both the upl d the dowl. Y x,c = Y x,c,d 1, + Y x,c,up,+1 (17) gves the totl umber of terfces of cpcty c per locto. Moreover, ll cses the upl cpcty s equl to the dowl cpcty of the hgher lyer. For stce for the l betwee the ccess locto d frst, the costrt s s follows u, (xiptv +x res +x bus +x P 2P x Y x,c,d, C c. ) c For the ls betwee d, The bdwdth of the upl of the frst ggregto level s clculted to be: ) the teret d busess trffc (o locl flows); b) f multcst fuctolty =1, the flow of the chels from the secod ggregto level x CDN ;c)fthere s ot multcst fuctolty 1,t =1o the frst level, the IPTV flow of ech subscrber; d) f there s routg fuctolty,t =1the P2P porto tht s ot frst level locl (1 p 1 )x P 2P. For smplcty we meto oly the s plced t the frst level,,a + ul3,b dowl costrts (the upl to re the sme). Smlrly the remg terfce cpcty costrts re clculted for the other two ggregto levels. The etwor elemets lso hve le crd cpcty. Ech le crd s seprte module tht hs specfc cpcty of ports d fuctoltes. We ssume two types of le crds, oe for swtches d oe for routers. Ech elemet my te ports of the sme type, 1Ge d 10Ge, d the port cpcty s determed by multplyg the umber of le crd slots to the umber of ports per le crd. Sce the umber of ports per le crd s ffected by the bdwdth of the terfces, the sme wll hold for the totl umber of ports per etwor VII. MODEL IMPLEMENTATION As mxed teger progrmmg model, the problem s cosdered to be NP-hrd (polyoml tme hrd). We ppled two heurstcs to decrese the umber of vrbles. After ths phse, we used the brch-cut-lgorthm from the CPLEX 11 ege. Flly, we used the CPLEX presolver to elmte redudt rows d colums. I the followg we descrbe the two heurstcs:

10 10 IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT, ACCEPTED FOR PUBLICATION u. ((ul3,a + ul3,c (1,t )S Y L2 sub gs )J +(ul3,b + ul3,d )(Sbus + J)) +,t S Y L2 sub gs (14) u,((,a +,B)x CDN +,t (1 p 1 )x P 2P +(1,t )x IPTV x HSI + x BUS + x P 2P )+x HSI + x BUS c +(1,t )(1 p 1 p 2 )x P 2P +(1,t )xcdn +,t xiptv t T 3 t T 3 x HSI +(1 3 =1 p )x P 2P + x CDN + x BUS c c x x x Y x,c,d, C c (18) Y x,c,d, C c (19) Y x,c,up C c (20) TABLE IV INPUT PARAMETERS FOR AGGREGATION NETWORK CHARACTERISTICS AND INTERFACE PROPERTIES Symbol Descr/Uts Smll SP Bg SP A Loctos I Loctos 6 50 J Loctos 3 5 K Loctos 1 SUB Subscrbers 200K 400K res Subscrbers 160K (80%) 320K (80%) bus Subscrbers 40K (20%) 80K (20%) S Subscrbers 200 Ch Chels 100 w % of vewers 50% C1G L2/CL2 10G Bytes 1G/10G C1G L3/CL3 10G Bytes 1G/10G co L2,1G $ 1K co L3,1G $ 2K co L2,10G $ 2K co L3,10G $ 4K Heurstc 1: Mmzg umber of vrbles. Geerlly the umber of ccess loctos A vres from hudreds to thousds mg the problem hrd to be solved. For ths, we mplemeted clusterg lgorthm to determe the umber of ccess loctos. The lgorthm strts wth sgle cluster cl =1, creses the umber of clusters every terto, d termtes whe both the tme to covergece s smller th predefed vlue t d the optmlty tolerce s lso smller th predefed vlue c. Ths mes tht the umber of ccess loctos wll be A = cl I, wherecl s the umber of clusters. The dvsve clusterg procedure s s follows 1: procedure CLUSTER(I,t,c ) 2: cl 1 3: A I 4: Ru model to determe t d c 5: whle t t d c c do 6: cl cl +1 7: Perform K-mes clusterg 8: A cl I 9: Ru model to determe t d c 10: ed whle 11: retur cl 12: ed procedure I every terto, the K-mes stce [16] s clled wth ttrbutes relted to the techcl chrcterstcs of the ccess devces. I our cse we used s ttrbutesthe L2 subscrber cpcty of the ccess techologes. After rug the optmzto model severl tmes, we determed tht f the model does ot coverge to soluto less th t = 120sec, t wll hrdly mge to coverge (soft threshold). Flly the optmlty tolerce ws set to I y cse, potetl error terms of Kbps wll ot ffect the soluto of the model (sce ll system cpctes re t the order of thousds of Gbps). Ech ccess locto s ssumed to corporte the sme ccess devce. However, the defto of the locto our model s ot strctly geogrphcl locto. Therefore, f the sme geogrphc locto dfferet ccess techologes re mplemeted, the these re treted s two seprte loctos. Heurstc 2: Mmzg executo tme. The optmzto hs teger vrbles tht re ether bry (qulttve) or o-bry (qutttve). I order to trsform the problem to teger progrmmg model, the vlues of BIGI c d BIGD were troduced. If these vlues re selected to be very bg, the the solver would requre sgfct mout of tme to coverge to optml soluto. If the vlues re selected to be smll, the soluto would ot be the optml (or the problem could be fesble). Thus the vlues were selected by tg to ccout the mout of trffc tht flows d the umber of VLANs the correspodg locto. A logcl upper boud for the umber of devces per ggregto locto c be derved from X BIGD = mx{ m{ct L3,t T }, sub m{subt L3,t T } } (21) For upper boud o the umber of terfces, we used the bove upper boud multpled by the most umbers of ports BIGI c = BIGD mx{p c,l3 t,t T }, c {1G, 10G} (22) Usg the bove vlues the solver ws determg the soluto less th 1m o Itel Core2 Duo T7700 wth 4GB RAM. VIII. EVALUATION AND RESULTS I ths secto, we use two exemplr rchtectures to evlute the foremetoed edge desg model. The frst

11 PAPAPANAGIOTOU et l.: OPTIMAL FUNCTIONALITY PLACEMENT FOR MULTIPLAY SERVICE PROVIDER ARCHITECTURES 11 TABLE V NETWORK ELEMENT FEATURES 5.2 x Mbps Iteret Trffc 7.6 x 104 4Mbps Iteret Trffc Edge Cost Cpcty IP Term. 1Ge 10Ge System co L3,t (K$) C t(gbps) subl3,t PL3,t 1G PL3,t 10G All HSI/VdeoBNG HSI/MSE HSI MSE Vdeo BNG Cost Swtchg VLAN 1Ge 10Ge K$ C t(gbps) vl PL2 1G PL2 10G Agg. swtch rchtecture, mely smll SP, s bsed o EU ISP wth 200K subscrbers. The secod rchtecture, mely bg SP s bsed o other EU ISP wth twce the umber of subscrbers, d te tmes more frst level ggregto loctos. We use severl trffc sceros per subscrber (very low up to very hgh). We performed ths vestgto such tht future trffc growth s corported our modelg. I tble IV, the detls of the rchtectures re gve. I tble V the vlues for ech edge system re showcsed. These vlues were provded by vedor d re represettve of hgh-ed systems t the tme of submsso 2. The umber of terfces the tble s derved by multplyg the umber of ports per le crd wth the cpcty of le crds per edge system. I ddto the locl (P2P) trffc does ot exceed 20% of the totl teret trffc [18] d P2P loclty probbltes p get vlues from uform dstrbuto. The questos tht we try to ddress re s follows Whch of the fuctoltes should the provder dstrbute closer to the subscrber? Does the sze of the ISP ffect the choce of the optml fuctolty plcemet? Should the provders choose fster (but more costly) le crds or fster bcple Edge Router? Wht s the usge (or how much redudcy exsts) per edge system for throughput, termto cpbltes d port vlblty? How does chge the umber of subscrbers ffect the tellgece dstrbuto? I Fg. 4 the cost of multple rchtectures s show for the bg servce provder. The cetrlzed d 2d level dstrbuted rchtectures re vestgted. The 1st level ggregto s the frst level bove the ccess etwor d smlrly for the rest. Due to the umber of 1st level ggregto loctos, we foud tht the cost of dstrbutg the fuctoltes t the 1st level ws hgher th the other two. For ths reso, the cetrlzed d the 2d level dstrbuted rchtectures were chose to be plotted. I the cse of smll mout of multcst flows, the cetrlzed uclustered seems to be the cost optml rchtecture. Ths s becuse most of the trffc goes through the cetrl loctos to the bcboe. However, crese of multcst trffc leds to sgfct crese the cost of the 2 The prces of those systems my vry over tme d offer. However those vlues re represettve t the tme of submsso through prvte commucto wth t lest oe vedor. A cremetl chge of those vlues does ot ffect the formulto of the problem. Cost (K$) Cetrlzed Uclustered 6.7 Cetrlzed Uclustered Cetrlzed Clustered (BNG/MSE) Cetrlzed Clustered (BNG/MSE) 3.6 Dstrbuted Uclustered (2 d gg. level) 6.6 Dstrbuted Uclustered (2 d gg. level) Dstrbuted Clustered (2 d gg. level for BNG) Dstrbuted Clustered (2 d gg. level for BNG) IPTV Mulcst (Mbps) IPTV Multcst (Mbps) Fg. 4. Cost comprso for the bg servce provder per ggregto etwor for 0.5Mbps d 4Mbps of locl d o locl trffc (Iteret). Cost (K$) 1.6 x 0.5Mbps Iteret Trffc 104 Cetrlzed Uclustered Cetrlzed Clustered (BNG/MSE) 1.5 Dstrbuted Uclustered (1 st gg. level) Dstrbuted Clustered (1 st gg. level for BNG) IPTV Multcst (Mbps) Cost (K$) Cost (K$) x 4Mbps Iteret Trffc 104 Cetrlzed Uclustered Cetrlzed Clustered (BNG/MSE) 2.3 Dstrbuted Uclustered (1 st gg. level) Dstrbuted Clustered (1 st gg. level for BNG) IPTV Multcst (Mbps) Fg. 5. Cost comprso for the smll servce provder per ggregto etwor for 0.5Mbps d 4Mbps of locl d o locl trffc (Iteret). cetrlzed rchtecture. O the other hd, the rte of cost crese for the dstrbuted s smller, d fter some pot t becomes cheper. The pot t whch the grphs meet s mportt. It effectvely shows t whch pot the SP wll eed to dstrbute the fuctoltes. For smll mouts of teret trffc (0.5Mbps per user) the meetg pot s roud 8 Mbps of multcst trffc, d for much lrger teret trffc (4Mbps per user) t s roud 4Mbps. I such lrge mouts of trffc, ether the cpcty costrts of the elemets or the port costrts re met, ledg to more devces/terfces. Therefore, the dstrbuto of IP tellgece s preferble, becuse () t llevtes the bottleec due to P2P trffc tht y other cse would eed to go the cetrl locto d (b) the multcst trffc s replcted closer to the ccess etwor. Flly, clusterg the devces does ot hve postve mpct (compred to the uclustered cse) to the cost. I the Bg SP there s eough cpcty (by cpcty here we me the shdow prce of the subscrber, trffc d port costrts) to support ll dfferet servces.

12 12 IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT, ACCEPTED FOR PUBLICATION Number of Iterfces Number of Iterfces Used terfces t the cetrl locto Mxmum supported terfces by the BNGs for the cetrlzed Used terfces per 2 d gg. level locto Mxmum supported terfces by the BNGs per 2 d level gg. locto Used terfces per 1 st gg. level locto Mxmum supported terfces by the BNGs per 1 st level gg. locto Bg Servce Provder Locl & No Locl trffc (Mbps) Used terfces t the cerl locto Mxmum supported terfces by the BNGs for the cetrlzed Used terfces per 2 d gg. level locto Mxmum supporterd terfces by the BNGs per 2 d level gg. locto Smll Servce Provder Locl & No Locl trffc (Mbps) Cpcty (Mbps) Cpcty (Mbps) Bg Servce Provder x Requred cpcty t the cetrl locto Offered cpcty by the BNGs for the cetrlzed Requred cpcty per 2 d gg. level locto Offered cpcty by the BNGs per 2 d level gg. locto Requred cpcty per 1 st gg. level locto Offered cpcty by the BNGs per 1 st level gg. locto Locl & No Locl trffc (Mbps) x Smll Servce Provder Requred cpcty t the cetrl locto Offered cpcty by the BNGs for the cetrlzed 12.8 Requred cpcty per 2 d gg. level locto Offered cpcty by the BNGs per 2 d level gg. locto Requred cpcty per 1 st gg. level locto Offered cpcty by the BNGs per 1 st level gg. locto Locl & No Locl trffc (Mbps) Fg. 6. Used ports vs vlble ports ggregto locto wth vrble Iteret d costt IPTV=6Mbps trffc. Fg. 7. Trffc cpcty d bdwdth of edge loctos plotted wth vrble Iteret trffc d costt IPTV=6Mbps trffc. I Fg. 5 we performed the sme comprso for smller provder. I ths rchtecture the dffereces mog the mplemettos become more ppret. For low vlues of multcst trffc, cetrlzed s optml. But the crese of multcst trffc ffects sgfctly the cost of cetrlzed rchtecture. Moreover ssumg costt teret bdwdth, crese of multcst trffc would ot ffect the cost of dstrbuted rchtecture. Gettg deeper to ths ssue, the IPTV flows re ucst, utl they rech router, whch cse they become multcst. The umber of ucst flows re t most equl to the umber of chels the SP provdes. For the worst cse scero of 100 dfferet chels to be wtched t HD (10Mbps), the totl trffc wll ot exceed the cpcty of terfce (1Gbps or 10Gbps). A cost bredow showed tht t s optml to use 10Gbps terfces, whch leves plety of bdwdth for eve more chels to be offered wthout hvg to crese the umber of terfces. Sce the replcto fuctolty s closer to the ccess etwors, the crese of multcst trffc wll oly ffect the dowl ports of the routers. A sgle 1Gbps port, tht s coected to ccess locto, wll be ble to hdle 100 HD IPTV flows. Sce every DSLAM s hvg subscrber cpcty of 200 customers d 50% of customers re ssumed to be regstered to wtch TV, the there s o effect o the umber of ports. Combg those results wth the sestvty lyss from Fg. 6, t loos tht there re eough slots to hdle eve bgger mout of multcst flows (therefore terfces). The optml cost wll oly be ffected by the cost of the terfces (shdow prce). Thus, dstrbutg the replcto fuctolty seems to be cost effcet. I smlr trffc sceros for the smll SP, the dstrbuted rchtecture costs two tmes less th the cetrlzed. I Fg. 6, sestvty lyss ws performed to determe f d how much the umber of ports s ffectg the soluto of the problem. I ths fgure the uclustered cse s plotted for vrble teret trffc. The brs re preseted sets; the frst br s the umber of used ports t ggregto locto d the secod br s the sum of the umber of vlble terfces t the sme locto. Thus, the secod br must be lwys lrger th the frst br, order for costrt to be stsfed. The steps of the y-xs re equl to the 10G terfce cpcty of BNG (24 ports). It s clerly show tht the cetrlzed uclustered topology, d for both smll SP d bg SP, the umber of requred terfces determes the umber of edge systems to be used (for exmple for 0.5, 1 d 4Mbps f oe less BNG ws used the port costrt would hve bee volted). A smlr cocluso c be derved for the dstrbuted uclustered cse t the frst ggregto level. Therefore, cresg the terfces bdwdth such tht they hdle more trffc or cresg the cpcty of the chsss for le crds would decrese the umber of requred edge systems (d therefore the cost). I Fg. 7 the mout of trffc tht flows through specfc locto d the mout of trffc tht the edge systems c hdle t the sme locto s preseted. Smlrly to the bove cse, the steps of the y-xsre equlto the bcplecpcty of BNG (160Gbps). I most cses, t s clerly show tht the bdwdth of router does ot hve effect o the umber of edge systems. For exmple, eve f hlf of the edge systems re beg used, the set of the bdwdth costrts would stll ot be volted. Therefore, crese the cpcty of the edge systems does ot hve sgfct mpct o the ggregto etwors. I Fg. 8, t s show tht for the Bg SP wth low volumes of teret trffc per subscrber d cetrlzed topology, the umber of edge systems seems to be ffected by the VLAN cpcty. However, s the trffc creses, the terfce cpcty costrt becomes the oe tht requres the ddto of more edge systems. A smlr ptter s followed by the smll SP. A terestg pot s tht the subscrber termto cpbltes hve o effect o the dstrbuted rchtectures. Flly, tble IV, bredow of costs s show for 1Mbps HSI d 6Mbps multcst trffc. For both the smll d the bg SP d whe dstrbuted topology s mplemeted, the edge router cost becomes domt. Due to the fct tht the trffc s dstrbuted over the ccess loctos, whe dstrbutg the fuctoltes closer to the subscrbers,

13 PAPAPANAGIOTOU et l.: OPTIMAL FUNCTIONALITY PLACEMENT FOR MULTIPLAY SERVICE PROVIDER ARCHITECTURES 13 TABLE VI COST BREAKDOWN IN THOUSANDS OF DOLLARS FOR IPTV=6MBPS AND HSI=1MBPS Agg. Swtch (L2) L2 1G L2 10G Edge Routers (L3) L3 1G L3 10G Cetr. Smll SP Dstr. Smll SP (2d gg. level) Dstr. Smll SP (1st gg. level) Cetr. Bg SP Dstr. Bg SP (2d gg. level) Dstr. Bg SP (1st gg. level) x Bg Servce Provder Customers t the cetrl locto Supported customers by the BNGs for the cetrlzed cse Customers per 2 d gg. level locto 7.68 Supported customers by the BNGs per 2 d level gg. locto Customers per 1 st gg. level locto 5.12 Supported customers by the BNGs per 1 st level gg. locto Number of Customers Number of Customers x Locl & No Locl trffc (Mbps) Customers t the cetrl locto Supported customers by the BNGs for the cetrlzed cse Customers per 2 d gg. level locto Supported customers by the BNGs per 2 d level gg. locto Customers per 1 st gg. level locto Supported customers by the BNGs per 1 st level gg. locto Smll Servce Provder Locl & No Locl trffc (Mbps) Fg. 8. Number of subscrbers tht re termted per locto wth vrble Iteret trffc d costt IPTV=6Mbps trffc. t s cost optml to use 1G le crds. I cse of cetrlzed topology, the optml soluto cossts of 10G le crds for the edge systems. IX. DISCUSSION Our results showed tht re-egeerg the edge frstructure s of mportce order to ccommodte tellget ggregto. More specfclly: 1) For smll SP the dstrbuted rchtecture s cheper, sce oly 2-3 BNGs re requred per 1st ggregto level. For the bg SP the dstrbuted rchtecture s lso less expesve, but the dfferece wth the cetrlzed s smller. 2) For smll SP the umber of BNGs s mly ffected by the umber of ports. Yet, f the SP wts to dd other edge system order to hve spre ports for reslecy or/d servce flexblty, the totl cost would ot surpss the cost of cetrlzed rchtecture. 3) For the bg SP, the umber of free terfces re less d the subscrber termto costrts hve smll shdow prce, ledg to smller flexblty. 4) Dstrbutg the fuctoltes smplfes the opertol flexblty sce the etwor dmstrtor oly hs to del wth the terfce costrts. Moreover, for both the smll d the bg SP, the cost of the dstrbuted rchtecture does ot crese whe the umber of IPTV chels crese. 5) Cetrlzed sgle-edge rchtectures hve bee prove to rech sclblty lmts, wheres clustered, multedge or dstrbuted rchtectures offer better rchtecturl sclblty, sce smller umber of subscrbers re termted per system. Dstrbuted rchtectures hve some further dvtges. Sclblty from the system resources pot of vew s better, sce the mout of stte formto (memory overhed) the edge system c be substtlly less th cetrlzed rchtecture. I fct dstrbuted rchtectures beeft from polcy eforcemet close to the subscrber (o eed to bchul trffc tht c be dropped). Oe other mportt spect s relted to the operto of the etwor. More specfclly, sgle-edge rchtectures llow provsog of ll subscrbers d servces o sgle system, thus fclttg QoS provsog usg herrchcl schedulers, s well s mml opertol expedtures (OPEX). O the cotrry, mult-edge rchtectures led to dstrbuted provsog for servces dested to the sme subscrber, thus requrg tellget protocols for proper QoS mgemet d geerto of sgfct mout of stte formto. Oe c me more spects tht our study hs ot cluded, but due to spce lmttos our m cotrbuto ws to costruct modulrzed model d provde severl sghts for the servce provders. We pl to exted ths modelg pproch to 4G moble rchtecture [9], [14], s well s vestgte how cchg rchtectures [25] ffect the flow dstrbuto. X. CONCLUSION Ths pper focused o qutttve, cost-optml herrchcl etwor model for dfferetted servces. The model ws bsed o edge systems, whch c receve extr fuctoltes s ttched sub-systems. The modelg pproch corportes physcl chrcterstcs, bdwdth d VLAN/IP termto cpcty, L2 versus L3, multcst d busess fuctoltes. I order to scle dow the problem, d decrese the executo tme, we ppled set of heurstcs tht re bsed o clusterg lgorthms. Our results dcte tht the wdely mplemeted cetrlzed Etheret bsed sgle-edge rchtecture hs reched ts sclblty lmts, hece dstrbutg the fuctoltes closer to the subscrber s fr more effcet. A smll SP wll beeft more from the tellgece dstrbuto th lrger SP d, depedetly of the sze, the SPs should cluster the busess fuctoltes o dfferet edge system. Flly, we showed tht SPs would receve oly mrgl beeft from hgher cpcty edge systems, d should rther focus o the proper llocto of the fuctoltes ther ggregto etwor. REFERENCES [1] Mgrto to Etheret-bsed DSL ggregto, TR-101, DSL forum, techcl report, Apr

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Networ Mgemet, vol. 19, o. 5, pp , Ios Pppgotou (S05, M12) receved the Dpl.Ig. degree Electrcl d Computer Egeerg from the Uversty of Ptrs, Greece 2006, d the M.Sc. d Ph.D. degrees Computer Egeerg/Opertos Reserch from North Crol Stte Uversty 2009 d 2012, respectvely. He hs bee wrded the best pper wrds IEEE GLOBECOM 2007 d IEEE CAMAD 2010, d he s lso the recpet of the IBM PhD Fellowshp, Acdemy of Athes d A. Metzelopoulos scholrshps. He s curretly Advsory Egeer IBM. Hs terests le the res of etwor desg, dt deduplcto, d moble trffc lyss. Mtths Fler (S97, M00) s dstgushed Techcl Mretg Egeer Csco s Servces Routg Techology Group (SRTG). He curretly focuses o Servce Provder rchtectures, d o ext-geerto brodbd rchtectures prtculr. Mtths wors o the evoluto of Csco s mdrge router portfolo, speclzg o techologes tht re prtculrly relevt for Servce Provders, such s Hgh-Avlblty, Brodbd Techologes or Qulty of Servce. Mtths reserch terests re the re of etwor rchtecture evoluto d trffc modelg. Mtths holds Ph.D. Systems d Computer egeerg from Crleto Uversty, Cd, d MSc Opertos Reserch & Iformto Systems from the Lodo School of Ecoomcs d Poltcl Scece, UK. Mchel Devetsots [S85, M94, SM03, F12] receved the Dpl.Ig. degree electrcl egeerg from the Arstotle Uversty of Thesslo, Greece, 1988, d the M.Sc. d Ph.D. degrees electrcl egeerg from North Crol Stte Uversty, Rlegh, 1990 d 1993, respectvely. I 1993 he oed the Dept. of Computer Egeerg t Crleto Uversty, Ottw, Cd s Postdoc Fellow. He lter becme Aduct Reserch Professor, Assstt d Assocte Professor 1996 d 1999 respectvely. I 2000, he oed the Dept. of Electrcl & Computer Egeer t NC Stte Uversty s Assocte Professor, d 2006 he becme Professor. Dr. Devetsots s member of the hoor socetes of Et Kpp Nu, Sgm X, d Ph Kpp Ph. He served s Chrm of the IEEE Commuctos Socety Techcl Commttee Commucto Systems Itegrto d Modelg, d s member of the ComSoc Educto Bord. He hs served s edtor d the edtorl bord of vrous ourls, d hs chred severl IEEE cofereces.