Dynamic Hybrid Topology Design for Integrated Traffic Support in WDM Mesh Networks 1 (Invited Paper)

Transcription

1 Dynamic Hybrid Topology Design for Inegraed Traffic Suppor in WDM Mesh Neworks 1 (Invied Paper) Mina Youssef Elecrical and Compuer Engineering Kansas Sae Universiy Manhaan KS, USA Baek-Young Choi Compuer Science and Elecrical Engineering Universiy of Missouri Kansas Ciy MO, USA Caerina Scoglio Elecrical and Compuer Engineering Kansas Sae Universiy Manhaan KS, USA Eun Kyo Park Ciy Universiy of New York Saen Island NY,10314 USA mkamel@ksu.edu choiby@umkc.edu caerina@ksu.edu eun.park@csi.cuny.edu Absrac The fuure Inerne will require he ranspor of a wide range of services including high bandwidh one-o-many applicaions, wih a dynamic inerconnecion of devices. WDM layer suppor realizes such services in a ransparen, reliable and efficien way. Mos of he recen sudies have been focused on efficienly building and configuring ligh-pahs for unicas or ligh-rees for mulicas in isolaion, and do no ake exising raffic demands and configuraion ino consideraion. In his paper we consider a dynamic design problem of inegraed raffic in a realisic WDM mesh nework. In such a nework, new raffic demands of eiher mulicas and/or unicas are suppored dynamically in he presence of an exising mixure of raffic. The amoun of bandwidh per wavelengh is abundan, while he wavelenghs and ligh spliing capabiliies on WDM swiches are limied. Using subwavelengh sharing among raffic demands of unicas and mulicas, we build a hybrid virual opology ha explois boh exising ligh-rees and ligh-pahs. By opimizing WDM resources in addiion o resource sharing wih exising unicas and mulicas demands, we ruly maximize he WDM layer capabiliy and efficienly suppor more raffic demands. We validae he efficiency of our approach wih exensive simulaions on various nework opologies. Keywords: WDM Neworks, Dynamic Topology Design, Unicas, Mulicas. 1 An earlier version of his work has appeared in he Proceedings of Inernaional Conference on Compuer Communicaions and Neworks (ICCCN) 08. Inernaional Journal of Compuer Neworks (IJCN), Volume (2): Issue (2) 115

2 1. INTRODUCTION As he Inerne raffic coninues o grow exponenially and Wavelengh Division Muliplexing (WDM) echnology maures, he WDM nework, wih era-bis per second bandwidh links, becomes a dominan backbone for IP neworks. Coninuously emerging bandwidh-inensive applicaions in curren and fuure Inerne, however, presen he need of efficien and scalable suppor in an underlying nework. Paricularly, i is increasingly imporan for he WDM layer o faciliae, in an efficien and scalable manner, high bandwidh one-o-many applicaions such as web cache updaing, ransfer of sofware upgrade, ransfer of video, audio, and ex daa of a live lecure o a group of disribued paricipans, whieboard and eleconferencing [1], [2]. In-nework replicaion or branching of mulicas raffic may be done in eiher an opical WDM domain or an elecronic IP domain. In IP over WDM neworks, mere IP layer mulicasing is no efficien enough wihou he suppor of he WDM layer. Enabling mulicasing a he WDM layer has clear advanages. Firs, wih he available opical layer resources (e.g. ligh spliers, wavelengh converers and wavelenghs) we can uilize a more efficien in-nework replicaion via an opical layer mulicas ree han an IP layer mulicas ree creaed wihou undersanding of underlaying physical nework. Wih he inheren ligh spliing capabiliy of opical swiches, i is more efficien o do ligh spliing han copying IP daagrams in an elecronic domain. IP mulicasing creaes copies of daa packes a inermediae rouers from an opical ino an elecronic domain and hen convers hem ino an opical signal, called O/E/O conversion. On he inermediae non-member nodes, his process inroduces exra-delays and consumes IP resources unnecessarily. Second, performing mulicas in opics is desirable and secure, as i provides consisen suppor of forma and bi-rae ransparencies across boh unicas and mulicas ransmissions wihou requiring he daa forma o be known o he upper layer. Wih no WDM layer mulicas suppor, IP mulicas sessions can be realized by having an IP rouer on a mulicas ree make copies of a daa packe in an elecronic domain and ransmi anoher copy o he downsream rouers. However, his requires O/E/O conversion of every daa packe a inermediae rouers on he ree incurs exra-laency and requires he daa forma o be known o he upper layer. When IP mulicas is suppored via ligh-pahs (i.e., WDM muliple unicass), i avoids he delay of O/E/O conversion a inermediae nodes. However, his scheme is no scalable wih a large number of mulicas members and number of groups in he nework. An ideal approach o supporing mulicasing a he WDM layer is o creae mulicas rees in he opical layer direcly. This can be achieved by ligh-ree [3], which uses opical ligh spliing a inermediae nodes as needed in order o replicae an opical signal o muliple downsream pahs. I minimizes he use of wavelenghs and bandwidh as well as O/E/O conversion. The minimal use of physical resources enables us o suppor larger sessions as compared o oher approaches. In supporing large mulicas groups and members, however, he WDM layer mulicas using wavelenghs only may no be feasible, especially due o he limied number of wavelenghs. Based on he observaion ha a high bandwidh capaciy per wavelengh is abundan enough o be shared by muliple raffic demands, [4] exploied exising unicas ligh-pah o build ligh-rees for he WDM layer mulicas wih he subwavelengh sharing approach. However i assumed ha here was no mulicas session se up iniially and only exising unicas ligh-pahs and available physical wavelengh were considered o build ligh-rees. In his work, we exend he idea of subwavelengh sharing o exising mulicas demands. We provide a more flexible and pracical framework where exising ligh-rees could be shared as well. A echnical challenge in subwavelengh sharing of ligh-rees is ha a ligh-ree is designed for a specific group and a wavelengh is no desirable o be shared by differen groups wih differen se of members. I is because he sharing of a ligh-ree for oher mulicas groups will cause all he desinaions on he ree o receive daa packes sen on he ree unnecessarily. We minimize he excess raffic due o ligh-ree sharing while opimizing all he resources. We bound he degree of Inernaional Journal of Compuer Neworks (IJCN), Volume (2): Issue (2) 116

3 sharing in order o mee he QoS of exising raffic. Our soluion is aimed for a dynamic environmen where new raffic demands need o be saisfied wihou disurbing he service of exising raffic. Our main conribuion is ha when new raffic demands, eiher unicas or/and mulicas, arrive, hey can be suppored incremenally, aking available resources and exising raffic demands ino consideraion. If desirable or physical resources are lacking, we allow he use of exising ligh-pahs or ligh-rees in conjuncion wih a possibly new (parial) ligh-ree. A challenging issue when lighrees are shared, is o minimize excess raffic incurred by he differen mulicas demand from he exising ree(s). In order o address ha, we formulae an opimizaion problem ha includes he overhead of excess raffic. We find ha his hybrid (ligh-rees and ligh-pahs) virual opology design enables us o esablish mulicas rees when i would oherwise be impossible. Thus, more raffic demands are suppored under pracical nework condiion of limied wavelengh consrains. Furhermore, our soluion maximally uilizes he available resources of exising ligh-pahs whose raffic demand does no reach full wavelengh capaciy, bu has bounded a degree of sharing for QoS of exising raffic. The idea of using exising mulicas ligh-rees and/or unicas ligh-pahs gives enormous flexibiliy in erms of a dynamically inegraed fuure Inerne raffic environmen, compared o a pure lighree approach. By opimizing he WDM layer mulicas as well as resource sharing wih exising mixure of unicas and mulicas demands, we ruly maximize he WDM layer capabiliy under a pracical environmen. The remainder of his paper is organized as follows. In Secion 2 we provide he background of our sudy. We summarize relaed works in Secion 3. In Secion 4, we formally sae he problem and discuss our approach. The evaluaion and validaion of our scheme is presened in Secion 5. We conclude he paper in Secion Background In Wavelengh Division Muliplexing (WDM) neworks, each direcional fiber opical link is pariioned ino muliple daa channels, each of which operaes on a separae wavelengh, permiing high bandwidhs. Rouers or swiches are conneced via semi-permanen opical pipes called ligh-pahs ha may exend over several physical channels via wavelengh rouing. A inermediae nodes, incoming channels belonging o in-ransi ligh-pahs are ransparenly coupled o ougoing channels hrough a passive wavelengh rouer, avoiding he unnecessary IP layer inerrupion wih O/E/O conversion. Meanwhile, a a node erminaing ligh-pah, he incoming signal from he channel is convered o he elecronic domain so ha packes can be exraced and processed and may be reransmied on an ougoing ligh-pah(s) afer elecronic IP rouing. The concep of a ligh-ree can be exended using opical ligh spliers, in order o replicae an opical signal o muliple downsream pahs. The ligh-pahs and/or ligh-rees esablish a virual opology on op of a physical opology made of opical fibers and swiches/rouers. A virual opology configuraion is consrained by a number of physical resource limiaions: 1) The esablishmen of each ligh-pah requires he reservaion of WDM channel on he physical links along he pahs and he number of available he WDM channels are limied on a link. 2) The number of ransmiers and receivers a each node limis he number of ligh-pah iniiaing and erminaing on he node. 3) The maximum lengh of a ligh-pah wihou signal regeneraion may be limied by he signal aenuaion along he ligh-pah. Therefore, opimizing he use of WDM nework resources is a crucial ask in order o process raffic demand efficienly. The concep of wavelengh sharing has been proposed before in he conex of unicas or mulicas individually. The work in [4] was he firs ha proposed he sub-wavelengh resource sharing among unicas and mulicas raffic demands and provided a general soluion under pracical consrains. Traffic grooming concerns grouping of small flows ino a single wavelengh, ha can be processed and roued as one eniy. Our work addresses he issue of sub-wavelengh sharing wih or wihou raffic grooming. The fuure Inerne will involve inerconnecions of large number of devices ha are Inernaional Journal of Compuer Neworks (IJCN), Volume (2): Issue (2) 117

4 aggregaed a access neworks. High bandwidh WDM mesh neworks a he backbone can be beer uilized wih sub-wavelengh sharing in he wavelengh assignmen and rouing. Subwavelengh sharing can be used in various nework business models. Differen nework business models can be considered as below [5]: Model A: An ISP ha owns he nework from he ground up (i.e., o he duc) and only delivers IP-based services. Model B: The business owns he layer-one infrasrucure and sells services o cusomers who may hemselves resell o ohers. I serves as he carriers carrier and offers wholesale services o ISPs Model C: An ISP ha leases fiber or ranspor capaciy from a hird par, and only delivers IP-based services. Model D: The business is a bandwidh broker. I provides mach-making by enabling a variey of ISPs (model 3) o lease bandwidh from a variey of nework operaors (model 2). Models B and C are complemenary whereas boh are inegraed in case of model A. Our work can be considered as he issues of model A, B or D. 3. Relaed work In recen years, many sudies have been conduced in regards o he problem of designing virual (or logical) opology for WDM neworks. The problem of mulicasing for IP over WDM neworks can be decomposed ino wo subproblems, namely mulicas-ree design, and rouing and wavelengh assignmen (RWA) for he designed mulicas-ree. As o he problem of mulicas-ree design, wo classes of approaches have been aken; namely, opimizaion and heurisics. The mulicas-ree design problem has been modeled ofen as a linear opimizaion problem o minimize he O/E/O conversions, as i is he main boleneck in uilizing he rue poenial of opical neworks. Oher objecives, such as minimizing he average hop coun or average number of ransceivers used in he nework [3] and he oal link weigh of he ligh ree [6] have also been used. In [7], he problem of opimal virual opology design for mulicas raffic is sudied using lighpahs. The auhors aim o minimize he maximum raffic flowing on any ligh-pah in he nework while designing he logical opology for he mulicas raffic. In he same work, he auhors have presened several heurisics for opology design such as Tabu search, simulaed annealing. Linear opimizaion echniques have been also used for he unicas single shores virual opology design [8], RWA [9], [10], resoraion and reconfiguraion [11], [12], [13] problems in WDM neworks. Several heurisics have been proposed o design he mulicas ree in WDM neworks. Alhough a minimum Seiner ree [14] (which is obained by solving Ineger Linear Programming ILP) is more desirable, finding one for an arbirary nework opology is an NP-complee problem [15], hus heurisics are ofen used o obain a near-minimum cos mulicas ree. Auhors in [16] have presened four heurisic algorihms: namely, Re-roue-o-Source & Re-roue-o-Any, Member-Firs, and Member-Only, for designing a mulicas fores for a given mulicas group. The minimum spanning ree (MST) heurisic or he shores-pah ree (SPT) heurisic [14] are also commonly used for designing he mulicas ree. Auhors in [17] have also presened wo such algorihms, Breadh Firs Search (BFS) and a dynamic and incremenal ree consrucion algorihm. Given an exising mulicas ree wih a large number of members, new member nodes perform an operaion of join/graf similar o CBT [18] and DVMRP [19]. Once a mulicas ree is designed, i can be implemened wih eiher wavelengh-rouing [20], [3] or Opical Burs/Label Swiching (OBS/OLS) [21], [22]. In he former case, mulicas daa will be swiched o one or more ougoing wavelenghs according o he incoming wavelengh ha carries i. Tha is a wavelengh needs o be reserved on each branch of a mulicas ree. In IP over WDM mulicas using label swiching, mulicas label swiched pahs are se up firs. Aferwards, only he opical labels carried by he burss need O/E conversions for elecronic processing, whereas he burs payload always remains in he opical domain a inermediae nodes. The major disadvanage of he wavelengh rouing approach is ha i may no uilize he bandwidh efficienly in case raffic demand is no up o wavelengh capaciy. I also has large seup laency and i is no efficien under bursy raffic condiions. Meanwhile, wih OBS/OLS, a burs dropping (loss) probabiliy may be poenially significan in a highly loaded OBS Inernaional Journal of Compuer Neworks (IJCN), Volume (2): Issue (2) 118

5 nework which can lead o heavy overheads such as a large number of duplicae reransmissions in IP layer. In addiion, i may ake a longer ime for an end hos o deec and hen recover from burs dropping (loss) [23]. In [24], he auhors inroduced a ligh-hierarchy graph renewal and disance prioriy ligh-ree algorihm (GRDP-LT), which was proposed o improve he ligh-rees qualiy for any mulicas under ligh spliing consrains. In a ligh-hierarchy, cycles are allowed, which is differen from he ligh-ree where no cycle exiss in he srucure. In a closely relaed work [4], a hybrid mulicas opology was firs designed given only ligh-pahs and physical links. The work is o suppor beer uilize he bandwidhs of wavelenghs for new mulicas raffic; assuming only unicas raffic was suppored iniially. In his work, we exend he concep of sub-wavelengh sharing o exising ligh-rees as well, in addiion o ligh-pahs, and build a hybrid virual opology which explois boh ligh-rees and ligh-pahs. We opimize WDM resources for new raffic while keeping he a priori configuraions for he exising raffic, so ha heir performances are no disurbed. 4. Problem formulaion In his secion, we formally sae he problem of designing hybrid virual opology for given se of mulicas demands using available physical, ligh-pah, and ligh-ree opologies. The nework channel resources are he available wavelenghs on he physical links, he available degree of v sharing of ligh-pahs, C and he available degree of sharing of ligh-rees, C for oher raffic demands. The number of available wavelenghs is bounded by he physical resources, and he degrees of sharing of ligh-pahs and ligh-rees are bounded for he QoS of exising raffic. Nex, we formulae our objecive funcion and discuss he consrains required for he design problem. 4.1 Objecive funcion min w m,n M s,m,n + α m,n Y s,m,n + β i T s,i,m,n s m n The objecive is o minimize he cos of he seleced hybrid opology componens, namely physical wavelenghs (M), ligh-pahs (Y) and ligh-rees (T). In he objecive funcion, m and n indicae a source and a desinaion of he corresponding link, respecively, and s indicaes he corresponding mulicas session. The cos componens, M, Y, and T are binary variables and are weighed by parameers of w, α, and β. New unicas raffic demand can be considered a special ype of mulicas where i has only one desinaion. Thus our objecive funcion adds all he cos of physical links, ligh-pahs, and ligh-rees for each link and each session, for saisfying eiher unicas or mulicas raffic demands. The weighs can be assigned depending on he deploymen or operaional coss. For example, in our evaluaions laer, we have used he weighs of he physical links o reflec he preference o a pah wih minimum hops. Tha is, all physical links have he same weighs. The weigh of a ligh-pah is se o he sum of weighs of physical links ha were used o design he ligh-pah. Then he weigh of a ligh-ree is he sum of physical links building he ree. The objecive funcion wih hose weighs indirecly minimizes he number of non-desinaion inermediae nodes beween differen physical links and ligh-pahs. I also selecs ligh-rees ha have a minimum number of foruious nodes [25], where a node in a ligh-ree is a foruious desinaion if i is no a member in ha session bu receives an excess copy of mulicas session packes [26] due o he configuraion. Our formulaion minimizes he unnecessary excess raffic o foruious nodes, since he cos of a ligh-ree includes he cos of all individual links. i (1) Inernaional Journal of Compuer Neworks (IJCN), Volume (2): Issue (2) 119

6 Daa Inpu adjacen p m, n adjacen V m, n ree i, m, n source s session s, w m, n α m,n β i pavailable C m, n C C v m Definiion Boolean marix. Represens he adjacency of he physical opology. Boolean marix. Represens he adjacency of he exising virual ligh-pah opology. Boolean marix. Represens he adjacency of he exising virual ligh-ree opology i. A source node number for he new mulicas session s. Boolean value. Represens if node member m belongs o he mulicas session s. Cos of using a physical link m, n. Cos of using an exising ligh-pah m, n. Cos of using a exising ligh-ree for mulicas session i. The number of available wavelenghs on he physical link beween node m and n. Degree of sharing on an exising ligh-pah. Degree of sharing on an exising ligh-ree. Decision Definiion variable member s, m Boolean value. member s, m =1 if node m is a session member or an exising ligh-ree member, for new session s. M s, m, n Boolean value. M s, m, n = 1 if he physical link m, n is used for he mulicas session s. Y s m, n Y,, Boolean value. s, m n = 1 if he ligh-pah m, n is used for he mulicas session s. T s, i, m, n Boolean value. T s, i, m, n = 1 if he physical link m, n in an exising ligh-ree i is used for he new mulicas session s. γ s,i Boolean value. γ s, i = 1 if an exising ligh-ree i is seleced o saisfy a new mulicas session s. f s m, n, Flow accommodaions ( m y s m, n physical links m, n., Flow accommodaions ( m s i, m, n s m ) from he source node of session s over differen lighpahs m, n., Flow accommodaions ( m member, member, s m ) from he source node of session s over differen member, ) over ligh-ree i o saisfy he mulicas demand s. s m TABLE 1: Daa inpu and decision variable definiions 4.2 Consrains We discuss a number of consrains o creae hybrid opologies in his subsecion. We carefully se he consrains so ha he number of variables and equaions necessary o be minimized, and be solved for a relaively large neworks. The consrains can be of hree major ypes, namely, consrains for ligh-ree design, flow conservaion, and resource bounds. Daa inpu and decision variables are defined in Table 1. 1) Consrains for ligh-ree generaion: The following se of equaions are o choose ligh-ree(s) i o saisfy a mulicas session s. They ensure ha he variable T s, i, m, n will mainain he opology of he seleced ligh-ree wih he Inernaional Journal of Compuer Neworks (IJCN), Volume (2): Issue (2) 120

7 necessary nodes. These equaions will also ensure ha rouing of any raffic flowing on he lighree i, T,,,, is feasible. s i m n T s,i,m,n ree i,m,n s, i, m, n (2) T s,i,m,n = ν s,i ree i,m,n s, i m n m n (3) T s,i,m,n + T s,i,k,n 1 s, i, m, n, k, k m (4) T s,i,m,n + T s,i,k,n + M s,m,n + M s,n,m + Y s,m,n + Y s,n,m 1 s, i, m, n (5) T s,i,m,n + T s,i,n,m + session s,m member s,m C m, s (6) i n Eq. (2) is o ensure ha if a link m, n is par of he seleced exising ligh-ree i o saisfy he new mulicas demand s, all links in he exising ree should be par of he new mulicas ree. Eq. (3) wih Eq. (2) guaranees ha he variable T s, i, m, n will include all he links of he seleced ligh-ree i o suppor he mulicas session s. Eq. (4) is o avoid he siuaion ha a node in he ligh-ree i receives more han a packe for he same mulicas session s. Eq. (5) ensures ha differen resources (channels) canno be used more han one ime for he same session s on he same link m, n (or ligh-pah m, n). I also eliminaes he case where he raffic flows on he same link m, n in differen direcions (m, n and n,m) for he same session s. Eq. (6) enables ha he members of he new ligh-ree o include he desinaions of used exising ligh-rees as well as he original desinaions of mulicas session s. C is a big posiive number. 2) Consrains for ligh-ree generaion: y s,sources,n + f s,sources,n + s,i,sources,n member s,k 1 s n source s (7) n i k y s,m,n y s,n,m + f s,m,n f s,n,m + s,m,n s,n,m member s,n s n source s (8) n i y s,m,sources + M s,m,sources + T s,i,m,sources = 0 s, i, m (9) s,i,m,sources = 0 s, i, m (10) Firs, Eq. (7) makes sure ha he source node of each session source s sends he raffic demand o all he desinaions using he virual and physical links and he ligh-rees aached wih he source node. The desinaions are he mulicas session s members, inermediae nodes and he ligh-ree members if an exising ligh-ree is seleced o saisfy he demand for he session s. Eq. (8) represens he flow balance equaion. Eq. (9) ensures ha he source node of session s will no receive a mulicas packe from he same session. The source node has no raffic demand for each mulicas session for he ligh-ree flow as shown in Eq. (10). Inernaional Journal of Compuer Neworks (IJCN), Volume (2): Issue (2) 121

8 3) Consrains for resource bounds: f s,m,n M s,m,n C s, m, n (11) M s,m,n s C pavailable m,n m, n (12) y s,m,n Y s,m,n C s, m, n (13) Y s,m,n C ν m, n (14) s s,i,m,n T s,i,m,n C s, i, m, n (15) s,i,m,n T s,i,m,n s, i, m, n (16) ν s,i C s i (17) M s,m,n P adjacen m,n s, m, n (18) Y s,m,n V adjacen m,n s, m, n (19) Y s,m,n + M s,m,n member s,m C s, m s (20) We assume ha he maximum number of physical wavelenghs of an opical link is C. We also assume he degree of sharing of a ligh-pah, and he degree of sharing of a ligh-ree are limied by v C and C, respecively, in order o ensure he qualiy of service of raffic performance. M, In Eq. (11), he physical link s, m n is used o suppor he mulicas session s, mulicas raffic can be sen over i. Eq. (12) consrains he number of mulicas sessions o number of available channels on he physical link m, n. Eq. (13) is similar o Eq. (11) bu used for ligh-pahs. The number of mulicas sessions ha can use ligh-pah m, n is consrained according o he degree of v sharing C in Eq. (14). Eqs. (15) and (16) force he raffic o flow on he links m, n of he seleced ligh-ree i and o be in he proper direcion. Eq. (17) consrains number of mulicas sessions ha can use ligh-ree i o C where C is he degree of sharing he ligh-ree. Eqs. (18) and (19) consrain he selecion of a physical link and a ligh-pah beween he exising ones. Eq. (20) guaranees ha all he inermediae nodes of he seleced physical links and ligh-pahs are included in member,. s m In summary, he above consrains of ligh-ree generaion, flow-conservaion and resource bounds enable us o use ligh-rees and ligh-pahs wihin he resources available and o mee he given mulicas demands. Noe ha he composie objecive funcion of physical and hybrid virual opology resources given in Eq. (1) provides a generic absracion for capuring a wide variey of Inernaional Journal of Compuer Neworks (IJCN), Volume (2): Issue (2) 122

9 resource and performance opimizaion such as wavelengh, hop coun and delays, by conrolling he weighs of he objecive. FIGURE 1: A simple nework opology (7-node). FIGURE 2: Designed hybrid opologies for new unicas and mulicas demands (7-node nework). (Thick black line: physical link, dashed line: exising ligh-pah, and black line: exising ligh-ree). 5. Simulaion resuls Exensive simulaions have been conduced o invesigae he validiy, feasibiliy and efficiency of our soluion. Firs, we use a simple nework opology o explain our soluion in deail and validae i. We hen apply our soluion o a larger nework o evaluae he feasibiliy and efficiency in a real scale nework. A simple nework opology wih 7-nodes is illusraed in Figure 1. Figure 1(a) shows he physical and virual ligh-pah opologies of he nework, and Figure 1(b) depics he virual opologies of exising ligh-rees prior o he arrival of new raffic demands. Each physical link carries a limied number of wavelenghs. We assume ha he number of available wavelenghs on p each physical link is C = 5. Firs, in order o validae our soluion, we suppose he inegraed demands of six new mulicas sessions and wo new unicas demands have been requesed. The mulicas sessions are S 1 ={1, 2, 3, 4, 6, 7}, S 2 ={1, 2, 3, 4, 6, 7}, S 3 ={1, 2, 3, 4, 7}, S 4 ={2, 3, 4, 6, Inernaional Journal of Compuer Neworks (IJCN), Volume (2): Issue (2) 123

10 7}, S 5 ={1, 3, 4, 6, 7} and S 6 ={3, 4, 5, 6} wih source nodes {4, 6, 1, 7, 1, 5}, respecively. Noe ha S 1 and S 2 have he same se of desinaions bu differen source nodes. Two new unicas raffic demands are requesed addiionally, and hey are U 1 ={1, 5} and U 2 ={1, 2} wih source nodes {1, 2} respecively. Figure 2 shows he creaed hybrid opical opologies wih he given new raffic demands, using our v ILP formulaion. The parameers used are w = 1, β = 0.01, C = 2, C = 2, and he value of α is proporional o he number of used physical links o implemen he ligh-pah. Noe ha for a lighree, he value of β corresponds o each individual link in he ree. We used he homogeneous weighs for concise discussions. However, he weighs can vary for each link as discussed in he previous secion. For example, he weighs may be proporional o he acual lengh of he links, so ha i would reflec he delays. The values of w, α, and β indicae he relaive preference of resource componens for he new hybrid opology design. Small value of β increases he preference of using he ligh-rees over he ligh-pahs and physical links. In he example scenario, ligh-rees are weighed leas, so ha hey would be preferred. The resul shows ha hey are all indeed he minimum cos rees ha parially exploi exising ligh-pahs, ligh-rees as well as physical link wavelenghs. In Figure 2, which represens session opologies, we can observe ha he ligh-rees are firs exploied enirely according o he degree of sharing C. The ligh-pahs and paricularly physical links are no used exensively due o heir high cos coefficiens w and α wih respec o he cos coefficien of he ligh-ree β. FIGURE 3: w vs. he number of links (op) and ligh-rees (boom) used (7-node nework). Nex, we invesigae he impac of opimizaion cos weighs as shown in Figures 3 and 4. Figure 3 v shows he variaion of he hybrid opologies when w is changed, while β is fixed o be 1 and C = C = 2. The figure shows ha he number of used physical links changes according o he number of used ligh-rees. The number of used ligh-pahs increases when w becomes more expensive o equalize he decrease in number of ligh-rees and physical links. Similarly, Figure 4 shows he v variaion of he hybrid opologies when β is changed, while w is consan o be 1 and C = C = 2. Inernaional Journal of Compuer Neworks (IJCN), Volume (2): Issue (2) 124

11 As β increases, he preference of using he ligh-rees decreases and he number of used lighpahs and physical links increases. When a ligh-ree is no longer used, ligh-pahs and physical links are used o overcome he shorage of resources o saisfy he raffic demands. We did no vary α, as we se he parameer α o be he sum of physical link weighs used for he ligh-pah. FIGURE 4: β vs. he number of links (op) and ligh-rees (boom) used (7-node nework). We now consider a larger nework wih 14-nodes as illusraed in Figure 5. Figure 5(a) shows he physical and exising ligh-pahs, and Figure 5(b) depics he exising ligh-ree opologies. The physical cos coefficien w is equal o 1, while he ligh-ree cos coefficien β is se o The ligh-pah cos coefficien α is proporional o he number of used physical links o implemen each v ligh-pah. Degree of sharing a ligh-pah C and a ligh-ree C are se o 2. The new mulicas demands used o evaluae he formulaion are S 1 ={1, 3, 4, 6, 9}, S 2 ={5, 7, 8, 10, 13, 14}, S 3 ={6, 7, 11, 12, 13}, S 4 ={9, 10, 11, 12, 14}, S 5 ={2, 3, 7, 8, 11, 12, 14}, S 6 ={1, 2, 13, 14}, S 7 ={1, 3 7, 11}, and S 8 ={3, 4, 7, 14}, wih source nodes o be {1, 13, 6, 9, 2, 2, 11, 14}, respecively. In addiion, wo unicas demands, U 1 ={1, 8} and U 2 ={3, 10} are requesed wih source nodes {1, 10}. The soluion was found successfully for he larger nework, and we show he creaed hybrid opologies for he unicas raffic in Figure 6, and for he mulicas raffic in Figures 7. We depic he opologies for he mulicas raffic only for he firs five demands, for a concise illusraion. Figure 7 shows he hybrid opology soluions for individual mulicas sessions. Mulicas session 1 uses he exising ligh-ree 1 in addiion o wo physical links beween nodes 3 and 4, and 6 and 9. The new mulicas sessions 2 and 3 use he exising ligh-rees 2 and 4, respecively, in addiion o oher ligh-pahs, o saisfy heir mulicas session demand. The new mulicas session 4 uses ligh-rees 3 and 4, and he new mulicas session 5 uses a physical link, an exising ligh-pah and he exising ligh-ree 5. Inernaional Journal of Compuer Neworks (IJCN), Volume (2): Issue (2) 125

12 FIGURE 5: A Larger Nework Topology (14-nodes). FIGURE 6: Designed hybrid opologies for new unicas demands (14-node nework). (Thick black line: physical link) FIGURE 7: Designed hybrid opologies for new mulicas demands (14-node nework). (Thick black line: physical link, dashed line: exising ligh-pah, and black line: exising ligh-ree) Inernaional Journal of Compuer Neworks (IJCN), Volume (2): Issue (2) 126

13 FIGURE 8: Number of links (op) and ligh-rees (boom) vs. w (14-node nework). FIGURE 9: Number of links (op) and ligh-rees (boom) vs. β (14-node nework) Figures 8 and 9 illusrae he impac of opimizaion cos weighs for he 14-node nework. Figure 8 shows he variaion of he hybrid opologies when β is changed and w is consan o be 1 where v C = C = 2. For small value of β, all ligh-rees are used o creae hybrid mulicass in addiion o some physical links and ligh-pahs. As β increases, more physical links and ligh-pahs are mainly uilized o keep he cos of creaing he hybrid mulicas opologies low. Similarly, Figure 9 shows v he variaion of he hybrid opologies when w is changed and β is fixed o 1 where C = C = 2. The figure shows ha he number of ligh-pahs increases while he number of physical links used is Inernaional Journal of Compuer Neworks (IJCN), Volume (2): Issue (2) 127

14 decreasing, because physical links become more expensive o ranspor he mulicas raffic demand. In addiion, boh Figures 3 and 8 show a similar srucure of he creaed hybrid mulicas opologies. The figures show ha here is a value of w a which he ligh-rees are no longer used o creae he hybrid opologies. This value depends on he nework srucure as well as he ligh-rees srucure. Similarly, Figures 4 and 9 show similar srucure of he creaed hybrid mulicas opologies, and he exisence of a value for β a which ligh-rees are no used o creae he hybrid opologies. We nex evaluae he number of suppored mulicas sessions while varying he degree of sharing v of ligh-pahs and ligh-rees, for his large nework. We assumed ha C and C are he same. FIGURE 10: The number of suppored mulicas sessions vs. degree of sharing of he ligh-pahs and he ligh-rees (14-node nework) Figure 10 shows ha he number of suppored mulicas sessions increases as he degree of sharing increases. Resuls are compared wih no hybrid approach ha does no use subwavelengh sharing. I also compares wih he previous work [4], ha was he firs work ha proposed sub-wavelengh sharing wih exising ligh-pahs bu he sharing of mulicas rees were no allowed. Figure 10 shows ha he number of mulicas sessions linearly increases as he degree of sharing increases. The proposed approach clearly saisfies more mulicas demands wih he sharing of ligh-rees as well as ligh-pahs. 7-node nework 14-node nework Sharing degree # Mulicas % increase # Mulicas % increase TABLE 2: Effec of sharing he wavelenghs Table 2 compares he small 7-node and large 14-node neworks o evaluae he impac of he sharing. I shows he percenage of he increase in he number of suppored mulicas sessions, wih he degree of sharing. The percenage increase is compued comparing wih he case of no sub-wavelengh sharing. Number of suppored sessions increases almos linearly wih he degree of sharing for boh 7-node and 14-node neworks, respecively. Inernaional Journal of Compuer Neworks (IJCN), Volume (2): Issue (2) 128

15 7-node nework 14-node nework Sharing degree( C ) # Mulicas % increase # Mulicas % increase v TABLE 3: Sharing degree ( C ) vs. number of suppored mulicas sessions ( C =1) v Sharing degree( C ) 7-node nework 14-node nework # Mulicas % increase # Mulicas % increase v TABLE 4: Sharing degree ( C ) vs. number of suppored mulicas sessions ( C =1) Tables 3 and 4 show he effec of degree of sharing ligh-pahs and ligh-rees for boh 7-node and 14-node neworks. The number of suppored mulicas sessions increases linearly wih he degree of sharing ligh-pahs and ligh-rees. The degree of sharing ligh-pahs gives more freedom o suppor more sessions han degree of sharing ligh-rees. The exensive simulaions wih small and large mesh neworks shown in his secion illusrae ha he proposed soluion creaes hybrid opologies for more raffic demands han pure wavelengh assignmen in an efficien and scalable manner. 6. Conclusions The fuure Inerne will require he ranspor of a wide range of services including high bandwidh one-o-many applicaions, wih dynamic inerconnecion of devices and services. Due o limied wavelenghs of WDM neworks, an opimal resource managemen is imporan for a new se of raffic service demands while keeping services for he exising raffic. We proposed a hybrid opical opology design over consrained WDM mesh nework, where boh ligh-pahs and ligh-rees are buil. Paricularly, exising ligh-rees as well as ligh-pahs are re-used o creae new hybrid mulicas virual opology. I is o increase he number of suppored inegraed raffic demands of boh unicas and mulicas for he fuure Inerne, using he excess bandwidh of a wavelengh. This sub-wavelengh sharing is done wihin a degree of sharing of ligh-rees and ligh-pahs. The degree of sharing allows and also bounds he amoun of sharing so as o mainain QoS of exising raffic. The problem of creaing a hybrid opical opology is formulaed using ILP approach, given exising physical, ligh-pah, and ligh-ree opologies. We formulaed he ILP in a compac manner, and he soluions can be reached for a relaively large nework in an reasonable ime. Our approach shows how he exising physical, ligh-pah and ligh-ree opologies are exploied for he newly arriving demands opimally wihou re-designing all he opologies from he scrach. This approach maximally uilizes he available bandwidh resources from exising ligh-pahs as well as ligh-rees whose raffic demand does no reach full wavelengh capaciy. We show his hybrid virual opology design enables us o esablish mulicas rees when i would oherwise be impossible wih a pure ligh-ree approach. The proposed soluion can be used in a real pracical environmen where boh unicas and mulicas demands are suppored, and new mulicas demands can be realized incremenally and opimally. Exensive simulaions are performed over various WDM mesh neworks, o show he validiy as well as feasibiliy wih relaively large neworks. As for a fuure work, an efficien heurisic approach can be made o speed up a soluion. Inernaional Journal of Compuer Neworks (IJCN), Volume (2): Issue (2) 129

16 7. REFERENCES 1. K. Hasings and N. Nechia, Challenges and opporuniies of delivering IP-based residenial elevision service. IEEE Communicaions Magazine, vol. 38, no. 11, pp , November R. K. Pankaj, Wavelengh requiremens for mulicasing in all-opical neworks. IEEE/ACM Transacions on Neworking, vol. 7, pp , L. Sahasrabuddhe and B. Mukherjee, Ligh-rees: Opical mulicasing for improved performance in wavelengh-roued neworks. IEEE Communicaions Magazine, vol. 37, no. 2, pp , February S. Bhandari, B.-Y. Choi, and E. K. Park, Hybrid opology for mulicas suppor in consrained WDM neworks. In Proceedings of 20 h Inernaional Teleraffic Congress, Oawa Canada, Jun E. L. V. e. al., Archiecuring he services in an opical nework. IEEE Communicaions Magazine, vol. 39, no. 9, pp , Sep N. K. Singhal and B. Mukherjee, Proecing Mulicas Sessions in WDM Opical Mesh Neworks. Journal of Lighwave Technology, vol. 21, no. 4, April M. Mellia, A. Nucci, A. Grosso, E. Leonardi, and M. A. Marsan, Opimal Design of Logical Topologies in Wavelengh-Roued Opical Neworks wih Mulicas Traffic. in IEEE Globecomm, vol. 3, 2001, pp G. Agrawal and D. Medhi, Single Shores Pah-based Logical Topologies for Grooming IP Traffic over Wavelengh-Roued Neworks. In Proceedings of 2nd IEEE/Creae-Ne Inernaional Workshop on Traffic Grooming, D.-N. Yang and W. Liao, Design of Ligh-Tree Based Logical Topologies for Mulicas Sreams in Wavelengh Roued Opical Neworks. In IEEE INFOCOM, D. Cavendish and B. Sengupa, Rouing and wavelengh assignmen in WDM rings wih heerogeneous wavelengh conversion capabiliies. In IEEE Infocom, D. Banerjee and B. Mukherjee, Wavelengh-Roued Opical Neworks: Linear Formulaion, Resource Budge Tradeoffs and a Reconfiguraion Sudy, IEEE ACM Transacions on Neworking, vol. 8, no. 5, pp , Ocober A. E. Gencaa and B. Mukherjee, Virual-opology adapaion for WDM mesh neworks under dynamic raffic, In IEEE INFOCOM, June B. Ramamurhy and A. Ramakrishnan, Virual opology reconfiguraion of wavelengh-roued opical WDM neworks. In Global Telecommunicaions Conference (GLOBECOM), vol. 2, F. K. Hwang, D. S. Richards, and P. Winer, The Seiner Tree Problem. New York: Elsevier, R. Karp, Reducibiliy among combinaorial problems. Complexiy of Compuer Compuaions, Inernaional Journal of Compuer Neworks (IJCN), Volume (2): Issue (2) 130

17 16. X. Zhang, J. Wei, and C. Qao, Consrained mulicas rouing in WDM neworks wih sparse ligh spliing. Journal of Lighwave Technology, vol. 18, pp , M. Jeong, Y. Xiong, H. C. Cankaya, M. Vandenhoue, and C. Qiao, Efficien Mulicas Schemes for Opical Burs-Swiched WDM Neworks. In IEEE ICC, pp , T. Ballardie, P. Francis, and J. Crowcrof, Core Based Trees (CBT): An Archiecure for Scalable Iner-Domain Mulicas Rouing. in ACM SIGCOMM, pp , Ocober T. Pusaeri, DVMRP version 3. draf-ief-idmr-dvmrp-v3-07. IETF, Augus R. Malli, X. Zhang, and C. Qiao, Benefi of Mulicasing in All-Opical Neworks. In SPIE Conf. All-Opical Neworks, pp , C. Qiao, Labeled opical burs swiching for IP-over-WDM inegraion. IEEE Communicaions Magazine, vol. 38, no. 9, pp , X. Zhang, J. Wei, and C. Qiao, On Fundamenal Issues in IP over WDM Mulicas. In IEEE Inernaional Conference on Compuer Communicaions and Neworks, Ocober M. Jeong, C. Qiao, and Y. Xiong, Reliable WDM Mulicas in Opical Burs-Swiched Neworks. Opicomm, pp , Ocober F. Zhou, M. Molnar, and B. Cousin, Is ligh-ree srucure opimal for mulicas rouing in sparse ligh spliing wdm neworks?. In 18 h Inernaional Conference on Compuer Communicaions and Neworks, B. Mukherjee, Opical Communicaion Neworks: WDM, Broadcas/Mulicas and Wavelengh-Rouing. Mc Graw Hill, T. Sern and K. Bala, Muliwavelengh Opical Neworks. Addison Wesley, Inernaional Journal of Compuer Neworks (IJCN), Volume (2): Issue (2) 131