On the throughput-cost tradeoff of multi-tiered optical network architectures

Transcription

1 1 On the thoughput-cost tadeoff of multi-tieed optical netwok achitectues Guy Weichenbeg, Vincent W. S. Chan, and Muiel Médad Laboatoy fo Infomation and Decision Systems Massachusetts Institute of Technology Abstact In this wok, we conduct a thoughput-cost study of seveal optical netwok achitectues: Optical Flow Switching (), Tell-and-Go (TaG), Electonic Packet Switching (), and Genealized MultiPotocol Label Switching (). The simple, multi-tieed optical netwok that we conside compises two goups of uses, each in a distinct metopolitan-aea netwok (), which wish to communicate ove a wide-aea netwok (). Ou netwok cost model focuses on initial capital expenditue: tansceive, switching, outing, and amplification costs. Ou esults indicate that: is the most scalable achitectue of all, in that it is most cost-efficient when the aveage use data ate is high and the numbe of uses in the netwok is lage; is most sensible when the poduct of the numbe of uses and the aveage use data ate is low; the achitectue, which is conceptually intemediate to and, is optimal when the poduct of the numbe of uses and the aveage use data ate is modeate; and, finally, thee does not exist an optimal egime fo TaG. I. INTRODUCTION Optical netwoking fist emeged as coppe and micowave adio links in communication netwoks wee eplaced by optical fibes. This decision, motivated by the enomous infomation capacity of optical fibe, pevented tansmissioinks fom acting as infomation bottlenecks in communication netwoks. Netwok nodes, which opeated puely in the electonic domain, thus became the point of congestion in communication netwoks when intenet bandwidth demand exploded. To make mattes wose, the heteogeneity of these netwoks equied costly optical-electonic-optical (OEO) convesions at nodes. While ecent yeas have witnessed the development of many novel optical netwoking devices, electonics has emained the clea choice with which to cay out logical opeations at netwok nodes. Thus, any sensible achitectue fo an expansive, teestial communication netwok in the nea futue will necessaily incopoate electonic and optical technologies. Netwok designes ae theefoe faced with the task of judiciously (i.e., economically) integating optical and electonic technology into a capable netwok achitectue. In paticula, the objective should be to design a netwok with excellent scalability: a deceasing cost pe use, pe unit of taffic, as the numbe of uses and individual use bandwidth demand incease. Ou aim in this wok is to addess this vey question of how to best use taditional electonic and emegent optical technology to ceate a scalable, expansive, teestial netwok. Specifically, we conduct a thoughput-cost compaison of seveal pominent netwok achitectues that incopoate vaying The eseach in this pape was suppoted by: National Science Foundation unde Gant No. ANI and DARPA unde Awad No. MDA ; and Natual Sciences and Engineeing Reseach Council of Canada. degees of electonics and optics: Optical Flow Switching (), Tell-and-Go (TaG), Electonic Packet Switching (), and Genealized MultiPotocol Label Switching (). The context in which we compae these diffeent netwok achitectues is a simple netwok compising two lage goups of uses, located in diffeent s, which wish to communicate ove a. Ou netwok model, though simple in that it only consides the communication of two sets of uses acoss a, is a building block fo moe complex netwok topologies, and, moe impotantly, captues the essence of the thoughputcost tadeoffs of these moe complex netwoks. One limitation of ou study is that it focuses on communication acoss the, and theefoe povides limited insight into how netwoks should be optimally designed to accommodate inta- and inta-local-aea netwok () taffic. Futhemoe, we ecognize that, while the thoughput metic is impotant, it is not the only pefomance citeion by which a netwok should be assessed. Delay, fo example, is anothe key pefomance metic that is not addessed in this wok. Finally, ou cost model focuses on the initial capital expenditue of a netwok, and neglects the ongoing opeational costs, which may constitute a significant potion of a netwok s cost and may vay substantially fom achitectue to achitectue. This wok is oganized as follows. In the next section, we outline the geneal stuctue of ou netwok and cost model. In Section III, we discuss the candidate netwok achitectues and pesent thei thoughput-cost chaacteizations. We conduct a thoughput-cost compaison of the diffeent achitectues with ealistic netwok paametes in Section IV. We conclude the wok in Section V. II. NETWORK AND COST MODEL The simple, multi-tieed optical netwok that we conside in this wok compises two s, each with n m / uses (0 < 1) of which n m ae active at any time which wish to communicate ove a. Uses ae gouped into s, o distibution netwoks, which, in the cases of the and TaG achitectues, ae passive, optical boadcast netwoks. The numbe of uses pe distibution netwok in these two achitectues will be limited to a few hunded owing to minimum powe equiements fo optical detection at end uses. Fo the, we assume that the physical topology connecting its m nodes is abitay, but identical fo each achitectue. The node design (i.e., use of an optical coss-connect (OC) o a oute), howeve, is dependent upon the netwok achitectue. Although ou netwok model

2 2 Notation c amp c mux c sch C x γ agg γ,m γ,w h m h w m n m p agg p eth p oxc p,m p,w S u t n,l t n,s t e t s t t,l w w x Definition EDFA cost pe wavelength pe hop Passive (de)multiplexing cost fo each end use tansceive scheduling pocesso cost Total cost of netwok x, x {ofs, tag, eps, gmpls} Ratio of active uses to total uses in a Pot utilization in a aggegato switch Pot utilization in a oute Pot utilization in a oute Avg. no. of hops fom a node to closest node Avg. no. of hops between nodes Numbe of nodes in a Numbe of active uses in a distibution netwok Numbe of active uses in a Bidiectional aggegato switch pot cost Bidiectional Ethenet switch pot cost Bidiectional OC pot cost Bidiectional oute pot cost Bidiectional oute pot cost Wavelength channel data ate Avg. active use data ate Optical nontunable, long-haul tansceive cost Optical nontunable, shot-haul tansceive cost Electonic tansceive cost t n,s o t e, depending on the channel ate and the achitectue Optical tunable, long-haul tansceive cost n ms u/, total wavelength esouces consumed by active uses No. of channels in netwok x, x {ofs, tag, eps, gmpls} TABLE I TABLE OF NOTATION USED Fig. 1. schedule OC w dedicated wavelength channels Illustation of the implementation. assume that an ebium-doped fibe amplifie (EDFA) is equied appoximately evey 50 km, and that a single EDFA is capable of amplifying 100 wavelength channels simultaneously. We omit fibe plant costs digging, cabling, leasing, and ightof-way costs as we assume that they ae appoximately the same fo all of the achitectues consideed. Futhemoe, we omit opeational costs of the netwok, which we ecognize to be an impotant cost component. Most of the notation used in the emainde of this wok is compiled in Table I. is esticted to have just two s, this simple model may epesent a subset of a moe complex netwok. Thus, the analysis of even such a simple case may seve as a useful building block fo moe complex netwok analyses. Fo the n m uses assumed to be active at any given time in each, we will assume a unifom taffic demand: each active use wishes to communicate with each active use in the othe at the same data ate. We will let S u, ou thoughput metic in this wok, denote the aggegate aveage data ate at which each active use tansmits o eceives. An end use is equipped with multiple tansceives, each of which can tansmit at a peak ate of, which is the wavelength channel ate in the netwok. When buffes exist in the netwok, whethe at end uses o within switches o outes, they ae infinite; that is, data loss due to buffe oveflow neve occus. In addition, we allow fo switches, outes, and OCs within the,, and to opeate below thei full line capacities (paameteized by γ), which is consistent with pesent-day opeation of these devices 1. In ou cost model, we addess the tansceive, switching, scheduling, outing, and optical amplification costs of the netwok entailed by bidiectional communication among the uses. In accounting fo the switch and oute costs, we fix a easonable opeating line ate (e.g., 10 Gbps) and device size (e.g., pots), and then assume that the device cost is a linea function of pot count. This assumption pemits us to employ pe pot costs fo switches and outes in ou cost model, although the accuacy of the esulting analysis diminishes wheage petubations fom this opeating point exist. With espect to optical amplification costs within the, we 1 b-capacity opeation of these devices ensues easonable delay of data tansactions, which is a consideation that is beyond the scope of this wok. Routes and switches, futhemoe, opeate well below thei capacities because of the computational bottleneck imposed by the netwok pocessing unit. III. THE CANDIDATE NETWORK ARCHITECTURES In this section, we opeationally descibe the fou netwok achitectues consideed in this wok and chaacteize thei thoughput-cost tadeoffs. A. In the netwok achitectue, tansmission of data is caied out in a scheduled manne between end uses, akin to cicuit switching, albeit fo shote duations [1], [2]. In ode to schedule data tansmission acoss the, uses communicate, via an off-band contol plane, with the scheduling pocesso assigned to thei espective s. These two scheduling pocessos, in tun, coodinate tansmission of data acoss the in an off-band contol plane. Motivated by the minimization of netwok management and switch complexity in the netwok coe, we equie that flows be seviced as indivisible entities and that bandwidth be dedicated fo each pai. The latte assumption of dedicated bandwidth, howeve, is not a a geneal featue of netwoks [1], [2]. Indeed, is consideed a centalized tanspot achitectue in that coodination is equied fo logical topology econfiguation, although we anticipate that such econfiguation would occu on coase time scales. This is a justification fo ou assumption that bandwidth is statically dedicated fo each pai. We futhe assume that wavelength convesion is not used in the netwok, although this too is not a equiement of the achitectue. In the event that seveal single uses have tansactions which ae not sufficiently lage to waant thei own wavelength channels, they may multiplex thei data fo tansmission acoss the. Note that, in netwoks, unlike packet switched netwoks, all queueing of data occus at the end uses, theeby obviating the need fo buffeing in the netwok coe.

3 3 The implementation of the simple, two netwok consideed in this wok is illustated in Figue 1. Each use is equipped with at least one tunable, long-haul tansceive fo data communication and one shot-haul tansceive with which to communicate with the schedule 2. In the and, switching of data occus all-optically via OCs. Thoughput-cost chaacteistics: In ou pevious wok [3, Theoem 2], we chaacteized the achievable thoughput in netwoks by viewing such netwoks as genealized switches. Using these esults, it can be shown that, unde unifom taffic, each active use can achieve an aveage data ate of w ofs /n m, whee w ofs wavelength channels ae dedicated to the pai in the. Convesely, since bandwidth is allocated at wavelength ganulaity, w ofs = n m S u / dedicated wavelength channels ae equied in the to accommodate an aveage active use data ate of S u. The aveage wavelength channel utilization in the is theefoe n m S u /(w ofs ). The thoughput-cost elationship of the implementation of ou simple netwok is given by: C ofs = 2n m ( ) 2nm t t,l t s + 2c sch + 2n m c mux + 2w ofs m (h m + 1) p oxc +w ofs (h w + 1) p oxc + w ofs h w c amp, whee is the numbe of active uses in a distibution netwok. In this expession, the fist tem epesents the cost of the S u / tansceives at the 2n m / uses in the netwok; the second and thid tems epesent the cost of scheduling in the two s; the fouth tem epesents the cost of boadcasting/combining data in the distibution netwoks; the fifth and sixth tems epesent the switching cost in the s and, espectively; and the seventh tem epesents the cost of amplification in the. Owing to the fact that, in ou model, esouces ae dedicated fo s communicating acoss a, the thoughputcost chaacteistic of each pai deived above would appoximately hold in a moe complex netwok containing many s. B. TaG The TaG achitectue, like the achitectue, is one in which data is communicated between end uses without being buffeed o pocessed at intemediate nodes [4], [5]. The majo diffeence between TaG and, howeve, is that tansmission of data is caied out in a andom-access fashion in TaG athe than in a scheduled fashion. This achitectue, while simple owing to the absence of scheduling and coodination, allows fo collisions of data to occu both on the wavelength channels and at the eceiving uses. The TaG implementation of the two netwok is depicted in Figue 2. As in, we assume an abitay OC-connected topology and dedicated wavelength channels in the. We emak 2 Altenatively, a single tunable, long-haul tansceive can pefom both data communication and scheduling. Fig. 2. OC w dedicated wavelength channels Illustation of the TaG implementation. that, had we allowed fo andom-access to wavelength esouces instead of dedicated esouces, then the netwok achitectue would be that of optical bust switching (OBS). Thoughput-cost chaacteistics: We view each wavelength channel in each distibution netwok as a multiple-access system. The w tag wavelength channels ae coupled in that, at any instant in time, a tansmitting use may only be tansmitting on one wavelength channel with each tansceive. Fo the sake of analytic tactability, howeve, we neglect this coupling constaint. Within each distibution netwok, we theefoe teat each wavelength channel as an independent (possibly slotted) Aloha netwok with vaiable length busts. Fo the special case of constant length busts 3 in which the bust length is a lage multiple of the slot length (if time is slotted), the thoughput pe wavelength channel emeging fom a distibution netwok is appoximately that of unslotted Aloha: S d,1 = Ge 2G, whee G is the aggegate tansmission fesh aival and etansmission intensity. The manne in which taffic is shaped by the netwok afte emeging fom the distibution netwoks is dependent upon the topology of the. Howeve, we povide an appoximate analysis that is not topology dependent. In paticula, we neglect popagation delay, and we assume that the logical topology is that of a tee in which OC pots mediate access to the wavelength channels. This latte assumption of mediation of the channel by OC pots enables channel captue; that is, if a wavelength channel is fee when a bust tansmission is attempted on it, then the channel is eseved fo the duation of the bust. We assume that each distibution netwok poduces, independent of othe distibution netwoks, a sequence of independent tansmit and idle states, in which the tansmit state epesents both the useful and gabled data (owing to collisions) fom its constituent end uses. The thoughput on each wavelength channel emeging fom the is given by: S m,1 = n m S d,1 ( e G ) nm 1, whee we have assumed independence among the n m nl distibution netwoks in the. In ou netwok, tansactions on the w tag wavelength channels ae coupled in that they may contend fo the same tansceives in the eceiving. We make the appoximation 3 Fo a fixed mean bust length, constant length busts can be shown to maximize thoughput [6].

4 4 oute oute oute oute OC w dedicated wavelength channels Fig. 3. Illustation of the implementation. that, fom the pespective of each of these tansceives, the data on each of the w tag wavelength channels geneates a sequence of independent tansmit and exponentially distibuted idle states, with expected tansmit length L (coesponding to useful data) and expected idle length L [n m /S m,1 1]. Following pevious wok [7], it can be shown that, fo the case of constant length busts, the faction of time that each wavelength channel contains useful data (i.e., data not involved in a eceive collision) is: n m ρ S tag = (1 + ρ) e(1 w tag)ρ, wtag whee ρ = [n m /S m,1 1] 1. This yields a use thoughput of S u = w tag S tag /n m. We emak that, if thee existed othe s in the netwok, then the achievable use thoughput would be futhe diminished by eceive collisions involving data fom uses in othe tansmitting s. Thus, the above analysis seves as a best case thoughput bound fo moe complex netwoks with multiple s. The cost-thoughput tadeoff of the TaG configuation is simila to that of except fo: i) the absence of scheduling equipment cost, and ii) the numbe of tansceives is linked to the attempted use intensity instead of the use thoughput: wtag G wtag G C tag = 2n m t t,l + 2n m c mux + w tag h w c amp + 2w tag m (h m + 1) p oxc + w tag (h w + 1) p oxc. Note that w tag, which is a function of S u, povides the link between thoughput and cost fo the TaG achitectue. C. In the implementation of the two netwok, dawn in Figue 3, the and achitectues esemble that of pesent-day Ethenet netwoks. Specifically, data fom an end use is fist aggegated at a Ethenet switch and is then futhe aggegated at a aggegato switch which multiplexes data fom seveal s. Taffic is then fed into the closest oute, and subsequently outed to the s oute. Within the abitaily connected, electonic tansceives ae used wheneve possible (e.g., wheine ates ae sub-gbps), as they ae fa less expensive than optical tansceives. As in the, data in the is statistically multiplexed anew at each hop en oute to the destination. In the, data is always sufficiently aggegated and intense Fig. 4. Illustation of the implementation. to waant optical tansmission. Pocessing of data, howeve, is caied out at each hop in the in the electonic domain. Thoughput-cost chaacteistics: In [3], [8], it is shown that statistical multiplexing of data in packet switched netwoks enables 100% utilization of communication channels. That is, unlike and TaG which employ dedicated esouces and have no buffeing in the and may thus waste wavelength channel capacity, statistical multiplexing in allows fo wavelength channels to be utilized to thei capacity limits, o to thei scaled limits dictated by oute computational bottlenecks. Thus, if we assume that wavelength channels ae loaded to thei γ-scaled capacity limits, then the cost of suppoting a cetain amount taffic is exactly equal to a 1/γ scaling of the cost of esouces that ae consumed in seving this taffic. To be pecise, within the, the assigned amount of wavelength esouces consumed is w/γ,m whee w = n m S u /; and within the, it is w eps = w/γ,w. The cost-thoughput elationship of the configuation is theefoe given by: C eps = 2n m η u nl S u +2 γ agg nm t s + 2n m (p eth + t s ) (p agg + t s ) + 2w (h m + 1) (p,m + t s ) γ,m +w eps (h w + 1) (p,w + t n,l ) + w eps h w c amp whee t s = t n,s o t e, depending on the wavelength channel data ate. In this expession, the fist tem epesents the cost of the S u / tansceives at the 2n m / uses in the netwok; the second and thid tems epesent the cost of multiplexing (demultiplexing) data fom (to) the end uses in the s; the fouth and fifth tems epesent the cost of outing data in the s and, espectively; and the sixth tem epesents the cost of amplification in the. As discussed peviously, statistical multiplexing of data in netwoks allows us to assign the cost of communication of the pai as the 1/γ-scaled cost of netwok esouces consumed, independent of the othe uses that may be shaing these esouces. Hence, the thoughput-cost chaacteistic of each pai deived above would appoximately hold in a moe complex netwok containing many s. D. The vesion of consideed hee is conceptually intemediate to and. Specifically, the and

5 5 c amp = $2000 c mux = $30 c sch = $5000 = 0.1 γ agg = 0.8 γ,m = γ,w = 0.3 h m = 3 hops h w = 5 hops m = 15 nodes = 30 uses n m = 10, 000 uses p agg = $300 p eth = $100 p oxc = $10, 000 p,m = $60, 000 p,w = $125, 000 = 10 Gbps t e = $30 t n,l = $1000 t n,s = $300 t t,l = $2000 TABLE II TABLE OF PARAMETERS USED IN SECTION IV. in is identical to that of, while the design is simila to in that all-optical tansmission along dedicated wavelength channels passing though OCs is employed in ode to cicumvent electonic pocessing at intemediate nodes 4. At the inteface of the and the exist ingess and egess outes that ae esponsible fo assembling and disassembling lage blocks of data, espectively. The achitectue is illustated in Figue 4 fo the two netwok. Thoughput-cost chaacteistics: In the, taffic is teated in the same way as in, so the amount of wavelength esouces assigned is w/γ,m whee w = n m S u /. Howeve, data taveses the though a fully optical path, akin to. Thus, data is outed though the using w gmpls = w/γ,w dedicated wavelength channels. The cost of the configuation is theefoe given by: C gmpls = 2n m nl S u +2 γ agg nm t s + 2n m (p eth + t s ) (p agg + t s ) + 2w γ,m (h m + 1) (p,m + t s ) +2w gmpls (p,w + t n,l ) + w gmpls (h w 1) p oxc +w gmpls h w c amp. By the same easoning as fo and, the above thoughput-cost tadeoff of each pai would appoximately hold in moe complex netwoks with many s. IV. ARCHITECTURAL THROUGHPUT-COST COMPARISON In this section, we cay out a thoughput-cost compaison of the fou netwok achitectues. The cost and achitectual paametes used, which eflect the state of pesent-day netwoks (e.g., [9]), ae summaized in Table II. Figue 5 depicts some esults of ou thoughput-cost study. In Figue 5(a), we plot netwok cost pe use pe bps vesus aveage active use data ate. The plot indicates that when uses have data ates less than appoximately 200 Mbps, the and achitectues have the lowest nomalized cost. Intuitively, this is because elatively little expensive electonic equipment is necessay to suppot the aggegate taffic in these achitectues; wheeas in and TaG, each end use is equipped with an expensive long-haul optical tansceive, even at low data ates. Beyond data ates of 200 Mbps, howeve, we see that is the most cost-efficient achitectue because the high cost of tansceives at end uses is offset by the low cost of povisioning wavelengths in the. In the and achitectues, by contast, high data ates equie much expensive electonic equipment in the and. 4, in its most geneal fom, pemits switching in othe domains besides wavelength/fequency. Netwok cost pe use pe bps ($/use/bps) Aveage wavelength utilization in the Electonic tanspot vs. optical tanspot Electonic NICs vs. optical tansceives at end uses Flattening of cuve and bump epesent moe eceive collisions and addition of expensive optical tansceives at end uses, esp (optical tanspot) TaG Bandwidth pe active use (Gbps) Damped oscillations as dedicated wavelength channels ae pogessively filling Utilization of is limited to that of because of undeutilization at edge outes (a) only wastes bandwidth because of oute undeutilzation Utilization bump because of an additional tansceive at end uses Utilization falling because of many eceive collisions TaG Bandwidth pe active use (Gbps) (b) Fig. 5. The opeating assumptions given in Table II ae made. The (optical tanspot) achitectue is identical to the achitectue, except that tansmission is always caied out in optics, even at low data ates. In Figue 5(b), we plot aveage wavelength channel utilization vesus aveage active use data ate. We note that, as the data ate inceases, the aveage wavelength utilization fo conveges to unity, wheeas the othe achitectues utilizations ae clealy bounded away fom unity. In the cases of and, utilization is bounded away fom unity solely because of the fact that outes ae undeutilized in these schemes. In the case of TaG, the undeutilization of the wavelength channels is intinsic to the achitectue: andom-access to the netwok s esouces esults in channel and eceive collisions which waste channel capacity. In Figue 6, we indicate the cost-optimal netwok achitectue as a function of the numbe of uses pe and the aveage active use data ate. We obseve, fo the same easons discussed in efeence to Figue 5(a), that and dominate fo low to modeate data ates. Howeve, this figue futhe indicates that pefoms best when the poduct of the numbe of uses and aveage active use data ate is low. Thus, is most sensible when thee ae many uses at vey

6 6 Numbe of uses pe 10 5 uses 10 4 uses 10 3 uses 10 2 uses 100 kbps 1 Mbps 10 Mbps 100 Mbps 1 Gbps Each active use s aveage data ate 10 Gbps 100 Gbps Fig. 6. Cost-optimal achitectue as a function of aveage active use data ate and numbe of uses. We use the opeating assumptions in Table II. low data ates (as in the case of today s Intenet), vey few uses at modeate data ates, o anywhee in between these two extemes. pefoms best when the poduct of the numbe of uses and aveage active use data ate is modeate. These obsevations ae intuitive since aggegate taffic is light in the fome case, in which case it is wasteful to povision entie wavelengths in the ; wheeas in the latte case, aggegate taffic is heavy, in which case povisioning entie wavelengths is sensible. In fact, it can be shown that, unde heavy aggegate taffic, the cost diffeence between and scales popotionally to the poduct of the aggegate taffic and the diffeence in cost between a oute pot (with a tansceive temination) and an OC pot. Anothe immediate obsevation is that, at high data ates, egadless of the numbe of uses, always dominates, implying that is the most scalable achitectue of all. In the high use data ate egime, aggegate taffic is always high, so equiing electonic equipment to suppot this taffic in the netwok even if only in the is expensive. In fact, in can be shown that the switching cost diffeence in the and is appoximately popotional to the poduct of the aggegate taffic and the diffeence in cost between a oute pot (with a tansceive temination) and an OC pot. This tend is futheed by the highe switching costs in the and achitectues. This tend, howeve, is offset somewhat by the highe tansceive cost at end uses in the achitectue. In paticula, the implementation equies a tunable long-haul tansceive and possibly a sepaate shothaul tansceive fo scheduling at each end use, wheeas and only equie a nontunable shot-haul tansceive at each end use. The oveall effect, as shown in Figue 6, is a highe cost unde and than unde as the numbe of uses and the aveage active use data ate incease. We note that thee does not exist a egime of optimality fo TaG. This is expected since the low cost of scheduling in yields geat pefomance benefit elative to the othewise identical TaG achitectue. Moe specifically, the savings in scheduling equipment in TaG is dwafed by the cost of suppoting many moe wavelength channels than in. Although delay is beyond the scope of this wok, we emak that thee exists a delay-utilization-blocking pobability tadeoff fo (with finite buffes) and TaG. We expect this tadeoff to be less attactive fo TaG since delay is expected to be especially poo in modeate/heavy taffic owing to many etansmissions. Segmentation and tee algoithms may impove TaG pefomance, but this comes at the expense of potocol complexity. Figue 6 also suggests that a hybid achitectue may be the most sensible design of all, especially when use demands ae heteogeneous. Fo example, a netwok in which high data ate uses employ and low data ate uses employ o would pefom bette than a netwok in which only one of the afoementioned achitectues is employed. As a final emak, note that, while the pecise bounday positions in Figues 5 and 6 ae sensitive to the exact paamete values in Table II, the geneal tends obseved ae manifestations of the pesent-day cost stuctues of the achitectues and thei device building blocks. Thus, in the absence of disuptive technologies with adically diffeent cost stuctues, we expect the tends obseved in these figues to hold fo a wide ange of paametes and fo moe complex netwoks. V. CONCLUSION In this wok, we studied the thoughput-cost chaacteistics of seveal optical netwok achitectues, TaG,, and in the context of a simple, multi-tieed optical netwok. Given the pesent-day cost stuctues of the achitectues and thei device building blocks, we show that is the most scalable achitectue of all, in that it is most cost-efficient when the aveage use data ate is high and the numbe of uses in the netwok is lage; is most sensible when the poduct of the numbe of uses and the aveage use data ate is low (as in the case of today s Intenet); the achitectue, which is conceptually intemediate to and, is optimal when the poduct of the numbe of uses and the aveage use data ate is modeate. Ou wok, while not exhaustive in its consideation of netwok achitectues and topologies, is valuable nevetheless in that it povides insight into the key popeties of netwoks that impact thei scalability. REFERENCES [1] V. W. S. Chan, K. L. Hall, E. Modiano, and K. A. Rauschenbach, Achitectues and technologies fo high-speed optical data netwoks, IEEE/OSA Jounal of Lightwave Technology, vol. 16, no. 12, pp , Dec [2] V. W. S. Chan, G. Weichenbeg, and M. Médad, Optical flow switching, Poceedings of the Wokshop on Optical Bust Switching, Oct [3] G. Weichenbeg, V. W. S. Chan, and M. Médad, On the capacity of optical netwoks: A famewok fo compaing diffeent tanspot achitectues, Poceedings of IEEE Infocom, [4] I. Widjaja, Pefomance analysis of bust admission-contol potocols, IEE Poceedings Communications, vol. 142, no. 1, pp. 7 14, Feb [5] J. Tune, Teabit bust switching, Jounal of High Speed Netwoks, vol. 8, no. 1, pp. 3 16, Jan [6] S. Bellini and F. Bogonovo, On the thoughput of an ALOHA channel with vaiable length packets, IEEE Tansactions on Communications, vol. 28, no. 11, pp , Nov [7] M. J. Feguson, An appoximate analysis of delay fo fixed and vaiable length packets in an unslotted Aloha channel, IEEE Tansactions on Communications, vol. 25, no. 7, pp , July [8] M. Masan, P. Giaccone, E. Leonadi, and F. Nei, On the stability of local scheduling policies in netwoks of packet switches with input queues, IEEE Jounal on Selected Aeas in Communications, vol. 21, no. 4, pp , May [9] S. Sengupta, V. Kuma, and D. Saha, Switched optical backbone fo costeffective scalable coe IP netwoks, IEEE Communications Magazine, vol. 41, no. 6, pp , June 2003.

7 7 EDFA OBS OEO OC TaG ebium-doped fibe amplifie Electonic Packet Switching Genealized MultiPotocol Label Switching local-aea netwok metopolitan-aea netwok optical bust switching optical-electonic-optical Optical Flow Switching optical coss-connect Tell-and-Go wide-aea netwok