Optical Switching and Networking 9 (2012) 13–24

Contents lists available at SciVerse ScienceDirect

Optical Switching and Networking

journal homepage: www.elsevier.com/locate/osn

Performance evaluation of large capacity broadcast-and-selectoptical crossconnectsA. Stavdas a,∗, A. Bianco b, A. Pattavina c, C. Raffaelli d, C. Matrakidis a,∗, C. Piglione b,e,C.(T.) Politi a,∗, M. Savi d, R. Zanzottera c

a Department of Telecommunications Science and Technology, University of Peloponnese, Karaiskaki Str, Tripolis 22100, Greeceb Dipartimento di Elettronica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italyc Dipartimento di Elettronica e Informazione, Politecnico di Milano, P. Leonardo da Vinci 32, 20133 Milan, Italyd Dipartimento di Elettronica, Informatica e dei Sistemi, University of Bologna, Viale Risorgimento 2, Bologna, Italye DCBU Modeling and Simulation Team, CISCO Systems, San Jose, USA

a r t i c l e i n f o

Article history:Received 4 July 2010Received in revised form 21 January 2011Accepted 24 February 2011Available online 17 April 2011

Dedicated to the memory of Fabio Neri

Keywords:Large capacity optical crossconnects

a b s t r a c t

In this work, two bufferless high capacity broadcast-and-select optical switching nodearchitectures are presented and their performance is evaluated. The architectures aremodular permitting the expansion from basic to complex structures by adding newblocks/components in a gradual way, enhancing at the same time the correspondingnetwork functionality. The blocking performance is assessed and scheduling algorithms areproposed to solve contention for a single node. Finally, physical layer modeling is carriedout in order to investigate node scalability and node cascadeability. Overall, the proposedsolutions are offeringmodularity, transparency to switching technology, graceful evolutionand high performance at an affordable cost.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Agile, efficient and future-proof core and metropolitannetworks are indispensable for supporting existing andemerging broadband services. Therefore, these networksshould be service transparent, expandable in termsof the aggregate capacity, and cost-effective. Opticalswitching is seen as a key enabler to extend optical fiberpoint-to-point transmission systems toward large scalenetworks having the aforementioned requirements [1,2].Despite intense research efforts over the last twentyyears, a number of issues related to the introductionof optical/optoelectronic technology in high capacitytelecommunication switching nodes are barely solved. TheEU funded e-photon/ONe network of excellence [3] tried

∗ Corresponding author. Tel.: +30 2710372241.E-mail addresses: astavdas@uop.gr (A. Stavdas), cmatraki@uop.gr

(C. Matrakidis), tpoliti@uop.gr (C.(T.) Politi).

1573-4277/$ – see front matter© 2011 Elsevier B.V. All rights reserved.doi:10.1016/j.osn.2011.02.002

to address the high cost of optical switching technologyas well as the concerns related to the physical layerand the network performance of systems deploying thistechnology. Two broadcast-and-select (B&S) switchingarchitectures were comprehensively studied from anarchitectural, networking and physical layer point of view,extending the previous work on these areas, in order toachieve an optimal solution in all respects simultaneously.These switching architectures are flexible, in terms ofthe deployed switching technology, and modular, in thesense that the various building blocks, at the subsystemand system level, can be gradually introduced in a pay-as-you-grow approach combining high performance withcost-effective introduction. In this paper, the network andthe physical layer performance of these architectures isstudied assuming that a ‘‘fast’’ switching technology isdeployed, paving theway toward optical packet switching.

The paper is organized as follows: Section 2 makesthe case of the service transparent dynamic λ-networkingdefining the framework under which these architectures

14 A. Stavdas et al. / Optical Switching and Networking 9 (2012) 13–24

are utilized. In Section 3, the base-line architecturesare presented in detail, giving emphasis to architecturalmodularity. In Section 4, various scalability considerationsare addressed whilst comparison with other architecturesis given. In Section 5, the packet loss probability ofthe architectures is discussed in association with theimplemented scheduling algorithms. Finally, in Section 6,an overview of the physical layer performance of theproposed architectures is presented with emphasis onnode scalability and node cascadeability.

2. Toward a service transparent dynamic λ-networking

The concept of Wavelength Routed Networks (WRNs)[4] has been a landmark in the proliferation of opticalfiber communications, since it exploits the idea thatthe transit traffic should transparently bypass the nodei.e. be forwarded from an input fiber to an output fiberwith no information content processing. This so-called‘‘optical bypassing’’ permits CAPEX and OPEX savings interms of expensive high speed electronic hardware, thatotherwise would be needed for node control and bit-by-bit information processing of the entire traffic passingthrough the node. In WRNs, the optical bypassing isachieved using all-optical, mainly passive, devices. Clearly,this technology sets restrictions on the attainable networkfunctionality and agility. Here, the notion of transparencyis extended toward service transparency which calls foreither the elimination or the minimization of bit-by-bitprocessing, regardless of the technological platform thatis used. Thanks to this extension, the interest is shiftedfrom technologies to functions and, hence, all-optical andoptoelectronic technologies become of equal interest inbuilding service transparent networks.

However, apart from service transparency, futurenetworks should be able to readily adapt to planned orunexpected events aswell as to dynamically and efficientlymanage their resources. This is necessary to accommodatea traffic profile showing temporal and spatial asymmetrywhile providing important networking functions, likealternative path routing, load balancing etc. So, in contrastto WRNs, this mandates not only the fast reconfigurationof established connections within the optical layer, butalso the sharing of link capacity among nodes which loadthe same path, thus allowing for a more efficient useof resources by means of statistical multiplexing. Dueto the latter, the total number of wavelength channelsspanning the network can be reduced leading to switchingfabricswith fewer input/output ports than solutionswherethe switching granularity is a complete wavelength likein legacy circuit-switched WRNs. This scheme delegatesmore functionality in the optical layer, leading to what isoften called dynamic λ-networking.

Various Optical Packet Switching (OPS) concepts triedto address these challenges using concepts borrowed fromtheir digital electronic counterparts. As of today, noneof these approaches made it to commercial deploymentmainly because they are not service transparent platforms,i.e. they still require significant bit-level processing, andbecause of their inherent technological shortcomings(complexity of optical packet signal processing, lack of

λ - module λ - blocker

λ - module

λ - module

λ - blocker λ - blocker

a

b

Fig. 1. A functional layout of (a) the λ- S-λ (Class-IIA) architecture and(b) the S-λ-S (Class-IIB) architecture.

optical buffer memories, complexity of optical 3R regener-ation, etc.). All these functions are easily provided by elec-tronic routers which despite their massive parallelism arestill more cost-effective.

In this paper, we differentiate from these approachesin two points: First, the proposed architectures are bettersuited for network concepts and architectures like thosein [5–9]. These networking schemes are relying neither onoptical buffers nor on optical signal processing to achievethe requested networking performance. Second, it is the‘‘wavelength’’ domain, instead of the ‘‘time’’ domain, thatis used in conjunction with the ‘‘space’’ domain to resolvecontentions and to provide grooming when needed.

Following the concepts developed in [5–9], in this workit assumed that the slot, a sub-wavelength bandwidthchunk, is the basic transportation and switching unit.The slots are of fixed size and are assumed to besynchronized at node inputs. Note that only packet-levelsynchronization, like in [5,10] is required, which makesthe overall implementation feasible as opposed to legacyOPS solutions that require complex circuitry for bit-levelsynchronization. To ensure continuity with the existingtransportation platforms, the slot could be an extensionof the G.709 frame as proposed in [9]. The final outcomeof these conditions is that the distinction between circuitsand packets is blurred since the former can be constructedby means of sequential concatenation of slots like in [5]further boosting the dynamic λ-networking concept.

3. The proposed architectures

A high-level representation of the proposed architec-tures is illustrated in Fig. 1(a) and (b). Both architecturesconsist of three stages made of two building blocks, theλ-module and the λ-blocker, arranged in different order.Each of these building blocks is a standalone switch andthus, it is argued here that the architectures of Fig. 1 can beobtained in three consecutive steps, each adding one build-ing block to the existing structure, with the migration pro-cess described in [11]. The corresponding steps are termedas Classes; one Class differs from the previous one in theoffered functionality and in the building blocks used for itsconstruction. The whole process is showing a high degreeof modularity which is necessary to achieve cost-effectivesolutions. The essence of this architectural modularity isthat the additional functionality, with the correspondingadditional hardware, is introduced onlywhen needed. Alsoit is noted that the starting point is a specific type of WSSswitch that is considered as themost probable architecturefor Optical Cross Connect deployment today.

In the remainder of the paper, it is assumed that eachnode consists of N input/output (I/O) fibers, each onecarrying M wavelengths.

A. Stavdas et al. / Optical Switching and Networking 9 (2012) 13–24 15

a

b

c

Fig. 2. Functional overview of (a) the configuration of the λ module used in this paper and one branch of (b) the λ-S-λ (Class-IIA) architecture and (c) theS-λ-S (Class-IIB) architecture.

Class-O is composed by a λ-blocker alone, which isa ‘‘Space Switch’’ and is labeled with the letter ‘‘S’’. Itwas initially proposed in [12], further elaborated in [13]and it is extensively used today either under the term‘‘λ-blocker’’ or wavelength selective switch (WSS). Itconsists of a group of N wavelength selectors (WS), eachconsisting of two grating Mux/Demux (or any devicewith equivalent functionality) in tandem, separated byM optical devices able to operate as a ‘‘shutter’’ (on/offgating).

The Class-I is emerging from Class-O adding oneλ-module, a subsystem allowing for wavelength conver-sion, forming up a ‘‘λ-S’’ structure where the letter ‘‘λ’’designates the λ-module. The λ-module is a wavelengthinterchange switch; each incoming wavelength per inputfiber is directed to a tunable wavelength converter (TWC),with each converter tunable over M wavelength chan-nels. This is an important asset, since in other solutions(e.g. [14]) the requested tunability is extended to M · N ,which could be impractical for a high capacity OXC. Of themany possible configurations of the λ-module, we assumea demultiplexer feeding tunable wavelength converters,followed by a passive router and an array of fixed wave-length converters followed by a grating multiplexer, asseen in Fig. 2(a). Other configurations of theλ-modulewithgenerallyworse physical layer performance are explored inRef. [11].

Finally, the architecture shown in Fig. 1(a) is designatedas Class-IIA or λ-S-λ and the one in Fig. 1(b) as Class-IIB orS-λ-Swithmore detailed schematics shown in Fig. 2(b) andFig. 2(c) respectively, for N = 3,M = 4. The stage addedin these architectures allows the selection of output wave-length in addition to output fiber, a feature not available inthe λ-S architecture.

An additional advantage of Class-IIB or S-λ-S is thatit can be implemented with a smaller number of (costly)λ-modules giving limited wavelength conversion capa-bility, with the number of modules increasing whenneeded [15]. It has been demonstrated that this architec-turewhere a limited number of TWCs serves all input fibersto properly forward the incoming slots to the desired out-put fiber/wavelength pair can provide performance closeto those of fully equipped configurations, thus ensuring arelative cost saving [16].

4. The scalability of the solution

The migration from Class-O to Class-II is made via welldefined steps, described in detail in [11], with each stepoffering higher networking functionality compared to theprevious one. It is important to point out the architecturalmodularity that allows building high capacity switches inincremental steps starting from low capacity structures.

– The addition of a new input/output fiber in Class-Orequires adding one WS per output fiber. This can beaccomplished in steps without disruption, provided theinput/output couplers are properly scaled in advance.

– The λ-modules can also be gradually introduced foreach I/O fiber port to a Class-O structure when needed.Therefore, some I/O fiber port could operate as inClass-IIA, whilst others as in Class-O.

– Different switching technologies can also co-exist. Forexample, in the previouslymentioned case, the I/O fiberports operate as Class-IIA switches can utilize SOA orElectro-Absorption Modulators (EAM) as a switchingelement, whist other ports, that still operate as Class-O,could use a different technology like beam-steering

16 A. Stavdas et al. / Optical Switching and Networking 9 (2012) 13–24

Table 1Comparison with other architectures.

Architecture Component count WC count WC tunability

Strictly Non-Blocking

Crossbar (NM)2 MN (fixed) –

3-stage Clos [18] 4√2(MN)3/2 − 4MN MN(fixed) –

WC + AWG [14] – MN (tunable) NMNM (fixed) –

3-stage AWG + WC [18] –

MN (tunable) 2M − 1(2M − 1)N (tunable) N(2M − 1)N (tunable) MMN (fixed) –

MWTN [21] (2M − 1)N2 (2M − 1)N (tunable) M(2M − 1)N tun. filters

DCS [22] 2MN2 MN (tunable) M

Rearrangeable Non-Blocking

Slepian–Duguid [19,20] 2√2(MN)3/2 MN (fixed) –

–2MN (tunable) M

3-stage AWG + WC [18] MN (tunable) NMN (fixed) –

MWTN [21] MN2 MN MMN tun. filters

S-λ-S 2MN2 MN (tunable) MMN (fixed) –

λ-S-λ MN2 2MN (tunable) M2MN (fixed) –

or MEMS. This means that the latter port is used foroptical circuit switching whilst the former can be usedfor optical burst/packet switching through the samearchitecture.

– Finally, wavelength channels can be added in eachwavelength selector either individually or as bands.Thus, with a careful selection of theWDMmultiplexingtechnology, newWDM channels are introduced at will,possibly in bands. For example, free-space concavediffraction gratings like in [17], have a useful bandwidthsignificantly exceeding the 100 nm; thus, new WDMchannels can be added at will, usually in blocks of 8 or16 WDM channels.

The complexity of a switch fabric can be measured as thetotal number of optical elements needed to construct agiven architecture. In this work, the switching fabrics areclassified as follows:

– Rearrangeable Non-Blocking (RNB), where every idleinput channel can be connected to any idle output chan-nel, requiring in some cases the internal rearrangementof some of the already set-up connections.

– Strictly Non-Blocking (SNB), where every idle inputchannel can be connected to any idle output channelindependently from the current network state (so re-gardless the already set-up connections and the inter-nal network resources engaged for them).

In Table 1, the complexity of the λ-S-λ, and of the S-λ-Sconfigurations is comparedwith the corresponding figuresof other known architectures: a single stage crossbar

switch, a 3-stage minimum-cost SNB Clos [18], a 3-stageminimum-cost RNB Slepian–Duguid [19,20], a single stageAWG router with tunable wavelength converters [14](WC + AWG), a 3-stage Clos-like configuration with AWGrouters and tunable wavelength converters like in [18](3-stage WC + AWG), the architecture of reference [21](MWTN) and the architecture of reference [22] (DCS).

Some explanations are necessary to correctly under-stand the figures shown in Table 1:

– Unlike the architectures we propose here, Clos, WC +

AWG and 3-stage WC + AWG are not fully modular;hence, a big part of the hardware should be installed inday-one, requiring significant first-day investment. Asan example for a Clos architecture the complete middlestage should be installed. Furthermore, those structurescannot be simply upgraded to accommodate highercapacity requirements. Finally, the DCS solution cannotbe wavelength and link modular simultaneously.

– In general, only broadcast-and-select architecturessupport multicasting and broadcasting, which is animportant feature for reducing the amount of trafficspanning a network under dynamic λ-networking.

– Tunable wavelength converters are counted as a singleelement. In reality, they include a number of SOAs and atunable laser, and despite the possibility of monolithicintegration, they are complex subsystems.

– The complexity of 3-stageWC+AWG shown in Table 1can be lowered and/or the requested wavelengthtunability can be reduced, exactly as in λ-S-λ andS-λ-S architectures. However, since this optimization

A. Stavdas et al. / Optical Switching and Networking 9 (2012) 13–24 17

is beyond the scope of this paper, the figures shownin Table 1 are obtained under the same operationalassumptions used here (i.e. a fabric withM wavelengthchannels per fiber).

The proposed architectures are attractive since theycombine in a unique way architectural modularity andbroadcast capability requiring a relatively low numberof components. These features ensure that the proposedsolutions could smoothly scale from low to high capacitiesin a cost-effective way.

5. Blocking performance

The scope of this section is to study the blockingperformance of the proposed structures. In WDM OXCs,two distinctive connectivity schemes between input andoutput ports can be identified:

– fiber-to-fiber (F2F) switching, in which the switchingproperties ensure only the addressing of the outputfiber, but not of the output wavelength channel;

– wavelength-to-wavelength (W2W) switching, where theswitching properties refer to the possibility to selectboth the output fiber and the output wavelengthchannel.

5.1. Blocking properties of the proposed architectures

To assess the blocking properties of the proposedarchitectures, we follow the approach of mapping theoptical interconnection network onto an equivalent repre-sentation in the spatial domain, as described in [23]. Therationale is to map the physical connectivity chosen in theoptical domain (which is based on the concepts of wave-length and space switching at the same time) onto a purespatial representation where any single (inter-stage) linkcannot transport more than one input/output connection.In this way, we can exploit theorems already used in theelectronic switching theory to provide formal proofs forthese OXC architectures. On the other hand, this approach,although viable, is rather complex as it is hard to find thespace equivalent representation of many optical devices.For this reason, we will take into account one architectureat a time, explaining themapping of each subsystemwhichcomposes that structure.

Since all the architectures include the same basicbuilding blocks, it is enough to provide space equivalentrepresentations of specific sub-components. In Fig. 3, weshow the space equivalent representation of the Class-Oarchitecture.

This mapping can be easily explained. Each lightpath(incoming data) carried on the same wavelength ondifferent input fibers cannot be routed to the same outputfiber even if other wavelengths are available on this fiber.This fact can be translated in a spatial domain by mappingeach incoming lightpath onto a 1 × N switching splitterthat grants access to all output fibers, albeit limited tothe specific wavelength it is carried on. As expected,in the space representation each inlet can reach only aspecific outlet for each one of the N groups of outputs(the equivalent of the output fibers in the optical domain).

Fig. 3. Space equivalent representation of Class-O architecture, for M =

N = 3.

Apparently, all input lightpaths carried on the samewavelength (in the optical architecture) are connected tothe same N outputs.

By considering that each lightpath is allowed to reachonly N outputs (instead of NM) and that two or morechannels cannot share the same combiner, we can statethat this structure is blocking, since its space equivalentversion is different from a crossbar.

Fig. 4 proposes instead the same Class-O space equiva-lent representation but after the reallocation of the inter-nal connections. In this case,we group together theN inputlightpaths carried on the samewavelength by the differentinput fibers and obtain M N × N crossbar trees (Fig. 4(a))followed by a shuffle pattern. Fig. 4(b) introduces the finalClass-O mapping: this configuration will be very useful inthe study of the remaining architectures, given that one ormore of their switching stages are based on this broadcast-and-select (B&S) structure.

To allow wavelength conversion an array of λ-modulesis added at the ingress of the structure giving us Class-I. Tostudy the blocking properties, we can exploit the mappingalready proposed in [23], where a similar subsystem isconsidered. The StrictlyNon-Blockingλ-module ismappedonto a square switchingmatrix (practically a crossbar). Thisis because routing through the AWG is fully managed bythe initial array of TWCs while the final array of FWCsensures conversion to the appropriate wavelength andcorrect multiplexing at the egress of the λ-module.

Following these considerations, we can map the initialstage of Class-I to an array ofN M×M crossbars in the spacedomain. Within the same representation, we can now adda further stage represented by the B&S equivalent version,shown in Fig. 4(b), obtaining the network proposed inFig. 5(a).

The network shown in this figure respects the non-blocking conditions expressed in the Slepian–DuguidTheorem [19,20], but it is only a 2-stage structure whilethe original RNB network of the theorem is based on threestages. For this reasonwe can state that the achieved spacestructure cannot grant the non-blocking behavior betweenany input and any output of the network, but only betweeneach incoming data and a group of M outputs connectedwith M different switching matrices at the second stage.Since M is also the number of wavelengths carried by

18 A. Stavdas et al. / Optical Switching and Networking 9 (2012) 13–24

a b

Fig. 4. Space equivalent representation of Class-O architecture, forM = N = 3, after the rearrangement of the internal connections with respect to Fig. 3.

0

0

1

M

0

1

M

0

1

N

0

1

N

0

1

N

1

M-1

01

M-1

01

M-1

01

M-1

01

M-1

01

M-1

01

M-1

01

M-1

01

M-1

01

M-1

01

M-1

01

M-1

MxM

Crossbar

NxN

Crossbar

NxN

Crossbar

NxN

Crossbar

NxN

Crossbar

NxN

Crossbar

MxM

Crossbar

MxM

Crossbar

MxM

Crossbar

NxN

Crossbar

MxM

Crossbar

MxM

Crossbar

MxM

Crossbar

MxM

Crossbar

MxM

Crossbar

a b

Fig. 5. Space equivalent representation of (a) Class-I architecture and (b) Class-II architecture.

each output fiber (in the optical domain), we can classifyClass-I as a RNB structure for the F2F switching case. Toachieve a RNB architecture in the W2W switching case,we should provide a further switching stage to choose aspecific output within theM available in each group.

In the optical domain,we can achieve another switchingstage using either a λ-stage or a pure space switching(s-stage) with respect to Class-I. Class-II considers boththese possibilities in its versions A and B, respectively(see Figs. 1 and 2). In both versions, the added stageis composed by building blocks already introduced, sowe can obtain the final space equivalent representationof the whole structure directly. In Fig. 5(b) the spaceequivalent representation of Class-IIA is shown. Thenetwork obtained exactly complies with the conditions ofthe Slepian–Duguid theorem, thus it is RNB in the W2Wswitching case. Considering the case of Class-IIB, we obtaina slightly different space equivalent network (the stagesare inverted), but the theorem holds anyway.

5.2. Scheduling and blocking performance of a single node

Loss performance depends on the input traffic pattern,on the intrinsic characteristics of the architecture, onthe scheduling algorithms used to control the switchwhen connecting inputs to outputs and on whether F2Fswitching or W2W switching is considered.

As stated earlier, we assume synchronous and slottedoperation, i.e., fixed size data, named data slots, arriveat input fibers synchronously, and scheduling decisions(i.e., input/output connections) are made independentlyat each time slot. Moreover, we do not consider anycontention resolution scheme; this implies that wheneverdata slots from more than one inputs should be routed tothe same output port (fiber or combination of wavelengthand fiber), only one can be accommodated, regardless ofthe considered architecture.

We define an incoming traffic as admissible if, lookingat a set of N × M data slots arriving at inputs in agiven time slot, none of them should be dropped due tooutput port/wavelength contention. For admissible traffic,the destination set of data slots at inputs can always berepresented as an input/output index permutation. Notethat uniform Bernoulli traffic is not admissible.

A scheduling algorithm is defined as optimal if it is ableto transfer with no losses any admissible traffic pattern.As a consequence, it is impossible to define an optimalscheduling algorithm for a blocking architecture. Non-admissible traffic patterns imply packet losses, regardlessof the adopted scheduler. Since optimal algorithmsmay betoo complex to be used in practice, we use them only as areference and we propose some simple round robin (RR)based heuristic, i.e. non-optimal, scheduling algorithms.When using heuristics algorithms, packet lossesmay occureven for admissible traffic patterns. This performance

A. Stavdas et al. / Optical Switching and Networking 9 (2012) 13–24 19

penalty is introduced by the simplified scheduler and notby the architecture itself.

In this section, we report only performance analysis ob-tained by simulation for heuristic scheduling algorithms.The interested reader is referred to [24] for a combi-natorial evaluation of loss performance under Bernoulliuniform traffic for optimal algorithms. The statistical sig-nificance of simulation results is assessed by runningexperiments until an accuracy of 2% under a confidence in-terval of 95% was reached.

Heuristics are based on round robin schemes, whereasoptimal algorithms exploit the Birkhoff von Neumann(BvN) decomposition. We only describe the general ideasbehind the optimal algorithms, providing more details onheuristics for each architecture later.

The optimal algorithms (when available) are based onthe BvN decomposition, which permits to decompose adoubly stochastic matrix, i.e. a matrix where all rows andcolumns sum to a given constant, into a weighted sumof permutation matrices, i.e., matrices where all rows andcolumns contain at most one element equal to 1 and allother elements are 0. We first create R = [Rij], a N × Nrequest matrix, where the element Rij represents a slotwilling to travel from input fiber i to output fiber j in theconsidered time slot. The goal is to find a scheduling thatavoids losses for admissible traffic. Thus, the traffic ismadeadmissible, according to either F2F or W2W switchingconstraints, by properly dropping conflicting requests.Then, the traffic matrix R is completed by adding dummyrequests if necessary, so that all rows and columns sumto M. The BvN algorithm is run on a normalized requestmatrix R∗

= R/M , such that each row and column sumsto 1. This is equivalent to runM sequential Maximum SizeMatching (MSM) on R, one for each available wavelength.This optimal solution can be used for Class-I architecturein the case of F2F switching, and for Class-IIA and Class-IIBfor both F2F and W2W switching. Note that in the case ofClass-IIB, for W2W switching, the request matrix is of sizeM × M , with all rows and columns summing to N , andthe algorithm is run N times. The algorithmic complexityis O(min(N4.5,MN2.5)).

5.3. Heuristic control algorithms

5.3.1. Class-O architecture — F2F switchingIn Class-O, the contention points are the N(N : 1) cou-

plers at outputs. A RR counter is kept to indicate the in-put fiber that has to be served first in the considered timeslot. At the beginning of each time slot, a setWj of availablewavelengths is associatedwith each output fiber j. Initially,|Wj| = M . Consider sequentially all wavelengths on the in-put fibers, starting from the ones on the fiber indicated bythe RR counter. Suppose the slot on the considered inputfiber on wavelength λ∗ is addressed to output fiber j∗; if λ∗

is inWj∗ , the slot is served andλ∗ is removed fromWj∗ , oth-erwise, the slot cannot be served and is lost. To ensure fair-ness, at the end of the time slot, the RR counter is increasedby one (modulo N). The algorithmic complexity is O(MN).

5.3.2. Class-I architecture — F2F switchingThe contention points are the N couplers at inputs and

the N couplers at outputs. The heuristic associates witheach input coupler/router a set of available wavelengthsW I

i (i indicates the router connected to input fiber i), andwith each output coupler a set of available wavelengthsWO

j (j indicates output fiber j). As in the Class-O algorithm,a RR counter is used to determine the input fiber that hasto be served first.Wavelengths are considered sequentiallystarting from the ones on the input fiber indicated by theRR counter. Suppose that on the considered wavelength λon input fiber i∗ there is a slot addressed to output fiber j∗;convert λ into the first available wavelength λ∗

∈ W Ii∗ ∩

WOj∗ ; if the intersection W I

i∗ ∩ WOj∗ is empty, the slot is lost.

Otherwise, remove λ∗ from setsW Ii∗ andWO

j∗ , and transmitthe slot. When all slots have been considered (transmittedor discarded), increase the RR counter by one (modulo N).The algorithmic complexity is O(M2N).

5.3.3. Class-I architecture — W2W switchingThe heuristic is very similar to the case of F2F switching.

We associate with each output fiber a set of availablewavelengths WO

j (where j indicates output fiber j), andwith each router a set W I

i (where i indicates the routerconnected to input fiber i). A RR counter is used todetermine which wavelength/fiber pair has to be servedfirst. Consider sequentially all wavelength/fiber pairs:suppose that on the considered wavelength, λi at inputfiber i∗, there is a slot aiming to wavelength λj and outputfiber j∗. If λj is in W I

i∗ ∩ WOj∗ , convert λi into λj and remove

λj from sets W Ii∗ and WO

j∗ ; otherwise, discard the slot. Atthe end of the time slot, increase the RR counter by one(modulo NM). The algorithmic complexity is O(MN).

5.3.4. Class-IIA architecture — F2F switchingUnder F2F switching, Class-IIA behaves like Class-I;

thus, the same control algorithm can be adopted. However,the tunable converter in the third stage, which improvesperformance for W2W switching only, must be controlled.Suppose that the fixed converter at the ith output fiberof each M × M router converts the incoming wavelengthto wavelength i, and that each fixed converter operateson a single input wavelength at each time slot. Since nospecific output wavelength is requested by slots at inputs,wemay tune all the TWCs to the samewavelength; thus, allslots exit from each M × M router on different fibers. As aconsequence, they will be converted to reach the desiredoutput fiber on different wavelengths. The algorithmiccomplexity is O(M2N).

5.3.5. Class-IIA architecture — W2W switchingIn this case, we do not need to use the first stage tunable

converters to directly convert the input wavelength to thedesired output wavelength; indeed, we can exploit inputconverters to pass without contention through the firsttwo stages, and use third stage converters to tune to thedesired wavelength. Again, we have to take control of theM ×M router; the wavelength at the inputs of each routershould be selected so that data will go out on the output

20 A. Stavdas et al. / Optical Switching and Networking 9 (2012) 13–24

Fig. 6. Class-O architecture: loss probability under Bernoulli Traffic(M = 4) for F2F switching.

where they will be tuned to the proper wavelength by theFWCs. Thus, the same heuristic described for Class-I underF2F switching can be used. The algorithmic complexity isO(M2N).

5.3.6. Class-IIB architecture — F2F and W2W switchingSince Class-II-B is an extension of Class-I with an

additional first stage of switching points, we exploitthe same heuristics presented for Class-I. However, theadditional switching stage allows to move the slot to anyrouter. As a consequence, whereas in Class-I each slotcan search for an available path only starting from theoriginal fiber (and router) in which the slot was received,in Class-IIB all N paths (routers) can be searched for witha proper setting of the input switching stage. Complexitiesare O(M2N2) and O(MN2) respectively.

5.4. Performance analysis of heuristic algorithms

The reported performance results are obtained by sim-ulation, for Bernoulli and admissible traffic, using heuristicalgorithms to control the architectures, under a uniformtraffic pattern. At each time slot, for every wavelength atevery input, slots are generated with probability depend-ing on the switch load. Destinations are randomly chosenamong all outputs for Bernoulli traffic, and among free out-puts for admissible traffic to obtain a slot destination setthat can always be represented as an input/output per-mutation. For Bernoulli traffic, which in general is not ad-missible, no major differences are observed when runningheuristics (simulation) with respect to optimal algorithms(analysis); thus, only heuristic algorithm performance isreported in the plots. Optimal algorithms, instead, guaran-tee zero losses for admissible traffic, by definition.

In Fig. 6, the loss probability for Class-O is shownas a function of the input load for different numbersof input/output fibers. Performance improves when thenumber of input/output fibers decreases and does notdepend on M, as expected. Loss probability is fairly highsince no contention resolution scheme is available.

In Fig. 7, we report loss probability for Class-I,Class-IIA and Class-IIB for F2F switching when theheuristic algorithms are adopted. Under F2F switching,

Class-I and Class-IIA are equivalent and are plottedtogether. Besides Bernoulli traffic, we also report resultsfor admissible traffic. First, note that: (i) Class-I, Class-IIAand Class-IIB provide much lower loss probability thanClass-O; (ii) performance is more sensitive to the numberof wavelengths rather than to the number of fibers,particularly for Class-I and Class-IIA; this demonstratesthat wavelength diversity is beneficial in contentionresolution for F2F switching. Second, admissible trafficis obviously easier to deal with, and the architecturesshow lower loss probability. Third, differences amongarchitectures are marginal for Bernoulli traffic. Finally,under admissible traffic, Class-IIB outperforms Class-I andClass-IIA; differences are increasing for increasing valuesof the number of wavelengths M and of the number offibers N . Note that Class-IIB performance improves withincreasingN , asmore input/output paths become availablebetween input and outputs, so that space diversity, inaddition to wavelength diversity, can be used to solvecontentions.

Fig. 8 reports loss probability for Class-I, Class-IIA andClass-IIB under W2W switching for admissible traffic. Nodifferences are visible for Bernoulli traffic (not reported).For admissible traffic, Class-I performs worse; Class-IIBperforms best when increasing the number of inputfibers, whereas Class-IIA benefits from an increase in thenumber of wavelengths per fiber. This is related to thepeculiar characteristics of Class-IIA and Class-IIB, whichrespectively exploit larger tunability and more spacediversity to solve contentions. Moreover, as expected,performance degrades with respect to F2F switching, dueto the additional constraint of W2W switching.

6. Physical layer performance

The capacity of a node is, by definition, equal to theproduct of the number of input/output fiber pairs per nodetimes the number ofWDMchannels per fiber times the linerate per channel. In this work it is assumed that capacityupgrades are achieved by means of new fibers and/orwavelength channels. As in all broadcast-and-select (B&S)type of architectures the main degradation stems from theexcess coupling losses that have to be compensated forby amplifiers. Trying to upgrade the supported capacityby increasing the number of input/output fibers meansthat the corresponding power splitter/combiner of theWSS (Class-O structure), which is an integral part in boththe λ-S-λ and the S-λ-S configurations, is proportionallyscaled, leading to higher passive losses [13]. Also thisaffects the crosstalk from the finite extinction ratio (i.e. theon/off ratio) of the gating devices. The combination of thetwo effects results in a trade-off between node capacity(scalability) vs. node cascadeability [11,25,26].

To overcome this OSNR degradation, the well-known‘‘distributed amplification’’ technique is applied whichis implemented by means of ‘‘amplified couplers’’ ase.g. those of [27,28]. Also in [28] the investigationof different fast switching gates showed that SOAsoutperform other technologies as for example EAMs [29]due to their high on/off ratio. Evidently the performanceinvestigation of the Class-O can be achieved through the

A. Stavdas et al. / Optical Switching and Networking 9 (2012) 13–24 21

Fig. 7. Class-I, Class-IIA and Class-IIB architectures: loss probability under Bernoulli and admissible traffic for fiber to fiber switching.

Fig. 8. Class-I, Class-IIA and Class-IIB architectures: loss probability under Bernoulli and admissible traffic for wavelength to wavelength switching.

calculation of the Q -factor or the BER interchangeablyas this is calculated with analytical methods taking intoaccount the OSNR degradation due to ASE accumulationand the in-band crosstalk, is used for comparing differentimplementations only.

When the λ-modules are introduced in a WSS leadingto the Class-I and Class-II (A and B), the concatenation per-formance of the architectures is improved due to the in-troduction of regenerators. The scalability is dictated bythe WSS node performance. Based on previous investiga-tions [11], all-optical wavelength conversion imposes lim-itations to the concatenation performance due to ASE andjitter performance. Hence here only optoelectronic regen-eration with tunable laser is assumed. An AWG introducessome crosstalk terms as it is considered to operate underworst case conditions.

Furthermore when Class-I and Class-II architecturesare considered, only BER that has an additive natureis meaningful since values of the Q -factor cannot beadded to measure the performance degradation betweentwo concatenated λ-modules (see Fig. 2 for example).Hence any degradation in the λ-modules that containregenerators cannot be accounted for bymeans ofQ -factorcalculations, which would be perfect at the output of theregenerator. Here we have used the methodology of [28]and present the BER performance of the WSS node asreference and comparison with the higher functionalityarchitectures.Modeling of Class-O: In Fig. 9 the effect of the capacityupgrade on the physical layer is shown and the concate-nation performance, making use of the modeling method-ology in [11,25] that is taking into account gain saturation

22 A. Stavdas et al. / Optical Switching and Networking 9 (2012) 13–24

a

b

Fig. 9. (a) BER as a function of M , for N = 16 and N = 64, (b) BER withrespect to the number of concatenated nodes.

of optical amplifiers assuming a line rate of 10 Gb/s. Also,for calculating the Q -factor performance of theWSS, 1× 2and 1×8 amplified couplers with realistic parameters [30]SOAs were assumed as gates, which are modeled as in [11]with 3 mW saturation power, on/off ratio of 45 dB, NoiseFigure of 11 dB and unsaturated gain of 20 dB. The mod-eling of crosstalk, which is of the order of −45 dB, due tothe finite extinction ratio of the gating devices, has basedon the formalism in [29]. Only in-band crosstalk is consid-ered whilst the number of crosstalk terms is of the orderof N − 1 which is the actually the worst case scenario. InFig. 9(a) the BER is calculated as a function of the Q -factorBER(n) = f (Q(n)) where Q(n) is the overall Q factor andBER is calculated as function of Q . It is noted that for the1×N coupler a chain of amplified couplers is utilized, withno specific effort to optimize the choice of couplers. WhenN = 16, one 1×8 and one 1×2 couplers were used.WhenN = 64 two 1 × 8 amplified couplers were utilized. Alsothe same input power per channel Pch has been assumed.In Fig. 9(b) the concatenation performance of the WSS isassumed where BER is calculated after the overall Q fac-tor. Note that for the purposes of the analytical modelingthe distance between concatenated nodes is assumed to be80 km, the loss per km of fiber is 0.25 dB/km and an EDFAsimilar to the one in [11] is used to compensate the losses.Modeling of the entire λ-S-λ and S-λ-S configuration: An im-portant aspect of the analysis is the deployment of regen-erating transponders (with a tunable transmitter) whichremove any restrictions related to node cascadeabilitywhich, otherwise, is limited as noted in [11]. So, the BERis used instead adopting the methodology of [29]. At theoutput of node n the BER is now calculated as:

BER(n) = f (Q(n)) +

n−k=1

BERreg(k)

a

b

Fig. 10. BER as a function of the number of wavelengths for N = 16 andN = 64 for (a) λ-S-λ and (b) S-λ-S configurations.

a

b

Fig. 11. BER as a function of concatenated nodes for N = 16 and N = 64for (a) λ-S-λ and (b) S-λ-S configurations.

Where BERreg(k) is the BER measured at the input ofthe regenerator of the kth node.Evidently λ-module hastwo regenerators and a chain of λ-S-λ nodes has doublethe number of λ-modules with respect to the S-λ-S. Thecorresponding two different solutions are benchmarkedhere assuming a WSS with SOA gates. The effect ofthe capacity upgrade on the physical layer performanceis evaluated by checking in Fig. 10(a) and (b) for the

A. Stavdas et al. / Optical Switching and Networking 9 (2012) 13–24 23

λ-S-λ and S-λ-S respectively. In Fig. 11 the concatenationperformance is investigated.

From the figures above important conclusions can bedrawn, considering that for the purposes of this studya BER of the order of 10−15 is considered acceptable:The scalability performance of both λ-S-λ and S-λ-S ispractically identical to that of theWSS (Fig. 9), as expectedand is only deteriorated by the crosstalk terms of theλ-modules. Evidently even for the case of N = 64, andM = 64 all node architectures operate well hence theargument for high capacity switch holds, hence a nodecapacity of 40 Tb/s can be achieved assuming 10 Gb/s perchannel. Fig. 11 shows that the concatenation performanceof λ-S-λ nodes outperforms the S-λ-S ones. When λ-S-λnodes are put in a chain, if we assume that the effects of thefibers can be negligible, everyWSS is followed by a block ofλ-modules, hence the signal is regenerated after everyWSS. This limits the ASE accumulation and improves thenode concatenation performance, that it is only degradedby a small amount of errors that are transferred. Whena chain of S-λ-S is studied, the signal goes through twoWSSs in a row before one block of regenerators, assumingall other effects minimal. Evidently this degrades theconcatenation performance which is still better than theWSS case. This is because according to Fig. 9 more thantwoWSS can be concatenated successfully for all capacitieshence in the S-λ-S case the signal has not deterioratedirreversibly before it is regenerated.

7. Conclusions

In this work, two bufferless broadcast-and-select opti-cal switching node architectures were proposed and theirperformance and capacity feasibility was evaluated. Thesearchitectures are modular permitting the expansion frombasic to complex higher functionality structures by addingnew blocks/components in a gradual way. The startingpoint is the widely investigated WSS (here Class-O) of-fering only fiber to fiber connectivity. Successive stepsimprove the network functionality, finally reaching wave-length to wavelength rearrangeably non-blocking fabrics.

The switching solutions were investigated in thecontext of dynamic λ-networking, assuming operationemploying fixed size slots. Scheduling algorithms wereproposed to solve contention for a single node. Theblocking performance was assessed under different trafficassumptions and was found similar for all architecturesunder Bernoulli traffic, while for admissible traffic thealgorithms performed better for Class-IIB.

Finally, physical layermodelingwas carried out in orderto investigate node scalability and node cascadeability. Thescalability performance of both Class-II architectures ispractically identical and the concatenation performance ofClass-IIA nodes outperforms Class-IIB. It was shown thatwith the appropriate technology (e.g. amplified couplers,SOA gates etc.) high capacity can be achieved withoutconsiderably increasing the cost.

Overall, the proposed solutions are achieving large ca-pacity while offering modularity, transparency to switch-ing technology, graceful evolution and high performanceat an affordable cost.

Acknowledgments

This work was partly supported from the EuropeanUnion’s Network of Excellence (NoE) e-Photon/ONe.

References

[1] Yao Shun, B. Mukherjee, S. Dixit, Advances in photonic packetswitching: an overview, IEEE Communications Magazine 38 (2)(2000) 84–94.

[2] S.J.B. Yoo, Optical packet and burst switching technologies for thefuture photonic internet, OSA/IEEE Journal of Lightwave Technology24 (12) (2006) 4468–4492.

[3] http://www.e-photon-one.org.[4] G. Hill, A wavelength routeing approach to optical communication

networks, British Telecom Technology Journal 6 (3) (1988) 24–31.[5] L. Dittman, et al., The European IST project DAVID: a viable approach

towards optical packet switching, IEEE Journal of Selected Areas onCommunications 21 (7) (2003) 1026–1040.

[6] A. Stavdas, H-C. Leligou, K. Kanonakis, C. Linardakis, J. Angelopoulos,A novel scheme for performing statistical multiplexing in the opticallayer, OSA Journal of Optical Networking 4 (5) (2005) 237–247.

[7] A. Stavdas, K. Kanonakis, G. Koukouvakis, H.C. Leligou, Th. Or-phanoudakis, J.D. Angelopoulos, Clustering core nodes allows effi-cient all-optical payload switching, Photonics in Switching 2006,Crete, Greece, October 2006.

[8] J.D. Angelopoulos, K. Kanonakis, G. Koukouvakis, H.C. Leligou,C. Matrakidis, T. Orphanoudakis, A. Stavdas, An optical networkarchitecturewith distributed switching inside node clusters featuresimproved loss, efficiency and cost, IEEE Journal of LightwaveTechnology 25 (5) (2007) 1138–1146.

[9] Alcatel 1674 Lambda Gate, Technical Description, 3AL 93106 AAAAEd. 05.

[10] A. Stavdas, A. Salis, A. Dupas, D. Chiaroni, An all-optical packetsynchronizer for slotted core/metropolitan networks, OSA Journal ofOptical Networking 7 (1) (2008) 88–93.

[11] A. Stavdas, C. Matrakidis, C. Politi, Migration of broadcast-and-selectoptical crossconnects from semi-static to dynamic reconfigurationand their physical layer modeling, Optics Communications 280 (1)(2007) 49–57.

[12] A. Stavdas, Ph.D. Thesis, University of London, 1995.[13] A. Stavdas, H. Avramopoulos, E.N. Protonotarios, J.E. Midwinter, An

OXC architecture suitable for high densityWDMwavelength routednetworks, Photonic Network Communications 1 (1) (1999) 77–88.

[14] D. Hunter, et al., WASPNET: Awavelength switched packet network,IEEE Communications Magazine 37 (3) (1999) 120–129.

[15] C. Raffaelli, M. Savi, A. Stavdas, Sharing wavelength converters inmultistage optical packet switches, in: IEEE Workshop on HighPerformance Switching and Routing, HPSR, Poznan, Poland, June2006.

[16] C. Raffaelli, M. Savi, A. Stavdas, Performance of scheduling algo-rithms inmultistage optical packet switcheswith sparsewavelengthconverters, in: Proceedings of IEEE Globecom 2006, San Francisco,CA, USA, November 2006.

[17] A. Stavdas, M. Manousakis, C. Scahill, A. Hadjifotiou, The designof a free-space multi/demultiplexers for ultra-wideband WDMnetworks, OSA/IEEE Journal of Lightwave Technology 19 (11) (2001)1777–1784.

[18] C. Matrakidis, A. Pattavina, S. Sygletos, N. Vogiatzis, F. Neri,A. Stavdas, New approaches in optical switching in the network ofexcellence e-photon/ONe, in: Conference onOptical NetworkDesignand Modeling 2005, pp. 133–139, February 7–9, 2005.

[19] D. Slepian, Two theorems on a particular crossbar switchingnetwork, Unpublished manuscript, 1952.

[20] A.M. Duguid, Structural properties of switching networks, BrownUniversity Progress Report, BTL-7, 1959.

[21] G.R. Hill, et al., A transport network layer based on optical networkelements, OSA IEEE Journal of Lightwave Technology 11 (5/6) (1993)667–679.

[22] E. Iannone, R. Sabella, Optical path technologies: a comparisonamong different crossconnect architectures, OSA/IEEE Journal ofLightwave Technology 14 (10) (1996) 2184–2196.

[23] G. Maier, A. Pattavina, Generalized space equivalent analysis ofoptical cross-connect architectures, in: IEEE INFOCOM, Anchorage,AK, USA, April 2001.

[24] A. Bianco, C. Piglione, F. Neri, Optical switching nodes: architecturesand performance, in: IEEE Workshop on High Performance Switch-ing and Routing, New York, NY, USA, June 2007.

24 A. Stavdas et al. / Optical Switching and Networking 9 (2012) 13–24

[25] A. Stavdas, Architectural solutions towards a 1000 channel ultra-wideband WDM network, SPIE Optical Networks Magazine 2 (1)(2001) 51–60.

[26] A. Stavdas, et al., IST-DAVID: concept presentation and physical layermodelling of the metropolitan area network, OSA/IEEE Journal ofLightwave Technology 21 (2) (2003) 372–383.

[27] http://www.teemphotonics.com/.[28] A. Stavdas, C.(T.) Politi, T. Orphanoudakis, A. Drakos, Optical

packet routers: how they can efficiently and cost-effectively scaleto petabit/s, OSA Journal of Optical Networking 7 (10) (2008)876–894.

[29] C.(T.) Politi, C.Matrakidis, A. Stavdas, D. Gavalas,MO’Mahony, Singlelayer multigranular OXCs architecture with conversion capabilityand enhanced flexibility, OSA, Journal of Optical Networking 5 (12)(2006) 1002–1012.

[30] Teemphotonics, private communication.