Fractional Lambda Switching for Flexible Bandwidth Provisioning in

Fractional Lambda Switching for Flexible Bandwidth Provisioningin WDM Networks: Principles and Performance�

Donato Grieco, Achille Pattavina*Department of Electronics and Information, Politecnico di Milano, P.za Leonardo da Vinci, 32-20133 Milan, Italy

E-mail: [email protected]

Yoram OfekDipartimento di Informatica e Telecomunicazioni (DIT), Universita’ di Trento, Via Sommarive, 14-38050 Povo (Trento), Italy

E-mail: [email protected]

Received June 2, 2004; Revised: August 19, 2004; Accepted August 25, 2004

Abstract. A new approach is introduced in this paper to make possible a flexible utilization of WDM networks using current

technology. It is shown that the bandwidth made available end-to-end by a single wavelength can be simply broken up into smaller

pieces, or fraction of lambda, by relying on a worldwide common time reference system, such as GPS, previously deployed for different

applications. The common time reference system is used to synchronize switches and to facilitate pipeline forwarding of data units.

Pipeline forwarding is a known optimal method widely used in manufacturing and computing. It is shown how this new approach,

called Time Driven Switching, behaves in terms of call blocking when the basic parameters of the scheme are varied.

Keywords: WDM networks, Fractional Lambda Switching, Bandwidth provisioning, Time Driven Switching

1 Introduction

Modern telecommunication networks use light totransport information; in WDM systems multiplecolors travel on optical fibers increasing the totalbandwidth. All optical networks are being studiedto avoid conversion from optical to electric signalevery time a switch is crossed, in order to forwardit towards the proper destination.

Present optical switches however can only divertentire wavelengths: all the data on a color must gofrom the same source to the same destination (seefor example [1] and [2]). This leads to some con-straints in the network itself, that is:

– A source needs a different color for eachdestination it addresses; if the network has Naccess points and they have to be all con-nected to each other, the number of wave-

lengths needed can grow up to N2 (the socalled N2 problem shown in Fig. 1 [3]);

– No aggregation/separation of multiple flowson/from a single wavelength can be operated:the wavelength travels unchanged switch byswitch;

– It is not possible to connect fast sub-networksto slow ones (unless using more than onecolor) because the capacity of a single wave-length cannot fit into that of the crossed link.

All these problems limit the extension of anall-optical network core, because of wavelengthsgrowth and bandwidth mismatch betweensub-networks. Therefore it is advisable to providedirectly the availability of fractions of the wave-length capacity so as to support ‘‘sub-lambda’’end-to-end connections [4]. Time Driven Switching(TDS) provides a solution to make available a

*Corresponding author.�Work carried out at Politecnico di Milano, Italy. A preliminary version of this paper has been presented at GLOBECOM 2003, San

Francisco, USA.

Photonic Network Communications, 9:3, 281–296, 2005

� 2005 Springer ScienceþBusiness Media, Inc. Manufactured in The Netherlands.

capacity equal to a fraction of that transported bya wavelength in order to permit the abovementioned operations; for this reason, a switchoperating according to TDS will be called aFractional Lambda Switch [5].

Furthermore, today there is broad agreementthat in the future the backbone network will con-sist of IP/MPLS at the edges while the interior of

the network will consist of an optical core. How-ever, with wavelength switching (WLS) the opticalcore will consist of multiple ‘‘islands,’’ as shown inFig. 2a. The main reason for having multiple‘‘islands’’ is due to the need of N2 wavelengths,where N is the number of access points to theoptical core. In order to further illustrate thisproblem assume that: (i) the optical core has 105

access points, (ii) the average transmission distancefor each wavelength is 1000 km, and (iii) eachoptical fiber carries 100 DWDM channels andweighs 0.1 kg/km (a 25 km spool of Corning fiberweighs about 2.5 kg); then the optical core wouldrequire 105Æ105Æ1000Æ0.1/100=1010 kg or 10 mil-lion tons of optical fiber – almost twice the weightof the great Khufu pyramid in Giza.

The problems arising with WLS are solved byTDS, which dynamically allocates fractions of anoptical channel or a lambda over predefined routesin the network, thereby solving the N2 problem.Each lambda fraction is equivalent to a leased linein circuit switching. Consequently, it is possible to

N-1 coloursto reachN-1 destinations

~N coloursto connectall nodes

2

Node 1Node 2

Node 3

Node N

Fig. 1. The N2 problem.

IP/MPLS

IP/MPLS

(Multiple Optical Cores)

WLS

WLSWLS

WLS

IP/MPLS

Fractional LambdaSwitching

(Single Optical Core)

IP/MPLS

(a)

(b)

Fig. 2. IP/MPLS with a plurality of optical core islands (a), a single optical core (b).

282 Grieco et al./Fractional Lambda Switching

realize an optical network with a single opticalcore (rather than with multiple separate islands),as shown in Fig. 2b, and thereby to extend theoptical core all the way to the edges of thenetwork.

The principles of TDS and allocation proce-dures are described in Sections 2 and 3 respec-tively. Some elements about switching fabricimplementation are given in Section 4, whereasSection 5 provides traffic performance results for asingle switching fabric.

2 Time Driven Switching

TDS uses time division multiplexing and framedstructures in order to give flexibility to opticalnetworks. Time is actually divided into TimeFrames (TFs) with equal duration (dT), grouped inTime Cycles (TCs), all containing the same num-ber (T) of TFs (see Fig. 3). According to the extentof these temporal intervals and to the link band-width, the amount of data which can be sentduring a TF can be simply calculated. Table 1gives some examples with typical values.

On setting up a connection for a new couplesource-destination, a free TF is searched in the

cycles associated to each link between them (TFsmay have been reserved by other connections; thepattern of reserved TFs is the same in every cycle).If found, they are entirely reserved for all theconnections between that couple. Up to C con-nections can be setup in the same TF; this quantitycan be easily found dividing the link bandwidthwith the connection bit-rate and the number ofTFs per cycle. As an example, more than 600video-on-demand (VoD) streams (at 1.5 Mbit/s)can be transmitted on a 1 Gbit/s link: in fact, bydividing a cycle into 100 TFs, each of them couldcontain 6 VoD connections. If the number ofsimultaneous connections exceeds C, a newsequence of TF is searched. TFs are released if alltheir connections are cleared.

The connection is lost if free TFs cannot befound, otherwise the sequence of TFs on the linkswill form a Synchronous Virtual Pipe (SVP): eachpacket put by the source on the SVP will pass fromTF to time frame until the destination is reached.Every crossed switch will be set to route the con-tent of the arriving TF to the proper one in theoutgoing link.

The whole network must be synchronized torecognize the time division, using a worldwideglobal system providing the absolute time

Table 1. Typical capacity in bytes of a TF.

Link bandwidth TF duration

12.5 l s 125 l s 500 l s

40 Gbit/s 62,500 625,000 2,500,000

10 Gbit/s 15,625 156,250 625,000

1 Gbit/s 1562 15,625 62,500

155 Mbit/s 242 2420 9680

45 Mbit/s 70 703 2812

0 0 0 01 1 199 99 99

TF

TC

Beginning ofa UTC second

Beginning ofa UTC second

UTC

1 second

Fig. 3. Time division in TDS.

Grieco et al./Fractional Lambda Switching 283

reference with given accuracy [6–9]. A typicalexample is given by the GPS system, whichglobally provides the standard time with anaccuracy up to 1 ls [6]. In this way switches willforward all information units contained in a TFin the right direction, without needing to readany header.

Dividing a single wavelength into independenttemporal fractions solves the problems mentionedabout optical networks [10]:

– each fraction of the same wavelength can beused for a different destination (Fig. 4);

– TFs can come from different up-links and go todifferent down-links (multi/demultiplexing);

– fast links can use short TFs and slow linkslonger ones, so that the amount of datatransmitted is the same and the content of aTF can be exchanged between them.

The sequence of TFs on each link from source todestination can be chosen according to two modes:

– Immediate Forwarding: data arriving at aswitch during a TF must exit during the nextone;

– Full Forwarding: data arriving at a switchduring a TF can leave the switch in any TF,that is during a TF between the next one andthe corresponding one in the next cycle(Fig. 5).

Immediate Forwarding gives more restrictionson finding free TFs and hence causes larger losses.Nevertheless, it grants minimum delay betweentransmission and reception, as packets do not haveto wait in the switches until the proper TF. Forthis same reason it minimizes buffer capacitywithin the switches. Full Forwarding has the

Node 1Node 2

Node 3

Node N

A source can reachall the destinationswith a single colour

A single colourcan connect all nodes

Fig. 4. TDS solution to the N2 problem.

Time (TF)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16TF

link :3 TF

b

link :2 TF

a

content of the TF

C

B

A

switch

data on this SVP enter Bin TF 4 and exit in TF 9

Delay

Fig. 5. Full Forwarding.


complementary advantages: minimum loss andlarger delay. Switches must also buffer packets fora longer time (larger buffers).

An intermediate forwarding technique (calledD-Frame Forwarding) can be used: in this case aTF can be forwarded up to D TFs later. Its per-formance ranges from that of Immediate For-warding, that is 1)F, to that of Full Forwarding,that is T)F: the same reasoning applies also tobuffer requirements and delay.

Another restriction to TDS operations canderive from the operations of the switch fabric: itcan be convenient (in terms of number and costof components, i.e., wavelength converters) not toallow that a TF arriving on a color could exit ona different one: this mode will be called NoWavelength Interchange (NWI). If no restrictionsapply in terms of wavelength, the operation isreferred to as Full Wavelength Interchange (FWI).FWI and NWI can be combined with both FullForwarding and Immediate Forwarding accord-ing to the characteristics of the switch fabric andthe traffic performance desired, as we will see inthe following.

3 Allocation Procedures

Every time a new SVP has to be setup between twonodes, a free TF has to be found for each crossedlink. With Immediate Forwarding this sequence ismade of consecutive intervals. Note that dataentering a link during a TF i will exit in the TFi+t, where t · dT is the amount of time taken bythe signal to cross the link itself. To make thesystem feasible the length of each link must besuch that it ‘‘contains’’ an integer multiple of TFs(an error of 200 m would cause a time uncertaintyof 1 ls).

Allocation procedures can be operated both bya central unit and by a distributed algorithm. Wewill discuss the latter: a central controller would bebetter where loops or alternative paths are present.

We will discuss Immediate Forwarding and FullForwarding with a single wavelength, and thenextend the procedure to WDM. These methods usea vector with T elements (one for each TF), passedand processed from switch to switch. The finalstate of this vector will show the most suitable TFsto be reserved.

3.1 Immediate Forwarding

Each node n computes a binary vector (Vn) whoseelements are 0 if the corresponding TF on theoutput link is reserved, 1 otherwise. When a nodereceives a vector from the previous switch, it isrotated towards increasing times by an amount ofTF given by the ‘‘length’’ of the incoming link plus1 TF to take into account the minimum delay inthe switch.

Then:

1. The source node creates (‘‘receives’’) thevector (X0=V0) containing the allocationpattern at its inlet;

2. Each node n, upon receiving a vector Xn)1,rotates it, constructs Xn=Xn)1 AND Vn andforwards it if it contains one or more ones(the value 1 means that all its correspondingprevious TFs are free);

3. The last node chooses a free TF in the vector(marked as 1) and sends the choice back tothe source node in order to reserve the wholesequence corresponding to that TF;

4. The sequence is reserved if, in the meantime,no other SVP has made an analogousrequest for any of these TFs.

3.2 Full Forwarding

The case of Full Forwarding is a little more com-plex: this method will find the sequence of free TFsminimizing the total delay. It differs from Imme-diate Forwarding in that each element Xn(i)(0 £ i £ T)1) of the vector Xn sent from node tonode will be a number indicating the minimumaccumulated delay in the best sequence terminat-ing with the corresponding TF. Upon initializationof X0 (X0(i)=0 for i=0,…,T)1), the vector Xn iscomputed from Vn as follows:

XnðiÞ ¼reserved if VnðiÞ ¼ 0min

j:Xn�1ðjÞ2NðXn�1ðjÞ

þði� jÞmod TÞ otherwise

8><

>:

The last node will choose the TF whose elementhas the least value, and the path leading to that TFwill be reserved (if still available).

This procedure can be more clearly illustratedby a trellis structure in which a path minimizingdelay is constructed stage by stage: each TF isconnected with the TF that, in the previous switch,


has accumulated less delay. In the last step onlyfew paths will be available, and the best one ischosen. Fig. 6 shows an example of best pathchoice using the trellis structure.

3.3 WDM Environment

In the case of NWI the algorithm is repeated foreach color, and the choice is made among them(random with Immediate Forwarding, minimizingdelay with Full Forwarding).

With FWI the elements of vector Vn are marked0 if the corresponding TFs on all colors arereserved, 1 otherwise: then the algorithm is appliedwithout any further changes. On setting up theSVP, the TF at each stage can be chosen on anyfree wavelength.

4 Switch Fabric

Now we briefly discuss about possible implemen-tations of a TDS switch. Basically it must be ableto receive/send signals from/to WDM links,performing every possible combination betweeninlets and outlets (and possibly between all wave-lengths), and it must store incoming data until theproper TF. The basic structure of a TDS switch is

depicted in Fig. 7; buffers are used to enable theproper forwarding of TFs. In principle theswitching core can be realized using either electri-cal or optical technology.

Every TF, each inlet can be connected to a dif-ferent outlet, and this configuration is held for thewhole interval; for this reason the switch fabricmust have, at least, a rearrangeable non-blockinginterconnection network (unless trading a simplerstructure with internal loss). As an example, aBenes topology can be used.

4.1 Electronic Fabric

In an electronic switching fabric wavelengths haveto be converted into electrical signals to be sent toelectrical interfaces; the switch configuration withWN inlets and outlets is shown in Fig. 8, in whichW is the number of wavelengths and N is thenumber of incoming fibers.

Buffers can be realized (for each outlet) asshown in Fig. 9: with Immediate Forwarding theremust be one buffer sending out data in the currentTF, and one receiving data for the next one; theirrole changes every TF. In Full Forwarding there isone buffer to send out data and T to get packetsfor the corresponding TFs. Each buffer must be

0

32

1

3

1

1

3

3

1

0

1

2

0

1

2

3

3

2

3

2

1

02

2

0

0

0

0

1

11

2

2 2

4

Node 1 Node 2 Node 3 Node 4

Allocation pattern rotated to the initial TC

Best SVP till this TF Best TF (best SVP)

Reserved TF Free TFAccumulated delay

Further dealy

Fig. 6. An example of trellis for Full Forwarding.


able to contain all the packets sent during a TF(see Table 1).

4.2 Optical Fabric

An optical switching fabric can be realized as inFig. 10, where an optical switch (N · N) performspermutations without changing wavelengths: toachieve full connectivity, wavelength converters(WC) must be equipped at each input interface ofthe switch fabric. Their absence would lead to theimpossibility to change connection wavelengthfrom source to destination: this is what we havecalled NWI mode. To compensate signal losses, aset of optical amplifiers must be provided at theoutput interfaces of the switch.

The optical buffers needed in the fabric can bemade using delay lines to keep packets inside theswitch till the proper TF. Note that a delay of 1 lsis obtained with 200 m of an ordinary fiber: toavoid using extremely long lines, the maximumdelay has to be quite short; so, short TFs andImmediate Forwarding are preferable (D-FrameForwarding can be used to trade loss withcomplexity).

With Immediate Forwarding only one line isrequired, without a demultiplexing stage; its lengthmust be such that the time taken by the signal tocross the whole switch equals one TF.

5 Switch Behavior

The most important aspect of TDS is how time isconsidered: the TF is the protocol basic tile, morethan packets or connections. That is, the behaviorof the switch can be seen as the forwarding ofentire TFs rather than single packets. So, thenumber of TFs per cycle is what mostly influencesits performance. Various parameters determinethis quantity, first of all the number of simulta-neous connections for a single input of the switch:on setting up a new path through the switch, acouple of TFs is searched in both sides of theconnection, so it is useful to grant a TF for eachpossible SVP passing through the same port, or formost of them. We have made the assumption thatup to V different SVPs are possible between thesame inlet and the same outlet of the switch. Every

Fig. 7. Structure of a Fractional Lambda Switch.

Fig. 8. Scheme of an electronic fabric of a Fractional Lambda Switch.


inlet can be connected to all outlets, and so thetotal number of TFs on all the wavelengths in thefiber (T · W) must be larger than N · V. The ratioTW/NV will play an important role in the fol-lowing discussion.

We analyze first the behavior of a single-wavelength switch, to examine then the results forthe case of multiple colors. We also assume the

traffic pattern to be a Poisson process at each inlet,with randomly chosen destinations. All graphs inthis section show the loss probability as a functionof the offered load normalized to total capacity ofan inlet (T · W · C).

Table 1 gives the amount of data which can besent during a TF: according to link bandwidth,packet size and number of packets in a single

data forcurrent TF

Data

(a)

(b)

forthe next TF

Buffer

Data forcurrent TF (i)

Current buffer forTF i+3

For TF i+1

For TF i+2

Fig. 9. Buffer structures for Immediate Forwarding (a) and Full Forwarding (b).

Fig. 10. Optical switch fabric.


connection, the number of connections per TF (C)can be computed. The value C should be largeenough to store all connections in a SVP: in thisway only a TF has to be reserved, and allocationprocedures are called only once (unless all calls onthe SVP are cleared).

Providing a greater TF helps maintaining itsoccupancy around the average offered load: lessconnections would exceed C and seldom new TFswould have to be reserved. This is clearly shown inFig. 11, which depicts the probability of callblocking Pbl with Full Forwarding operations inthe case of two TFs per SVP. For larger values ofC the event that an idle TF is not found occurswith a smaller probability.

In the case of Immediate Forwarding it isimportant to distinguish between the two causes ofcall blocking. A requested call is not setup eitherbecause there is no bandwidth available to serve iton the addressed output (event of call refusal) orbecause the constraint of immediate forwardingdoes not allow the call setup in spite of theavailability of idle TFs (event of call rejection). Inthe former case we refer to refused calls, in thelatter case to rejected calls. The probability of call

rejection (Prej) is shown in Fig. 12: if we comparethese results to those accounting for both causes ofcall blocking (see Fig. 13), it is clear that callrefusal is the main cause of blocking. The figureshows that with Immediate Forwarding the diffi-culty in finding proper TFs makes loss probabilityalmost independent of C.

To reduce blocking it is then useful to providemore than one TF per SVP: in this way blockingwould occur only reserving the last TFs amongthem. This may be achieved, preserving cycleduration, decreasing C (see again Table 1). Fig-ure 14 illustrates this situation in which thequantity T · C (i.e., the capacity of a time cycle) iskept constant: larger T values provide better per-formance, despite of a smaller capacity C. Notethat there are some ‘‘intermediate’’ values that arealmost equivalent, when the advantages providedby larger T values are compensated by the smallervalue of the capacity.

Fig. 15 shows that this property holds also forFull Forwarding, albeit for a different reason. Infact, providing a number of TFs equal to themaximum number of SVPs, even for smallloading all TFs will be probably reserved

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110

10

10

10

10

10

100

Normalized offered load

Pro

babi

lity

of c

all b

lock

ing,

Pbl

C=1 C=10 C=50 C=100

Fig. 11. Influence of TF capacity with Full Forwarding.


(although with few connections inside) and nofurther resources could be used for connectionsexceeding C. If their number is increased, for low

traffic only necessary TFs would be occupied(almost fully), and free TFs will be available toreceive new call requests.

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110

10

10

10

10

100

Pro

babi

lity

of c

all b

lock

ing,

Pbl


C = 1 C = 10 C = 50 C = 100

Fig. 13. Influence of TF capacity with Immediate Forwarding.

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110

10

10

10

10

10

10

10

100


Pro

babi

lity

of c

all r

ejec

tion,

Pre

j

C = 1 C = 10

Fig. 12. Rejection probability with Immediate Forwarding.


The importance of the number of TFs for eachSVP is expressed by Figs. 16, 17 and 18: in allthese graphs, the performances of switches with

the same ratio T/NV are very similar, despite ofnumber of ports (N, Fig. 16), or TFs (T, Fig. 17),or different SVPs in the same couple of ports (V,

Fig. 14. Performance of Immediate Forwarding for different TF capacities.

Fig. 15. Performance of Full Forwarding for different TF capacities.


Fig. 18); also forwarding does not affect loss forsmall values of this ratio (Figs. 17, 18). Only whenthe number of TFs per SVP is changed the trafficperformance vary: larger values reduce the block-ing events (see Fig. 18).

We now examine the behavior of the switch in aWDM environment; the value W indicates thenumber of wavelengths on each input or outputlink. We recall that the switch can operate in FWIif any color on inlets can be connected with any onoutlets, or in NWI if the color cannot be changedwhile the circuit is switched. Obviously the formergives better performance (providing more possi-bilities for each connection). They can be com-bined with Full Forwarding and ImmediateForwarding to give four combinations of switch-ing fabric operations: FF/FWI, FF/NWI, IF/FWIand IF/NWI.

While IF gives restrictions on the choice of TFs,NWI does the same for wavelength, and they are

somewhat complementary. In FF/FWI connec-tions can freely choose between all TFs andwavelengths as well: if their product is kept con-stant, performance is not affected at all. In IF/FWIand FF/NWI, instead, the best performanceshould be obtained by shifting resources in thedimension which grants more freedom, that is Win FWI and T in FF. Fig. 19 confirms this con-jecture; a comparison among them also showsthat, if W>T, IF/FWI provides a lower lossprobability than FF/NWI.

Fig. 20 plots the four cases with four and eightcolors (W=4,8) assuming a fixed ratio TW/NV. Itresults that the difference between NWI and FWIarises for intense traffic, where the loss probabilityis relatively high, while for low traffic they givequite similar results. The opposite behavior occurswith IF and FF: they differ for small load values,where some TFs are still not reserved and callrefusal is the major cause of loss. Upon increasing

Fig. 16. Blocking performance for different N and T/NV values.


the number of wavelengths, Immediate Forward-ing performance gets closer to that obtained withFull Forwarding.

Optimal performance is obviously found withFF/FWI. However, delay requirements and switchfabric constraints could make IF or NWI more

Fig. 18. Blocking performance for different forwarding techniques.

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 110

10

100

N = 16, W = 1, C = 10, 1.25 TF/SVP


Pro

babi

lity

of c

all b

lock

ing,

Pbl

Fig. 17. Blocking performance for different forwarding techniques and T values.


0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 110

10

10

10

10

10

100

N = 16, W×T = 200, C = 10, V = 5


Pro

babi

lity

of c

all b

lock

ing,

Pbl

Fig. 19. Blocking performance for different W values.

Fig. 20. Blocking performance for non-integer values of T/N.


attractive. As seen, the use of a larger number ofwavelengths can reduce call blocking.

An interesting behavior of the system is depictedin Fig. 21, where plots having slightly different Tvalues are drawn. When the number of TFs perinlet (T/N) is an integer, each SVP has the samenumber of TFs and, since the load is uniformamong inlets and outlets, for high traffic, when acall exceeds the capacity T/N, no other TF isusually available and therefore the call is lost. Forlow traffic, exceeding calls occur seldom and theSVPs can have, in traffic peaks, more than T/NTFs. By increasing T, T/N is no longer integer andSVPs compete for these ‘‘extra’’ TFs, i.e., the newTFs can, when needed, be associated to the SVPthat currently has calls ‘‘in excess’’: this is anadvantage for low traffic, where it is likely thatonly one SVP at a time would ask for them, butleads to a worse performance for high traffic,where two or more SVPs can need to get furtherTFs (note that the load is normalized to the linkcapacity, proportional to the number of TFs).

As low traffic gives a loss probability moresuitable for a practical use of the switch, it can be

useful to have a number of TFs dynamicallyvarying from SVP to SVP, in order to accommo-date better peaks of the offered load. Note that theloss performance is rather insensitive to the num-ber of TFs exceeding the integer T/N.

6 Conclusions

Time Drive Switching has been shown to be aneffective solution to the problem of providingend-to-end connections with arbitrary capacity inan optical network. Its simplicity relies on theexploitation of worldwide synchronization sys-tems such as GPS. Interworking among opticalnetworks based on different transmission tech-nologies is made easier. Traffic performance hasbeen evaluated under various assumptions ofinternal switch operation (type of forwardingwavelength conversion). It has been shown that,given a certain switching hardware, a givenblocking performance can be obtained by prop-erly selecting the parameters of the framing

Fig. 21. Switch behavior when T/N is not integer.


structure and forwarding rule, while limiting atthe same time the offered load.

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Donato Grieco Born in 1976 in Cernusco sul Naviglio

(Milan), Italy, he received in 2001 the Laurea (Dr. Eng.)

degree (summa cum laude) in

Telecommunications Engineering at

the Politecnico di Milano, Italy. His

main research area has been the

synchronous TDM/WDM switching,

with interests in optical

communications, switching techniques

and microwave circuits; he is also

interested in physics, mathematics

and computer science. He is currently

consultant in management of DB2

applications.

Prof. Ofek has been awarded the

Marie Curie Chair Professor in Trento

(Italy) by the European Commission.

He received his B.Sc. degree in

electrical engineering from the

Technion-Israel Institute of

Technology in 1979, and his M.Sc.

and Ph.D. degrees in electrical

engineering from the University of

Illinois-Urbana in 1985 and 1987, respectively. From 1987 to

1998 he was with IBM T. J. Watson Research Center,

Yorktown Heights, New York. For his invention of the

MetaRing and his contributions to the SSA storage products

(multi-billion dollar business for IBM) Dr. Ofek was awarded

the IBM Outstanding Innovation Award. He has written 42 US

patents and 100 journal and conference papers.

He has initiated, invented, and managed the activities of six

novel network architectures: (1) Ring networks with spatial

bandwidth reuse with a family of fairness algorithms: global,

local and Max–Min, the prime example is the MetaRing,

which is used as the underlying network for ANSI Standard

X3T10 and numerous IBM network storage products. (2)

Optical hypergraph for combining multiple passive optical

stars with novel conservative code for bit synchronization,

synchronized flow control, and distributed clock

synchronization. (3) Embedding of virtual rings in arbitrary

topology networks – for bursty data traffic with no packet

loss and reliable/real-time broadcast/multicast. (4) Global

packet networks for real-time and multimedia, which utilize

UTC and pipeline forwarding to guarantee deterministic

operation. (5) Optical fractional lambda (wavelength)

switching and grooming for WDM networks. (6) Remote

authentication of software during execution that can be used

for (i) protection on networks and servers, and (ii) distributed

trusted (GRID) computing.

Achille Pattavina received the degree

in Electronic Engineering (Dr. Eng.

degree) from University ‘‘La Sapienza’’

of Rome (Italy) in 1977. He was with the

same University until 1991 when he

moved to ‘‘Politecnico di Milano’’,

Milan (Italy), where he is now Full

Professor. He has been author of more

than 100 papers in the area of

Communications Networks published

in leading international journals and

conference proceedings. He has been author of the book

Switching Theory, Architectures and Performance in Broadband

ATM Networks (John Wiley & Sons). He has been Editor for

Switching Architecture Performance of the IEEE Transactions

on Communications since 1994 and Editor-in-Chief of the

European Transactions on Telecommunications since 2001. He is

a Senior Member of the IEEE Communications Society. His

current main research interests are in the area of optical

networks and switching theory.


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Fractional Lambda Switching for Flexible Bandwidth Provisioning in