TOWARDS OPTIMUM DESIGN OF STATIC WAVELENGTH-ROUTING OPTICAL WIDE-AREA

PACKET-SWITCHED NETWORKS

A thesis subrnitted CO the Depamnent of Elecmcal and Cornputer Engineering in partial fulfdhent of the requirements for

the degree of

MASTER OF SCIENCE (ENGINEERING)

Queen's University kngs ton, Ontario, Canada

September 1999

Copyright O Nabil A. Naas, 1999

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To my FAM%LY with love

Abstract

The erponen~ally growing aaffic demands in packet-switched opcical LVide Area Nenvorks (WANs) can be satisfied by exploiting the huge capacity available in the fiber h k s using the Waveiength Division Multiplexing (WDbI) technique. Given the fact chat componenn are s a expensive, it is important to concentrate on opamizing die cost of the WDbI-segment to be added to the exisung networks wMe satisfying traffic requirements. In this thesis, a novel heu& algorithm is presenced to solve nvo problems simultaneously: Rouung and Wwelengrh Assignment (RWA) and Nenvork Cost Opamizauon (NCO). The integrated RlVA/NCO problem is solved for a given physical topologv (or a fiber Iavout), average uaffic demands between aii network nodes, resuicbons on ai node pairs delay, resmcaon on the virtual h k uolization, maximum number OF wavelengths per fiber, and WDM components costs.

In order to achieve the best possible solution for rhis problem, Our

investigation proceeds in NO directions. Fint is the choice of the besc node architecture; where \lie investigate the impact of die network node architecture on reducing the overaii nework cost and reducing the wavelength requirements to buiid the virtual topology. For chat purpose, cwo node architectures are suggested: the single-Gber architecture and the multiple- fiber architecture. Moreover, the significance of employing opacai wavelength converters in these architectures is investigated. The second direction consists of building a least-cost virrual topology. Here we provide the arguments chat (1) solving the RWA sub-problerns (vimiai topology design and packet routing) sequentiaiiy yieids better resdts than solving hem simultaneously; (2) a carefui consideration of the nework aaffic demands results in a lower COS virmal topoiogy; (3) the best pnoritv polim, among odier suggested policies, used in seMng source (s)-destination (4 pairs while building die vimal topology, is subjecr to many factors: the nenuork trafic pattern, the-constraint requirements, and the physical topology.

ACKNOWLEDGMENTS

1 wish to express my deepesr gratitude ro my thesis supemisor, Professor Hussien

T. Mouftah, for his continuous support, guidance, and encouragement throughout

the course of this work.

Many thanks also go m Dr. Jaafar ElmLghani of die University of Northumbna,

Sewcasde, CK, and Dr. Zouheir Mansouraa and his group ar Nonel Seworks of

Ottawa for many consmctive discussions 1 had with them.

I would also like to dia& die Libyan Minisuy of Educaaon, Canadian Bureau of

International Education (CBIE), and Communication and Information Technolog

Ontario (CITO) for rheir encouragement and hanciai suppon.

Finallv, I wodd like to chank my parents who have raised me wirh love and

understandmg, my wife, Inas, for her paaence and support during these Fan, and

mv son, Yaseen, whose smde has inspired me through die whole course of my

thesis work.

LIST OF FIGURES

Fig. 2.1: The low acrenuation bands of die singie-mode fiber. ....................... 4

Fig. 2.2: A WDM nenvork showing connections benveen different node pairs ~ossibly at different wavelengths. ....................................................... .6

- Fig. 2.3: Unidirecrional-bus Architecture. ................................................

.............................................................. Fig. 2.4: Star Architecture. .?

Fig. 2.5: A wavelength-rou~g nenvork .....

Fig. 2.6: A fixed optical-switching mamx with N input-output port pairs and .CI wavelengths: (a) no wavelength conversion; (b) with wavelength conversion. The local ports are nor shown. .............................................................. 1 3

Fig. 2.7: A configurable oprical-swirching matrk with X input-output port pairs md /CI wavelengths: (a) no wavelengrh conversion; (b) \iiid.i wavelength

......................................... conversion. The local ports are not shown. .14

Fig. 3.1: The single-fiber archi tecnue. ................................................ 30

.......................................... Fig. 3.2: The multiple-fiber archirecrue.

C) ') Fig. 3.3: A 4x4 opacal switch reaiized using Spanke Architecture. .............. .JJ

Fig. 3.4: A global view of the approach used to solve die RWA problem. ..... ..U

.............. Fig. 3.5: Illusrration of the conanuous dear iightpath connecaon. .lj

Fig. 3.6: Uusuation of the non-continuous dear lightpath connecuon. ........ .46

......................... Fig. 3.7: Uustrauon of the undear iîghtpath connecrion. .47

Fig. 4.1: The 7-node wide-area nework example. ................................ ..69

........................... Fig. 4.2: The 7-node Wnid topology p p h ac I w I = 4 -72

Fig. 4.3: Detaiis of the &ai hardware requirement at Node 5 at IwI = 4 ......... 74

Fig. 4.4: The 19-node EON wide-area nenuork. .................................... 78

Fig. 4.5: Resuln of comparing the node architectures using Scheme 1. ........ ..83

Fig. 4.6: Resdts OC comparing the node architectures using Scheme 2. ......... .84

Fig. 1.7: Resdts of comparïng the node architectures using Scheme 3. ........ ..85

Fig. 4.8: Results of comparing die node architectures using Scheme 4. ......... .86

Fig. 4.9: Opamum nenvork cost vs. traffic pattern variations for R W Schemes 1-5 with and without imposing a urne-consaaint F is the traffic density and P is the naffic intensity. ..................................................................... g7

Fig. 4.10: O p h u m aggregare interfacing-part cost vs. uaffic pattern variarions for RiVA Schemes 1-5 with and without imposing a cime-conscraint. F is the

......................................... uaffic density 'and P is the uaffic intensity. -98

Fig. 4.11: Opamum aggregare opacal-switching matir cost vs. naffic pattern variations for RWrA Schemes 1-5 with and wichour imposing a urne-constrainc. F

.................................... is the traific density and P is the uaific inrensity. 90

Fig. 4.12: Minimum number of wavelengths required to achieve 100% X m r k Tbrorrghput vs. uaffic pattern vaiations for RWA Schemes 1-5 with and without imposing a cime-consuaint. F is the uaffic densiry and P is the traffic intensity.

Fig. 4.13: Number of wavelengths required to achieve the optimum nenvork cosr vs. uaffic pattern variations for RWA Schemes 1-5 with and mlthout imposing a ame-constraint F is the traffic density and P is the uaffic intensiy.

Fig. 4.14: Percentage of uaffic arnount considered in the WNd topology design vs. traffic pattern variarions for RWA Schemes 1-5 with and without imposing a rime-consaaint F is the traffic density and P is the uaffic intensiry.

102 ...........................................................................................

Fig. 4.15: k a g e c d del. at the optimum nenvork cosr vs. uafftc pattern variarions for RWA Schemes 1-5 with and without imposing a urne-consuaint. F

................................. is the traffic density and P is the traffic intensiry. .IO3

LIST OF TABLES

Table 4.1: Results of using the RWhVCO algorithm to solve the 7-node nenvork ................................................................................... example. 1

17 Table 4.2: A complete description of the virtual topolog): at IWI= 4 ............. - Table 4.3: Packet-rouang solution for ail s-d pairs at I WI= 4 . (a) The first-phase

7 ............................................... solution (b) The second-phase solution. ! 3

Table 4.4: The o p h u r n hardware requirement, which is the final hardware -- .................................................................. requircmenc ac IWI = 4 , 3

Table 4.5: Switches permutations for ail nenvork nodes ac IWI = 1 ................ 76

Table A.l: Results of employing die single-fiber architecture without wavelength converters and using Scherne 1 in the RWANCO algorithm ovcr the range [2,IwI 1. ............................................................................*.. 113

Table A.2: Results of employing the single-fiber architecture with wavelength conveners and using Scheme 1 in the RWANCO algorithm over the range. [ 2 , 1 ~ l $ , ] . ............................................................................... 115

Table A.3: Results of employing the multiple-fiber archirecmre withour wavelength conveners and using Scheme 1 in the RWANCO aigorithm over the range [î, 1 wl,]. ......................................................................... 1 13

Table A.4: Results of employing the multiple-fiber architecture with wavelength conveners and using Scheme 1 in the R\Vrii'cTCO algorithm over the range [2,lwl,,]. ............................................................................... 114

Table AS: Results of emplo ying the single- fiber architecture without wavelength conveners and using Scheme 2 in the RWANCO algorithm over the range [2,l~l,,]. ............................-...............................-.................. 114

Table Ab: Results of employing the single-fiber architecture with wavriength converters and using Scheme 2 in the RWANCO algorithm over the range [~,IwI,]. ............................................................................... 114

Table A.7: Resulrs of employing the multiple-fiber architecnue wirhouc wavelength converters and using Scheme 2 in the R W M C O algorithm over die range [2,1 W I , ~ , ] . ......................................................................... II 4

Table A.8: Results of emplo ying the multiple- fiber architecrue with wavelength converters and using Scheme 2 in the RWANCO aigorithm over the range [3,1 wl,,,]. ............................................................................. . . I l5

Table A.3: Results of employing the single-fiber architecture wirhout wavelength converters and using Scheme 3 in the RWAiüCO algorithm over the range [~,IwI,,,, 1. ..................................................-............................ 113

Table A.10: Resdts of employing the single-fiber architecture with wavelength conveners and using Scheme 3 in the RWANCO aigorithm over the range [~,IwI~~,]. ............................................................................... 113

Table A.11: Resdts of employing the multiple-fiber architecture \%lthour wavelength converters and using Scheme 3 in die RWANCO algorithm over the range [2,1 wltU,]. ........................................................................ 11 3

Table A.12: Results of employing the multiple-fiber architecture with wavelength converters and using Scheme 3 in the RWANCO aigorithm over the range

............................................................................... [2,1~1,$~>]. 116

Table A.13: Resdts of employing the single-fiber architecture withour wavelength conveners and using Scheme 4 in the RWANCO algorithm over die range 2 W u , .......................................................................... 116 LI 1 1 Table A.14: Results of employing the single-fiber architecture with waveienmh conveners and ushg ~ c h e m e 4-in the RWANCO algorithm over the ra&e [2, ( w I ,tu, 1. ............................................................................. .A16 Table k15: Resdts of employing the multiple-fibu architecture without wavelengrh conveners and using Scheme 4 in the RWANCO aigorithm over the range [2,1 w(,]. ..................... .. ............................................. 117

Table A.16: Resuits of ernploying converters and usine: Scheme 4

the

-X-

multiple-fiber architecture with wavelength in the RWANCO algorithm over the range

4 a -

Table B.l: Average results with 95% confidence interval without urne conscraint.. ............................................................................. -1 19

Table B.2: Average resula with 95% confidence interval with strict urne c0nstra.int ................................................................................ 1 20

CONTENTS

Abstract III

Acknowledgrnents IV

List of Figures V

List of Tables VI11

1 Introduction 1

1.1 Introduction .......................................................................... 1 7 1.2 Research Moavauons ............................................................ ....,

1.3 Thesis Outline ...................................................................... 3

2 WDM-Based Optical Networks 4

2.1 Inuoduc tion ......................................................................... 4 ............................................................. 2.2 Nework ,gLtchitectures 5

................................................ 2.2.1 Broadcast-and-Select Nemorks G 2.2.1.1 OpoEai Medium Topologies .............................................. 6

............................. 2.2.1.2 Single-Hop Broadcasr-and-Select Nenvorks 8 .............................. 2.2.1.3 Mulu-Hop Broadcasr-and-Select Nenvorks 8

.... 2.2.1.4 Broadcast-and-Select Architectures and Wide-Area Environment 9 2.2.2 Waveiengdi-Rou~g Ketworks .............................................. 10

............................... 2.2.2.1 Opucal-Switching Mauis ,bchtectu.res. -12 2.2.2.1.1 Fived Optical-Switching Maabc ..................................... 12

............................. 2.2.2.1.2 Configurabie Optical-Switching Mams 13 ........................... 2.2.2.2 Single-Hop Wavelength-Routing Nenvorks -15

......................... 2.2.2.3 Mulriple-Hop Wavelengrh-Rouhg Xeworks 16 2.3 Solutions to the S catic-Suuc RWA problem .................................... 20 . . . .

2.3.1 ~&fuummg Congestion ......................................................... 20 2.3.2 Minimizing Electronic Hops ................................................... 23 2.3.3 Mïnimizing Congestion with a Carefüi Traffic Considerarion ............... 25 2.3.4 Conclusion ...............................-..................................... 26

3 Design of Static Wavelength-Routing Packet-Switched Networks 29

3.1 Introduction ...................................................................... -29 3.2 The System ......................................................................... 29

.......................................................... 3.2.1 Node Architectures 29 3.2.1.1 Opticai-Swirchuig Ma& ................................................ 32

. 3.2.1.2 Interfaànp Part ......................................................... -3

3.2.1.3 Elemonic-Switching Matxiu ............................................. 33 .......................................................... 3.2.2 Nework Operation 36 - 3.3 Solution of the Integsated R\VA/NCO Problem ................................ 31 ........................................................... 3.3.1 Problem Statement 37

................................................................... 3.3.2 Assurnptions 37 3.3.3 Solution Approach ........................................................... 40

3.3.3.1 LNH Module ............................................................. -42 3.3.3.2 RLVA Module .............................................................. 33

3.3.3.3.1 VTD Sub-Problem Solution ....................................... 44 3.3.3.2.2 Sutic Packet Routing Sub-Problem Solution. ..................... 60 3.3.3.2.3 RtWASchemes ...................................................... 63

3.3.3.3 FNH Module ............................................................. -64 3.3.4 Performance Merrics Calculations .......................................... 65

4 Numerical Resdts and Andysis 68

4.1 Introduction ....................................................................... - 4 8 4.2 Application of die R'VCrANCO Aigorithm ......................................... 69 - -. 4.3 Cornparison of Node Architectures ............................................... . / - 4.4 Cornparison of RWA Schemes ..................................................... 8:

5 Conclusions and Future Research 106

5.1 Conclusions ....................................................................... 106 5 2 Future Research .................................................................. 109

Appendix A: Resdts of Node Architectures Cornparison 113

Appendix B: Results of RWA Schemes Cornpanson 118

References

VITA

Chapter 1

Introduction

2.1 Introduction

The continuous growth in multimedia senices and the dramatic increase in the number of

nenvork users make it difficult for single-wavelengdi-based opucal nenriorks, such as

S ynchronous Op tical Network (SONET), to handle rhis unavoidable huge aggregare uaffic,

simplv because such neworks are limited by rhe peak elecuonic speed of the nerwork

components (a few tens of Gb/s), whereas a single-mode fiber c m carry data at speeds up ro

cens of 'Ibits/s. Therefore, there is a necessicy to develop high-capacis, opacal nenvorks rhar

'ln more can satisfjr ail users' naffic requirement without going into the painfd process of la! ' g

fibers in the ground.

Fortunately, thanks to Wavelength Division Mdaplexing (WDM) technology, diis opto-

elecuonic bandwidth rnismatch can be aileviated by taking advantage of die available

enonnous bandwidth chat exists in the single-mode fiber layout. This is achieved by

subdividing the bandwidth arnong many independent wavelength charnels, where each

channel cm handle the maximum elecuonic processing speed. Using any one of chese

channels adds a new iink to the network, wirh a new capaciv equal to the wavelengrh

channel bandwidth. We will interchmgeably use the rem virtual link or dear Iighrpadi

v c 1 9 9 1 ] to refer to chis type of link. Vimd links constitue the WNal topology, which is

embedded h t o the physical topology and aimed to handle the traffic demands of aii

source(s)-destinaaon (d) paûs h t a single-wavelength nerwork c m o t handle. How to build

dus Wnial topology, properiy assign wavelengdis to in entire links, and perfom packet

routing over it requires solving the so-cded Routing and Wavelength Assignrnent (RWA)

problem. Since this problem is NP-hardi m a 1 9 9 4 ] [Rasil9941 pIBILM96] pasil9961

wKH1997] pSi19981, most of the work that has been reponed in the iiterature resorrs

ro either approximations or heurisuc approaches in order to ease the problem cornplexiry, as

both the network size and the dowable number of wavelengths p u fiber inctease.

1.2 Research Motivations

Given the fact that the achievable number of wavelengths per fiber can be suKcient to build

a virtuai topology in different ways thac guarantees the uaffic requirement of every single 1-d

pair in a Wide-Area Nework ~VAK) environment, and thar rhe cost of WDM components,

which are die building blocks of die v h a l topology, are s d espensive, an optimum design

of a WDM-based packet-switched nenvork rhen requises choosing a

leads CO the least WDM-segment cost. This can only be achieved

problems simultaneouslp: the RWA problem and die Nenuork Cost

pro blem.

virtual ropology chat

dirough solving nvo

Opamization (';CO)

In this thesis, a novel algorithm, the RWANCO algoridim. is presented to consider the

above-menaoned problems at the same urne. We present a solution that not only opamizes

the WDM-segment cost, but also optimizes routhg and capaci'y assignment and keeps

necwork delays within permissible values.

Another motive for dus work is to answer the debatable quesaon about the utilirv of

wavelength converters in sta tic wavelength-rou~g packet-switched neworks.

The RWA probiem is an ~ ~ p l c of a mixcd inrcgcr i i n a mathemaad p r o p (MILP), and i n c c no cfficiont dgurithms are known for the àoiuaon of diaary MLPs, rhis problcm is considcrcd as m NP-hîrd problcm llUi19981.

1.3 Thesis Outline

The rest of this thesis is organized as foliows. In Chapter 2, we descnbe the differenr

architectures of WDM nenvorks, parcicularly concenuare on wavelength-routing neworks,

define and dassify the RWA problem, and review some work thac has been done in solving a

paxticular dass of the RWA problem in the case of packer-switched nenvorks, stauc-static

RISA problem. In Chapter 3, we firsc describe the node architecmes to be considered bv

our approach. Then, we present our simplified assurnpaons to solve che inregrared

RiVA/NCO problem. After chat, the approach and the methodology used to solve the

problem are erplained. In Chapter 4, we highljght some important results, through the use

of numerical examples. We fust demonstrate the appiicauon of the RKANCO algorithm. c.

Then, we compare the suggested node archtecnires with and without employing wavelengrh

conveners. After thar, we evduare the proposed RVCrA schemes under unifom and non-

unifom uaffic and with and without urne-deiay constrainc. Finally, in Chapter 5, Our

concluding remarks and suggestions for future work are presented.

Chapter 2

WDM-Based Optical Networks

2.1 Introduction

Opticd fiber is now widely recognired as the most effective medium for hgh-capauty long-

distance uansmission, due to the combination of high bandwidth and low loss [GREE1992].

Since the maximum bit-rate ar which each user can transmit is iimited bu the electronic

speed, mdtiplexing techniques are requircd to make efficient use of the opacal

bandwidth available in the low-aaenuation regions of the single-mode optical fiber, about 30

THZ, as shown in Fig. 2.1 vAi;E199G].

1.30p 1 . 5 5 ~ BBnd Band

Wavelangth (microns)

Fig. 2.1: The low anmuarion bands of the single-mode fiber.

Wavelength division mulaplexhg (WDM), among othcr techniques such as cime-division

mulâplexing PM), code-division muitiplexing (CDM) and space-division muitiplexing

(SDiM), is emerging as the most practical and fume-proof solution to the ever-growing need

of today's end usen for more bandwidth [GREEl996] uAJS1999]. WDM is baùcally

fiequency-division multiplexing (FDLM) in the opcical frequency range, where carrier

frequenùes are refened to as wavelengrhs. Thus, WDM partirions the opticai bandwidth into

separate channels, each at a different wavelength, operathg ar transmission rates compatible

with the elecrronics speed available today, to support transmission and recepuon at an

aggregace bandwidth beyond any single channd system.

2.2 Network Architectures

A WDM nenvork rnight be visualized as shown in Fig. 2.2 wMA1993]. Ic consists of a

shared opacal medium and access nodes, through which users are connected ro the nenvork.

Traffic sent bo each user actached to the access node, which mighc be an aggregated one, are

delivered by the network to the intended desanacions. Thus, each node must have the

capabiliy of doing the following [ACAM 9941:

1. Converthg the applied user's signal from the elecnonic domain into the optical domain

on a cenain wavelength (E/O conversion)

2. Placing the optical signai ont0 the medium

3. Remeving . h m the medium those wavelengths intended for itself

4. Convehg the received signai fiom the optical domain inco the electronic domain (O/E

conversion)

j. Performing switching and/or routhg on wavdength signai or electronic signai

6. D e i i v e ~ g electronic signal to the intended usen anadied to the node.

WDM n e m k s cm be ciassificd inco two main categories based on the used opacal

medium architecture [CREE1 9931 wIA1993] [GERS19961 [MC'KH1997] wSIl998]

PCCh19981: broadcast-and-select neovorks and ~ a ~ d u i g d r - r ~ ~ ~ g nenvorks. Each of

chese categories can in tum be dividcd into rwo classes: single-hop nenvorks, sometimes

known as al-opticai nemorks (AON) or fully transparent networks, and mulu-hop

networks, sometimes also cded elecnonic-opcical networks @ON) or pmiaily transparent

networks.

7 : T r a n r m l i t e r R : R e c t i v t r 1

Fig. 2.2: -4 WDM nerwork showing connections berneen differenr node pairs possibly ar diffuen t wavdengrhs.

2.2.1 Broadcast-and-Select Networks

In a broadcast-and-select nenvork, each node injecrs irs signal into the medium using a

different wavelength from other nodes. This signal is broadcast to d nenvork nodes. Ac the

receiver node, the intended wavelength signai is exaacted from the superimposed signals.

2.2.1.1 Optical Medium Topologies

The most cornmonly used topologies in implemen~g this kind of nenvork axe the star

topology and die bus topology, as shown in Figs. 2.3pNR1989] and 2.4wiCMl993],

respectively. Both topologies use passive optical couplers as combiners and spliners.

In the bus architecturey each node uansmits into the "talk side" of the bus, via a

direcaonal coupler, then aaffic is broadcast to receivers on the " listen side" via a second set

of couplers. This feanire makes the unidirectional bus the recommended architecture for

high-specd networks in order to o b u k an efficient collision-free acccss. However, this

architecture is impnctical with fiber as an opacal medium, because it wastes signal power as

follows: in an N-node nework, if each node aansmits with power P, then only P/N' useful

power is delivered CO each node p N R l 9 8 9 ] .

In the star architecture, as s h o w in Fig. 2.4, the Nx! ! star coupler simultaneously

accepts/ broadcasts signals from/co aii nodes. Thus, each

VENR19891. Thesefore, in ternis of power consideration,

the bus topology.

node receives a power of P/X

the star

Directional Coupler Side sTdk

n I I Listen 4 u Side

Fig. 2.3: Lniduectional-bus rtchitecnue.

Passive Star

Coupler

preferred

2.2.1.2 Single-Hop Broadcast-and-Select Networks

Generaily, in single-hop neovorks, whether it is broadcast-and-select nenvorks

wavelength-rou~g networks, optical signais aavel from source to destination without

encountering elecuonic regeneraaon. Single-hop nenvorks are " fdy transparent" for optical

signals with different modulation formats.

If the number of neouork nodes is fewer han or equal to

wavelength channeis, then a complecely comected necwork can be

the number of avaiiable

achieved on a broadcast-

and-select nenvork. Othenvise, this architecture requkes a significant amount of dynarnic

coordination beween nodes ro access the medium in order to reduce wavelength

requiremencs and avoid both collisions and destination confiicts [h.EKH1992a]

[RL\M1993] [ML'KHI 997. This process requires nansminers and/or receivers to have the

capabilicy CO be rapidly tuned over a wide wavelength specaum with a high selecuvitv, which

can be done by using any of the foliowing combinations wKH1 99îa] WiH19931:

A fixed-nined transmitter Oaser) and a tunable receiver (optical füter)

A tunable

A tunable

However,

transrnirter and a hed-tuned receiver

transmitter and a tunable receiver.

the fact that the runing ranges of the curent opacai devices are limited and

their achievable tuning times are st i l i long compared wich die packet duration in a high-speed

nework, single-hop broadcast-and-select neworks must runain &cuit-swi tched und

rapidly ninable devices are commercialized WKH1992al [RAiU1993].

2.2.1.3 Multi-Hop Broadcast-and-Select Networks

Gencrally, in multi-hop networks, co~ections consist of a sequcnce of single-hop padis chat

are joined by means of elecuonic switching so that uaffic cm be dmpped and added dong

che connecrion. Therefore, mulu-hop connections are not inherendy opacally transparent; in

other words, they are 'partially transparent". Moreover, because of the nature of chis

architecture, dus nenvork cannot be circuit-switched but c m be packet-switched.

Since multi-hop networks c m efficiendy exploit the capaùty of single-hop connections;

as a result, fewer wavelengths are required to establish connections benveen nerwork node

pairs without the need of a compkaced dynarnic media access protocol, which requires

tunable transceivers.

In h s network, each node consists of a number of both fixed-runed uansmitrers and

fixed-tuned receivers. Each of these uses a unique wavelength. A node can direcdy trr-smit

packets only to those nodes that are tuned to one of the uansminer assigned wavelengths. A

packet may have to hop duough more intermediate nodes und it reaches its destination.

Thus, over' the physical topology, a virtual topology wiii determine the acmd connectiviry

benveen network node pain pEKH1992b] @M1993]. Therefore, choosing a "good"

vinual topology is one of the factors towards desigmng an optimum mulu-hop network.

Another factor c m be a simple nodal processing complexity achieved by emplo!lng simple

rouang mechanisms in order co reduce queuing ddays at inrennediate nodes, which are

significant in local-area nework (LM3 and meaopolitan-area nenvork (MXh3

environments wKH1992bl.

2.2.1.4 Broadcast-and-Select Architectures and Wide-Area Environment

The advantages of these architectures lie in their simpliciv and nacural muiticasting

capabilicg. However, th. are not suitable for a WAN environment (but they are sall suitable

for MN and MAN environments), becausc of the foiiowing main Iunitaaons w 1 9 9 3 1 :

8 They require a large number of wavclengths (at least as many as the number of nework

nodes) because they do not enable the reuse of waveiengths.

i The splitang of the combined signal at the passive star coupler weakens the opacal signal

received at the destinaaon nodes, and these nodes are geographicdy distanced, which

adds extra losses to the received signal. Ni of these necessitate using a cascade of opacal

arnplifiers to compensate for these losses. Unfortunately, these arnplifiers c m provide an

overaii flac gain over only a smail portion of the 30 THZ bandwiddi. Therefore, the

nurnber of usable wavelengths wdl significan* be reduced.

2.2.2 Wavelength-Routing Networks

In a wavelength-routing network, which is the best recipe for die WAS environment, as

shown in Fig. 2.5, neoüork nodes are interconnected by fiber links, which may aiready be in

place. Every nenvork node essentially consists of two parts:

i Opucal-switching matrk (aiso caiied wavelength router): composed of passive

wavelength-selective cornponents which, based on the incorning wavelength, can select a

signal from one of its input pons and c m route that signal to a different output port,

possibly on a di fferent wavelength.

Access node': consists of an eiectronic switch, which could be eicher a packet swltch or a

circuit switch dependhg on the supponed traffic. Some of the switch input/ourput ports

are comected to the opacal-switching ma& via fked-tuned or tunable

receivers/transmitten sets. Other ports are sources/sinks of network traffic; these pons

c m be comected to sub-nets, other elecuonic switches, or end users.

The combination of fiber iinks and opticai-switching maaices consarute the optical

medium, in conaast to the opacal medium used in broadcast-and-select nenvorks. The key

idea of this medium is how waveiengdis are spatially used among neoxrork Wts. Thus, the

numbcr of one-hop connecrions that the network c m support can be more chan rhe nurnber

of wavelenghs that are available in a single 6be.r. This is deady iuusaated in Fig. 2.5, where

NO separate one-hop comections, from Node O to Node 3 and fiom Node 3 to Node 4, are

both carried ar the same wavelength il, as long as the nvo paths do not physicaily overlap.

Various types of connections cm be set up in the wavelength-routing network. For

example, as shown in Fig. 2.5, Node O can have a direct opticai path on wavelength A, to

Sade 3, which does not involve any intermediare electronic processing. This type of

comecuon is known as a vistuai hk, a dear lightpath, or a one-hop comection. We can dso

have a dear Lightpath from Node 3 CO Node O. The oniy difference benveen the former and

the latter is whedier the comection uses the same wavelength dong the path or uses

different waveiengths. In the former, die w a v e e n - o n constrainr wKH199 ;1 is

saasfied; therefore, this comection is known as a continuous clear iighrpath. By contrast, in

the latter, A, is used from Node 3 to Node 1 and chen 2, is used from Node 1 to Kode O

(because A , on chjs fiber is used by anocher connection and A, is free, we need ro use a

wavelength converter in the optical-nuitchhg manis to do the change opticah). This means

chat here the wavelength-continuity consaaint is no longer sausfied, and therefore d U s rvpe

of connecâon is known as a non-con~uous clear lightpath. Clear lightpath connections can

be used in both circuit and packet-switched neworks. Another type of comection c m onlv

be used in packet-switched neworks, where, for example, uaffic from Node 1 to Node 4

can first be sent to Node 5 using h, where it is eleceronicdy processed and forwarded to

Kode 4 using & (it is possible that the same waveiength is used). Therefore, this rype of

comection is known as an unclear iightpath or a multi-hop connection. Undear lightpaths

provide greatu capacicy ucilitation, reliability, and fiexibility in the entire network.

' We M have more than one access node attached to the opticai-switching matnx. such as is the case in [BaCh199fl.

Wavelcngth Converter

Optical-Swirching Matrix

Network Node

Fig. 2.5: A wavelength-rou~g network

2.2.2.1 Optical-Switching Matrix Atchitecnires

There are m o kinds of opacd-switching mamx architectures: the fixed architecture and the

reconfigurable archirecnue NMA19931 [BUCI 9961 WKH1997 Wi19981. Each

archirecnue can d o w waveiength conversion.

The fked architecture, shown in Fig. 2.6 [BRAC199u], can be consaucted with multiplexers,

demulaplexers, and possibly wavelength converters, as shown in Fig. 2.6(b). The

demultipleier separates the superimposed wavelengths at the input port onto differenr

spatial pons so that each wavelength is directed to a differenr demultiplexer port, and vice

versa for the multiplexer. Thexfore, using muluplexe~s and demulaplurus in a back-to-back

' For simplicity. the add/drop local ports in 111 opticai-switching maüh architectures are not shown.

configuration allows the interchange of wavelengths

prearranged pattern. Using wavelength conversion

wavelengdis in the nework.

benveen input and output fibers in a

in berween improves the reuse of

In order to be able to change the virtual comectivicy benveen neovork nodes, every

nework node that uses such a . p e of atchiteccure must have the capability of selecting

different wavelengths at each access node, which requires using rapid-tunable uansrnineis

and/or receivers [ChBa1995].

a

Mux Dcmux

Fig. 2.6: A Lved opacal-miitchhg mamv sith N input-output port pairs and LM wavelengrhs: (a) no wavelength convusion; @) with wavelength convenion. The local ports ate not shown.

2.2.2.1.2 ConQuable Optical-Switching Mauix

In this architecture, as shown in Fig. 2.7 pRAC1996], the interchange of wavelengths

beween input and output fibers is mechanicdy, electricaily, or opticaliy controiied bÿ a set

of circuit-based opacal space-division etches, where each switch is dedicated CO a certain

wavelength among M wavdcngths that can be available in a single fiber. In order co avoid

the intemal blocking of the saxne wavelength signds inside the switch fabzic, a non-blocking

switch architecture, such as Crossbar, Benes, Spanke-Benes, Spanke, or Banyan-Type

[SPAN1987j [j&101995] psi19981 [vaLe1998], s requirrd. A possible way to do

waveien* conversion in such a reconfigurable optical-switching mamx is to use a dedicated

wavelength c o n m e r at each output port of an opacal space-division switch FLi1993]

pKH19971, as shown in Fig. 2.7(b).

Accordinglv, a nenvork diat uses such type of architecture requires only hed-tuned

uansmitters and receivers at access nodes in order to change the vimal comectkiw and

dierefore avoids the tuning cime problem of the tunable transceivers [ChBa1995].

Dcmux Mux Spact-Dlvblon Oprical Swltch

Fig. 2.7: A contigurable optical-switching mamx witb N input-output port pairs and M waveiengths: (a; no wavelength conversion; @) with wavelagrh conversion. The local ports are not shown.

2.2.2.2 Single-Hop Wavelength-Routing Networks

In a single-hop wavdength-routing nenvork d connections must be dear Lightpaths. Based

on the wavelength-rou~g concept, where intermediate nodes dong the dear Lightpath

opticaily route the signal, node pairs c m establish point-to-point dear lightpadis. Therefore,

one c m say that today's technology provides the necessq optical devices CO achieve dl-

optical &cuit-suitched necworks. However, due to the h t e d technology in optical logic

and buffering, ail-opacal packet-switched nenvorks are not yet feasible WMh19931

P N 1 9 9 6 1 PKH1997 PSi19981.

The rouring and wavelength assignment (RWA) problem in single-hop wavelength-

rouùng circuit-switched nenvorks can be described as ioiiows PaCh19961. Given a set of

requests for dear lightpaths benveen nenvork nodes, the problem is to (1) find routes from

source nodes co thUr destination nodes, and (2) assign wavelengths to these clear lightpaths.

The RWA can be dassified as folows [BaCh1996]:

Stahc RWA: in which all clear Iightpath requests that are CO be set up in the nerwork are

known in-advance. The goal here is to rnaximize the rotai nurnber of dear lightpaths

which c m simultaneously be established in the nenvork or, altemaavely, rninirnize the

nurnber of wavelengchs required co establish a given set of clear lightpaths.

Djnumic RWA: in which dear lightpath requesa arrive randomly and each dear lightpath

has a random holding t h e afier which it is taken down. Often, the objective in such a

problcm is to minimize the requcst b l o c h g probability. Since the RWA problem has

been shown to be NP-hud [CGKa1992] and die nwnber of wavelengths is iimited,

several heuristics3 [CGKaI 9921 p l 9 9 4 1 [ChYu1994] (ChBa1 9951 bSi1995a]

FLi19961 [BaCh199u] and approxhauon techniques [BaMu199u] wKH1997] have

been proposed to reach the sub-optimum solution.

Stauc one-hop wavelength-rouring packet-switched neworks are possible in the sense that a

clear lightpath(s) is/are dedicated for eveq nework node pair, provided thar the avadable

number of wavelengths is suffiuent to establish all these connections. However, this

approach still has the pitfali of undenicilizing the capacity resources chat can be made

avdable by the established clear lightpaths by keeping in rnind that in packet-switched

nenvorks, unlike circuit-switched networks, each de= lightpath can be shared by a number

of access node pairs and uaffic benveen a pair of access nodes may travel via undear

lighrpaths. lVe will elaborate on diis issue in Chaprer 4.

Mula-hop wavelength-routhg packet-switched nenvorks are currend!- more anracave

than all-optical packet-switched networks, since it is premacure to talk about opacal packet

switching at this stage. However, in the next stage (second-generaaon opucal neworks),

when oprical packet switching can be realized, it is evpected that one-hop wavelength-

routing optical packet-switched neworks will cake over [SaBo1998].

The routing and wavelength assignment (RWA) problem in multiple-hop wavelength-

routing patket-nvitched nemorks can be described as follows. Given uaffic demands

betweai neouork nodes, the problem is to (1) choose a "good" WNal topology, (2) assign

wavelengths to the vimial topology links, and (3) h d routes for packets fiom source nodes

A heuristic is an algorithMc technique which usually, but not always. works or givcs nearly the right answer. 1 is usehl in the sense that sornc problems, such as the RWA, take far too long to compute an exact optima solution, but r o m good heuristics can be fan and, at the umc tirne, Snd a solution no more than a few percent wone than the optimal one.

to dieV destination nodes wILM199u] wKH1997] . The RWA c m be dassified into four

categories4 based on the reconfiguration of both die +al topology and packet switches at

access nodes, and they are described as follows:

Stdtirfiutic RW-4: dus problem is solved for the nemork uaffic demand maàu that

represents the long-terni average uaffic demands between ali node pairs. The solution

vields both a rtatiir virtual topology and a rtorir packet r o u ~ g . This means that in a real

situation a packet wiu folow a predetermined route, which is decided upon solving the

problem. Accordingiy, packet switches pemutaaons at ali access nodes must be static.

One of the primaq objectives here is to minimize the maximum v h a l link utilkation.

hocher objective is to minimize the network ame delay. Since diis problem has been

shown to be NP-hard PfRBM19941 paSi1994] vILM1996] [Rasil9961 wKH19971

paSi1998] (because many sub-problems of the problem are NP-hard), man'

approximation techniques psi19961 [BaMu1997] pWKH1997] [BYCh1997]

[Rasil9981 and several heuxisacs have been proposed CO reduce the search space of the

problem. Generally, heurisacs that are used to solve such a problem can be divided into

two dasses, based on the shape of the intended vimal topology. The firsr dass is of the

regular5 virnial topology-based heurisacs [CGKa1993] ) l a 1 9941 wRM1996]

wKH1997], in which a regular topology, such as Hypercube, Shufflenet, Manhattan

Sueet Nenvork poroid), Ring, Kautz graphs, etc. PaSa19941 pVe1997], is embedded

into the physical topology as a v h d topoiogy. For a regdar topology, solving the RWA

problem is reduced to a node-rnapping problem. Here the nodes of the regular vimai

topology are mapped to the nodes of the physicd topoiogy so that some predefined

This classification is bascd on the worlc that has been r c p d in the litcraturc. ' In a reguiar vimai topology, the number of clar lightpaths that are initiami and teminateci at every nodc is the same. If this number is diRecent h m a node to another, then we wiil end up wifh an imgular topology.

op&zarion criterion is satisfied and the nurnbu of used wavelengths at evev fiber

does not exceed the technological or a cenain given lunit. A regular WNal topology

enjoys many advanrages, such as simple packet routing. This rneans that the processing

complexity at access nodes c m significantly be reduced, and the architecture is both

fadt-toleranc and scalable in the sense that nodes are added and removed from the

nework with minimal impact on the nenvork performance. However, regular v h a l

topologies usuaily do not perform weii under non-uniform naffic patterns since extra

vimd Links (extra cost to simpiie packet routing) are built without efficiently urilizing

heir capacity resources. Therefore, the use of regular Wnial topologies in WANs is sail

questionable [SiRa1998]. The second class is of the inegular vimial topology-based

heunsucs [Rasil 9941 psi1 9961 [BYCh1997l [Bahdu1 9971 Pn'KH 1997. The

irregularicv of the vimd topology stems from the effort to be made to reduce the

number of vimial links by efficiently utilizing cheir capacity resources. We will cover

these heurisucs in more details when we corne to rhe related-work section.

Static-Dynamic RWA: d i i s problem first combines choosing a "good" virtual ropolop

sub-problem and assigning wavelengths to che vimial topology links sub-problem as one

sub-problem. The inregrared sub-problem is solved for a given nenvork traffic demand

mamu, which represents the long-terni average uaffic demands bemeen ali node pairs.

n i e solution of this sub-problem yields a static virtual topology. One of the objectives

here is CO maxirnize one-hop naffic (Le., node pairs thai have large naffic demands

receive vimial links). Since diis sub-problem has been shown to be NP-hard [ZhAc1994]

[ZMcI 9951, approximation and heurisuc techniques [ZMc1994] [ZhAc1995] have been

suggested to ease the complexity of the sub-problem. Thm, the remainîng part of the

problem is ro find routes for packca from source nodes to their destination nodes over

the resultant Wnial topology under a realistic traffic model, whose average values are

used to build the vimial topology. The solution then is to find an efficient dynamic packet

r o u ~ g scheme [ZMc1994] [ZhAc1995] (i.e., a packet route is decided on the flv;

accordingiy, packer switches permutations at aii access nodes are evpected CO be

dynamic) that satisfies a cenain petformance critena, for example, the cell loss

probability in the case of using ATM (Asynchronous Tram fer Mode) uaffic.

h L p i v e RWA: rhis problem is solved for several network uaffic demand mauices

(aaffic patterns), where each rnaPi~ represents the average traffic demands over a certain

period of cime (could be hours, days, or rnonths) berween aii node pairs. The solution

yields both a srauc virmal topology and a staac packet routing for the intended period of

time, and both virtual topology and packet rouang must adapt to traffic pattern changes.

One of the primary objectives, while maintainhg the ones mentioned in the staac-static

RWA problem, is to minimize the differences in the intended virtual topologies in order

to minirnaliy disrupt the naffic when the virtuai topology has to be reconfigwed.

Solutions to this problem have been proposed in w c l 9 9 4 ] PaiMu1997j

8 Dynurnic RFA: this problem handles a realisuc traffic situation by dynamzcaib

reconfiguring both die virtuai topology and the packet switches at aii access nodes. This

type of problem is suitable for connecuon-oriented6 packet-switched nemorks, because

nenvork resources (hardware and capacily) can efficiently be utilized by setting up and

teaxing d o m co~ect ions . These c o ~ c c t i o n s can be eitha dear lightpaths or undear

"n a conncction-oriented network, packets procecd thmugh th- wcll-dcfined phases: connection establishment, data transfcr, and connection rclease. Examples ATM and Multi-Protoc01 Lcvci Switching (MPtS), which is newly designcd to provide baret qudity of ~ M c e for Intemet RMocol (fP) tnffic without relying on ATM or SONET. On the o k r fiand, in a conncctionltss network. communication takcs place without fonnd co~cction establishment Examplu are Ethmct and Internet IP.

lightpaths. One of

comection request

the primary objectives in such a problem

blocking probabiliy. The soluaon CO d i i s

is to minimize the

problem has been

proposed in pSe1996] .

2.3 Solutions to the Static-Static RWA Problem

In fis section, we briefly mke a close look at the related heuristic work that has been done in

solWlg the static-stauc RWA problem. In panicular, we are going to concentrate on the

irregular Wtud topology-based heuristics. The goal of chis section is to provide a better

background and perspective of our work. However, dus is not a complete survey of ail the

work in this area.

2.3.1 Minirnizing Congestion

In [Rasil9941 [RaSi1996], Rarnaswami and Sivarajan argued thac the objective of the

problem must be rninimizing the maximum virnial link uulizaaon (congestion) or

mauimizing the offered load rarher than minimizing the average nenvork delay, which,

however, can be reduced by rescric~g the delay seen by every node pair CO be no more chan

some mulaple of the minimum possible delav. Their argument is based on the foIiowing:

since the problem is solved for an average uaffic rnams, but not die acmal value of ~af f ic ,

the solution must maumize the total aaffic that the necwork c m support (note: this is the

definition of the nenvork hroughput, as we will see in Chapter 3).

It is interesthg «, observe in diis regard that Ramamami and Sivarajan referred CO the

work that had been done in W a 1 9 9 4 1 , where the objective was to minimite the average

deiay. Taking Ramaswarni and Sivuaian's argument into consideration, the same group of

researchen in [MRBa1994] modifïed thur old work by adding the near objective, as we have

seen in wRM1996]. Moreover, some members of this group proposed anothu work in

~arMu1997J using a similar notion to Ramaswami and Sivarajan's, where the objective is to

minimite the average elecwnic hop. This is equivalent to mawirnizing the offered load in

the sense that dupl ica~g traffic dong the multi-hop pach can be reduced by decreasing the

number of electronic h o p

Ramaswami and Sivaraian put a restriction on the virtuai degree of any necwork node.

This is defined as the number of clear lighcpaths originaang or termularing in a node, so that

it does not exceed the minimum of both the number of the provided transceivers (by

assuming that the number of transmitters is equai to the number receivers) and the nurnber

of ports the packet switch can handle.

To solve the problem heurisucdy Iùr a given physical topology, naffrc mauix, delay

restrictions, maximum ailowable virtual nodal degree, and ma?rimurn allowable number of

wavelengths per fiber, the problem is divided into two sub-problems. The first is the virtual

topology design, where both choosing a "good" vimial topology sub-problem and assigmng

wavelengths to virtual h k s sub-problem, in which the wavelength-continuiq consuaint is

imposed, are solved simdtaneousl~. The second is the packet r o u ~ g . Here for a given

virtual topology, packet uaffic is routed over the virtual topology by formulaung the sub-

problem as a linear programming (LP) problem, which is uacrable at least for nenvorks with

tens of nodes. Also here, packet naffic c m be bihcated with different componenrs flowing

rhrough different sets of dear lightpadis.

For the virtud topology design sub-problem, the foliowing heurisac aigoiduns are

proposed: HLDA (Heuristic Logical (vimal) Design Algcnthm), MLDA (Mmhnum-cielay

LDA), and TILDA (Traffic Independent LDA). These algonduns are bnefly describeci

below.

8 HUM: The algorithm places k k u a l links benveen node pairs in decreasing order of

their uaffic demands. Establishing a vimial Mc is subject to constraints on the number

of transceivers at the w o end nodes and the availability of the sarne wavelength in the

best available path connecting the nvo end nodes. The goal is to route m a t of the traffic

in one hop to lower congestion. It does not consider delay constraints w M e designing

the vinual topology, but they cm be imposed later \hile solhkg the packet rouang sub-

problem. Ramaswarni and Sivaraian showed that this algorithm works well under non-

unitorm traffic.

.\ILDA: This algorithm is valid only when the vimal nodal degree is larger than the

phvsical nodal degree. It creates a pair of directed virtual links for each physical link and

the remaining virtual links are added according CO HLDA. Ramaswami and Sivaraian

daim chat the resultanc virnial copology can route al packets on the shortest physical

path and chus sausfies the ughrest delay consuaints that are phvsically possible. In our

view, we s d cannot guarantee die tightest delay for aii node pairs, because, intuiuvely,

routing node pair uaffic in die shonesr physical path, which consists of a set of vircud

links, is subject CO the availabiiiry of die remaining capaciues dong chis path that satisfies

the node pair uaffic demand.

TLDA: This algonthm designs ~ i x u a l topologies withouc considering die rraffic

demands. It hrst places vimal links between al1 one-hop neighbors in the physical

topology, dien benveen ail NO-hop neighbors, then benueen ail diree-hop nùghbors,

and so on. This algorithm minimizes the number of wavelengths required CO build n

vktual topology by reducing the number of physical links used by a clear iightpath. They

showed that chis algondun is appropriate if the trafic is either &own or uniform.

Using any of the above heuisucs, diey showed rhat inaeasing the virtual degree and

fixing the aiiowable number of wavelengths results in a decrease in the congestion.

Furrhermore, they showed thac increasing the dowable number of wavelengrhs and fising

che virtual degree yields M e r reducrion in the congesuon.

2.3.2 Minimizing Electronic Hops

In ~ ~ \ I u t 9 9 ? ] , lollowing Ramaswami and Sivarajan's approach as we rnentioned earlier, D.

Banerjee and Mukhejee's objective is to rniminimize che average electronic hops and to restricr

the delay of a node pair. However, Banerjee and Mukherjee's approach diifers in the

following: ( I j They use che number of uansceivers as an dternaave term CO the virtual

degree (this is m e in die contest o i the previous work, if the number of ports of the packer

switch is more chan the nurnber of uansceivers). However, a resuiction on the number of

uansceivers at every node is added here so rhat it must be equal or greater than the phvsical

desec of the node. (2) Wavelength assignrnent of virtual links does not necessarily sacise

the wavelength-conanuiw conscraint, which means chat wavelengrh converters are required.

(3) A new heuristic algorithm for solving die virnial topology design sub-problem is

proposed. As a marrer of fact, two heunscic aigorithms are proposed here, but, in o u rieu.,

we rhnk char the firsc one is sirnilar to HLDA. However, the algorithms are bneflv described

below.

i\Iaximi@ng Jitgfe-Hop Trafic He~nsh'r. Virtual h k s are es tablished between node pairs in

die decreasing order of theù uaffic demands. Establishing a vimd link is subject to

consmaints on die number of transceivers a t the nvo end nodes and the availabiliy of a

wavelengrh in the path c o n n e c ~ g the tsvo end nodes.

MuaanIi@ng hI~~hple-Hcp T r e c Heunhi-c V i d links are establis hed between node pairs

in the decreasing order of their anffic demands mdupiied by dieir fewest (physical or

iUnial) hop requirements.

&neje= and Mukhejee found thac the second algorithm achieves bercer average

elecaonic hops than the Gnt one. Moreover, they found that very few wavelengdi

conc-eners arc needed co solve the problem.

Similady, they showed, by using any of the proposed algorithms, that increasing the

number of uansceivers and Luing die allowable number of wavelengths results in a decrease

in the average electronic hops. Funhermore, diey showed that increasing the dowable

number of wavelengths and using die number of uansceivers yields further reduction in die

average elscrronic h o p .

Another rhing wonh menuoning in r h i s work, which we have not seen in rhe iiteranire,

is how to -do cosr modeling of a wavelength-rouung nenvork. Banejee and Mukherjee

considered the followhg opacd components in rheir model as a function of the number of

rnnsceivers and die number of wavelengths per fiber: (1) Transceivers: where they assumed

chat the cost of borh a transmîtter and a receiver is same. (2) Multiplesers/Demulaple?tcrs:

where the- assumed thar the cost of a mulapleser/demultipleser is the same for dl sizes. (3)

Opacal space-division switches: where they used a blocking architecture instead of a non-

blochng architecture. The objective of dus cost model is to do a cost evduation of the

soluaon of the RWA problem ar a certain number of nansceivers and wavelengths. R u s ,

from rheir point of view, in order to oprllnize the nenvork performance for a given nenvork

cost, we first need to obtain the nenvork cost for ail possible combinations of uansceivers

and wavelengths. Then, to o p h d y solve the RWA problem, we only consider the

combinaaons of uansceivers and wavelengths which yield nerwork cost diat satis$ the cost

consuut .

Nthough Banerjee and &Iukherjee proposed this iterative approach in hnding the

opamum solution, they concluded that a significant amount of resources may be

undenxrilized because the nework cost is independent of the ucilization of wavelengths and

uansceivers.

2.3.3 Minimizing Congestion with a Careful Traffic Consideration

In p C h 1 9 9 7 ] , S. Banerjee, Yoo and Chen proposed a new approach rnouvated by the fact

chat in some of the heuristic algonrhms proposed earlier oniy a subset of the rraftic demands

are considered whife consmcting the \+tual topology in the sense thar beyond diis subset ir

is not possible to estabiish other virnial links. This has the drawback of creating a i i m a l

copology in which all uaffic demands chat were not considered are routed via few links of

the vimal topology, rherefore causing higher congesuon in those links. The objective in this

approach is thus to minimize the maximum Wmai link udzaaon and ro consider aii uafhc

demands at the same urne.

To solve the problem heuristicdy for a given physicai topology, uaffic mams, delay

constrainrs, masimum dowable number of uansceivers, and masimum dowable number of

wavelengths per fiber, the RWA problem components are sknultaneously solved using die

Lnk Elirninaaon via Matching Scheme (LEM-LI?) , as follows:

1. Assume that the limitation on the number of waveiengdis is not considered, create initial

çimial links for all node pairs on the physical topolog using die shonesr padis (note: in

this algorithrn, it was assumed thar the wavelengrh-conrinui. consaaint is imposed). If

there are many shonest paths, rhen choose the one that has the minimum wavelength-

congestion (number of Wnial links rhat pass duough a certain physical iink) on anv

physical iink dong its path. If this Wrual copology does not saris. die number of

transceivers and wavelengths restrictions, chen go to Step 2.

2. Create a complete multi-graph with nvo partitions where each partirion contains ali

nework nodes, N. These partiaons are interconnected by unidirectionai links, which are,

in fact, the WNal links. The Iùiks are weighted using the naffic-congesuon mecric

(inindi, t h i s memc is equal to the naffic demand of the coaesponding node pair).

3. From the complete multi-graph, eliminate AT least congesced iinks from die gaph and

reroute traffic that was routed over those eliminated links over the remaining links in the

nework using minimum congested unclear Iightpath connections subject to the given

delav consuaints (note: in this algondun, it was assumed that the uaffic is non-

bifurcated). This process is repeated und the degees of ail die nodes are reduced CO the

ailowable number transceiver S.

4. Now, die virtual copologu is decided with a rninirnized congestion. A graph-coloring

technique called die coloring adaptive path graph (CAP) heunsac algorithm, which was

proposed by the same audiors in paCh19961, is used to minimize the wavelength

requiremencs.

j. From die virnial t o p o l o ~ gaph, idenufy which physical links have a wavelength-

congestion more than die maximum number of waveiengths. If there are, rhen uace the

vimial links that have assigned a wavelength index greater than the ma-ximum number o i

wavelengths. hfter thac, remove these virtual iinks from the graph and reroute their

uaffic, one by one, dong minimum congested unclear lightpath connections.

2.3.4 Conclusion

Based on this summarized review, the following observarions can be made:

In di diese menrioned works, h d k g die besc solution to the problem that achieves a

minimum congestion is based on uying different cornbinaaons of cwo variables: the

number of nansceivers (or Wnial degree) and the nurnber of wavelengths per fiber.

Moreover, Baneee and Mukherjee reduced the search space of the problem by adding a

neovork cost constra.int. In our view, a funher reducrion in the search space of die

problem c m be obtained if we c m do the following: (1) Solve the problem only for the

number of wavelengrhs per fiber variable, since, as we d see in Chapter 3, the number

of uansceivers variable is mai+ a function of the number of wavelengths per hber

variable and the physical-topology graph (which is a constant). None of the mentioned

work has considered this issue. (2) Make sure, at a cenain combination of the mentioned

vanables or number of wavelengths as a global variable, that the appiied load or uaffic

on the network is 100% mapped into die virtual ropology (in Our contest, we wiil reier

to rhis as 100°/o iletwoork Throwghput). None of the mentioned work, except Banerjee, Yoo,

and Chen' s work PYCh 19971 (although in a differenc concest), has considered this

issue.

The solution of the problem, ac a certain combination of the menuoned variables or

number of wavelengths as a global variable, can be improved if we make a careful

consideration of the uaffic demands. This also has an impact on reducing the nework

cost, as we will see in Chapter 4.

It is weU known that the main reason for using the L%DM technique as a means ro

increase rhe nenvork capacity is to avoid both the hassle and the high cost behind adding

more fibers to the necwork. However, given the fact chat \ W M components are s d l

espensive, then if we do not carefully solve the RWA problem, we rnighr end up with a

Wnial topology whose cos2 can exceed the cost of adding more fibers. Sone of the

audiors paid attention to "optimizing the Wnial topology cost". Nthough Bane rjee and

Mukhe j e e [BaMu1997] tried to opàmize the neiwork performance under the nenvork

cost constraint, they faiied to define the Wnial topology cost, which is the nenvork cost

' The vinual ropolog cost is defineci as the aggregate cost of the WDM componcnû rquired to build the vinual topology. The size and nurnber of thcsc components is decided upon solving the RWA problem.

in fact, because they calculaced the nenvork cost before solving the RWA problem.

Therefore, designing a "least cost Wnial topology" will be our theme in die nest chaprer.

The significance of wavelength converters has not been darified yet.

Chapter 3

Design of Static Wavelength-Routing Packet- Switched Networks

3.1 Introduction

In d i i s chapter, a novel heurisac approach is presented where the sratic-stacic RUVA problem

and the NCO problem wili be considered as one problem. This is moavated by the fact thar

none of the previous work has conrenuated on opumizing the WDM-segment OF the

nework while solving the RIVA problem. We first describe w o nenvork node architectures

to be considered in solving die integrated RLVA/KO problem, and then procred ~virh the

detailed esplanauon of rhe approach and the mcchodology used to solve the problem.

3.2 The System

3.2.1 Node Architectures

-1 wavelength-routing wide-area optical packet-swirched nenvork consists of a group of

nodes interconnected by fiber-optic Links chnt c q uaffic at severai wavelengchs. Evenr

nenvork node can be accessed by end users, subnets or packet switches. Two nework node

architectures are suggested to be used by our approach: the single-hber architecnite and che

multiple-fiber architecture, as shown in Figs. 3.1 and 3.2, respecavely. In general, both

architecnires consist of three main pans: the optical-swicching ma&, the ïnterfacing part,

and die elecnonic-switchlig ma&. We wiii in nun explain each of hem as foIlows.

hl* Al, * *A

E Iectronic O S witching a O Ma trix O

, end usrrs or subnra +

Optical Switching .--' Matrix

O

=-*., \ a

--o., \ a

**.* \

a WDiU Demultiplextr D WDM Multiplexer

/hl Re-conZigurablc Optical Space-Division Switch

Dedicatcd Wavclcngth oprathg at vsvrlrqth: )c, Convcrtcr

Cf_l Fixcd-Wavcltngth Trammitter Fiied-Wavclength Recciver

1 --* ............ L Al , km-i

Fig. 3.1: The single-fiber architecture.

Input fhrr I

\ '

/ \ ------ \ -----

70 othrr A TM suitches From orher A TM swirchrs , end usrn or subnru a : . end users or subnets

r a WDM Dtmultiplextr D WDM hlulriplexcr

Ihl Rt-configurabte Optical Space-Division Switch Dedicalcd Wavtlength opratiag at wavekngth: hx Converter

Fixed-Wavtltngtb Traiumitter Fixed-Wavdength Receivtr

Lb C........... b L Lw4 ---

Fig. 3.2: The multiple-fiber udiirecnue.

3.2.1.1 Optical-Switching Ma&

The optical-switching ma& consists of WDM demulaplexers, optical space-division

switches, %"DM muluplexers, and wavelength converters. A demuluplexer separates the

carried wavelengths on the input fiber Link (each fiber cm support IWI wavelengths, where

lCVl is the cardliality of set W , which is the set of a l possibie wavelengrhs per fiber) onto

different spatial ports so that each wavelength is direcred to a different port. Each opacal-

switching macris cm contain up to I WI independent optical space-division switches, where

inputs to each switch are aU signais at uiwelengdi A, , where k E {0,1,2,. . . . , I WI - 11, and

each output of the switch is direcred to a different multipleuer. Two main hncaons are

performed by each switch: @assing, in which the switch routes an incoming signai from a

demulcipleser to a multiplexers, and ~otuI rozrting, in which the swirch routes an incoming

signal from a demulàpleser to die elecuonic-suitching pan and from the elecuonic-

switching parr to a mulupleser.

Since it is important ro use a non-blocking switch architecture in order to aiiow a signal

at a parucular wavelength on an input port CO be routed to any outpur port (as long as no

ocher signal ac the same wavelength is being routed to the same output port), Spanke

architecnue [RaSi1998], as shown in Fig. 3.3, is suggested. It is a popular architecrue for

building large nonintegrated switches and has die foilowing complesity requirement to be

smcdy non-blocking [Rasil 9981:

corn pl ex if^^,,^^ (&6) = 26(S - 1) Ix2switches (3.1)

where 6 is the switch size and musr be a power of 2. The routing function of the switch cm

Fig. 3.3: 1 I x l opacai switch realued using Spanlie .irchitecnue.

If it happens chat a signa at a certain wavelength, A, , is to be routed to a certain output

fiber link where the wavelength channel at A, is occupied by another signal, but, on the

orher hand, there is a free channel at A,#, where k'# k , then the only solution to this

situation is to use a wavelength convener that is able to change (preferably opticaiir rather

than elecuonicaiiy) the wavelength signai from A, to 1,. . Therefore, we assume that each

ourput port of the opacd space-division switches c m be equipped with a dedicated

wavelength convenez FLi1993]. C'sing wavelength converters leads to the situation where

more dian one swirch output is connected to the same mdaplexer.

One might ask why, if we are going to have a staac wavelengrh-rouang nenirork, we

shouid use opacal space-division Ntches? The answer is that it is possible to exdude diese

switches fiom the node architecnire, but by doing that we are unable to (1) implement

proper 'necwork provisionkg, (2) cope with node/iink failure; Le., the restoraaon process

becomes difticul~ (3) adapt the nenuork to the aaffic pattern changes at diffuent ames by

changing the WRial topology connectivity. hlrhough we are not going to consider these

issues in d i s work, we feel that it is imponant to consider optical switches for the sake of

continuicy of this work

3.2.1.2 Intetfacing Pan

The interfacing part, carrying the funcuon of optical/elecnonic interface, consists of a set of

fised-~ave1en~g.h uansmitters and fixed-wavelength receivers. The Fised-wavelength

uansmitrer modulates the elecuonic data coming from the elecuonic-switching matris on to

a certain wavelength. Conversely, the fixed-wavelength receiver recoven the elecuonic data

carried on a certain wavelength.

M uansmiaen and receivers are disecdy connected to the opacal-switching iabcic via

opacal' fibers. The only difference beween the nvo node architectures is the L a y

wavelengrhs are assigned to the nmsmitters/receivers set'. In the single-fiber architecture,

every transrnitter/receiver musc use a unique wavelength. Accordingly, an. opacal su-itch

operaung at a certain wavelength has a nngh input/output dedicated to the interfacing part.

The upper bound of die number of transminers/receivers can be decided bv the foiiowing

where / 1 R~ 1 is the number of hxed-wavelength transmitters/receivers at Node i. On the

other hand, in the mulaple-fiber architecture, a group ot umsmners/receivets c m ualize

the sarne wave1engt.h as long as signais are directed cowards/coming from different adjacent

necwork nodes. Thus, any optical swicch has rnultfph inputs/outputs dedicated to the

' This technique has originally betn introduced in [MBRM 19961 and clcariy pracnted here.

interfacing part. The number of transrniaers/receivers is bounded by the following equaiicy:

1 ~ 1 5 ~ : - 1 ~ 1 (3.3)

r A; .lwl

where A: is the physical degree of Node i, which is d e h e d as the number of nenvork nodes

chat are physicaiiy attached to Node i.

By equaung ( T I / I R ~ I in equations (3.2) and (3.3), it is dear chat fewer wavelengths per

fiber d be needed if the mulaple-fiber architecture is used. In other w-ords, the multiple-

fiber architecture has a better spatial-reuse propeq of wavelengths. Because of this, using

the multiple-fiber architecrue requires more opâcal-switching fabric cornplesin;. T h ~ s can

dearlv be esplained chrough the foliowing esample: assume a scenario where only Sods i

communicates with its 4 adjacent nodes (i.e., A: =4). Then, in the case of using the

multiple-fiber architecture, ail uansmitters wiii be nined to the same wavelength, A,;

therefore, IWI= 1 will be suffiüent to establish ail comecrions. In the case of using the

single-fiber architecrure, nansmitters wiU uniquely be assigned a wavelength from the

following set: {A,, A,, Al , A,); cheretore, I WI= 4 di be required to establish a11

connections. Now, b y using equauon (3. l), the aggregate oprical switching complexiry at

Node i employing the multiple-fiber architecture will be 24 7x2 switches (one 4x4 optical

switch, o p e r a ~ g at A,) and employing die single-fiber architecrure \di be 1G 7x2 switches

(four 2x2 opticai witches, each operathg at a different wavelength).

3.2.1.3 Electronic-Switching Matrix

The elecnonic-suitchhg ma& can be a large ATM switching fabric or IP router, where

some input/output ports are comected io end users, subnets or odier packet switches using

different q e s of physical interfices. Other pons are anached to the opticai-switching

ma& via the interfacing part. This electronic-switchkg rnatrkv is important to improve the

udization of capacir). resources available in dear lighrpadis by using undear iighrpaths. This

happe& by allowing node pairs to c o m m ~ c a r e chrough a sequence of clear lightpaths using

intermediate nodes, where, at each of these nodes, packers carried on a certain dear lighcpach

is converted to the elecrronic domain, switched elecuonicdy and then convened back ro the

optical domain on a dear lightpath enroute to their destinations, which can operate on the

same or a difkrent wavelength (i.e., free wavelength conversion).

3.2.2 Network Operation

Since we are dealing widi the static-stauc RIVA problem, both the virtual topolog- and the

packet-routing solution have to be decided a prion based on the solution of the integrared

RW..%/NCO problém. In order to embed die resultant virtual topolog into the given

physicd topology, opricd space-division switches, ar eveq nenvork node, musr be

configured in a certain way. Moreover, in order to realize the static rouang of di r-d pairs

packet traffic over the Wtual ropology, lookup-table enuies for rhe elecuonic-switchine

maaix, at every nework node, are required. YVe wiH refer to some of these

receiver-uansmitter encries in the sense rhat the IN/OL'T of the enuy is direcdy

Y

enuies as

connected

to a certain fixed-wavelength receiver/uansmitter. These enmes deude what sequence of

clear lightpaths is needed to esablish undear lightparh connections. In the remaining enuies,

the IN/OUT is known and the OCT/IN is not known. In this case, die OUT/IN can be

d e s ~ e d to/launched bom many electronic-switchg outpur/input ports that are direcdy

connected to users, subnets, or decuonic switches.

3.3 Solution of the Integrated RWA/NCO Problem

3.3.1 Problem Statement

Consider the foiiowing facts: (1) Embeddhg the v i d topology into die network physical

topology can be done in difkrent ways that provide enough capaury not o d y to guarantee

the capaciw assignment of ali node pairs naffic, but also to keep al node pairs ame-delay

requireAent within permissible values. (2) WDM componenrs char are used ro build the

virtual topolog are suli very eupensive. In order to obrain a least cost virtual topology, then

we need to bring and solve nvo problems at the same ame: the RiVA problem and the X O

problem. The integrated R\VA/NCO problem wili be solved given the foiiowing: the

phvsical topology (or the fiber layout) of the nework, the long-term average uaific dernands

benveen ail node pairs, tirne consmaints for aü node pairs, ma,uimurn number of wavelengths

per iiber, and K'DM-components cosrs. Since such a problem is NP-complete in a sense

that the R\VA problem is NP-hard, we s-iil resort ro heuristic techniques to handle the

complesiry of the problem.

3.3.2 Assumptions

In order to facilitate solving the integrared RWi\/NCO problem, our simplifjmg

assumpaons are as foiiows:

PhynaL topolog, b,: Assume that the single-mode-fiber backbone of the x-node

nenvork already exists, and the physical topology is represented by nvo N x N symmetnc

matrices: tirs& the comectivity mauix, f , with an entry Pm is equal to 1 if there is a

physical ILik benvcen Node n and Node n; othennise it is equal 0; second, disrance

rnaaks, - D , with uiay D,, represents the length of the fiber link beween Node m and

Virtuc1itopo/ogy, Gd, : Assume rhat W N a l links are simplex; i-e., a virtual link from Node i

ro Node j, Zi;, and a WNal link from Node j to Node i, 1,;. , do noc necessady share the

same physical pach. However, the simplex mode is more general rhan assuming f d -

duplex links.

Modeling neltvork trafic Assume an .AT x X rraffic mauix, A , where the (r , d ) I h element,

A,, represents the long-terni average uaffic requirement benueen Kode s and Kode d.

The conmini: Assume an 2: x X Orne-consuaint ma&, lm , where the (s,d)" element,

r" , represents die masimum allowable urne del. (including both propagation delay(s)

and qucuing deIay(s) in the route to its destinaaon)' benveen Sode s and Node d thnt

sacisfies the requiremencs of d s-d services.

I/irtua/-/ink c"pannp Assume chat d virmal Links have the same capacity, c . In other

words, ail wavelen,d charnels have the same bandwidth, and the capacity uulizauon

c m be consaained by the factor p, ; Le., any virtual link can have a capacity equal to

c.p,, . In general, P,, is used to reduce die network sensitivi~ to naffic variations;

however, aithough this issue will be left as an estension to dus work, diis factor w d l only

be considered in our algorithm implementarion. In Chapter 4, we will alwavs assume

chat p,, = 1 .

Non-bifrcated tr@c Assume diat ATM naffic is used as an example of non-bifurcated

craffic, and oniy one -al link c m be established becween any r-d pair; therefore, aü

~nffic rnatri-x elements must comply with the following consuaint: A, < c. p, .

Other delay components are ignored, such as the queuîng deiay wirhin the elccuonic-switching fabric and the delay due to the eiectrooptic conversion (movinp information from the electronic domain to the optical dornain and vice versa).

M&,ing queuing delaj Since the Wnial link is initiated/terminated at the output/inpuc

porc of the elecuonic-switching marrk, several queuing models c m be used. Here we

assume diat the output-buffered ATM nvitch, with infinite output buffer at ali switch

ports, is used at evey network node. Therefore, we model our Wniai topology as a

nenvork OF M / D / 1 queues with infinite buffers. The average queuing delay at a virtual

link benveen Node i and Node j , based on I(leinrock's independence assumpuon

[SCH\V1988], is espressed as:

A

where is the average arrivai rate (Poisson) [ ceUs/sec] or the aggregate uaffic on 1,;

A

(for Poisson amvais), where Ai, < c p,,,, and p, is the average service rate

(Detenninistic) of the ATM switch port at Sade i rhat launches the virtual link ij;

[cells/sec]. Furdiermore, we assume chat the port service rate can fully esploic the

Xelluork tort model: Assume that the cost of the necwork is the aggregate cost of K P M

components required to b d d the virtual topology. We esdude the foiiowing from Our

cost model: (1) the opticai-fiber layout, since it already exists; (2) the opucal fibers used

inside the nenvork nodes to interconnecc optical components, since diese fibers are v e q

short in the sense that al1 these components reside in the same box; (3) opacal

amplifius, because the exact placement of these ampli fiers requires doing opucal signal

power-budge~g which is beyond the scope of this work; (4) opucd-switchïng conaol

&cuirni, if we assume that the conuol is to be done electronically.; (5) Elecuonic

(AR.) switches, since electronic switches are akeady being used by die single-

wavelengrh packet-switched nework (i.e., what we are doing is just upgrading the

e s i s ~ g one-wavelength network by increasing its capauty through the use of WDbl

rechnoiogy). We d inrerchangeably use the r e m WDM-segment cost, the virnial

topolog cost, and the upgrading neouork cost as alternative terms to the nenvork cosr

xetwork Re(irrbz(is: Assume that reliability consideraaons regarding die possible failure of

fiber links or nodes are not considered.

S o d e Compledy: Assume that there is no minimum LK'DiCI-hardware requirement at an-

nework node upon solving the integrated RWA/NCO problem.

3.3.3 Solution Approach

In the previous work, reported in Chapter 2, usually nvo variables are independendy used in

solving the RWA problem: IWI and the number of uansceivers or virnial nodal degree, d .

Therefore, obtaining the optimum solurion, regadless of the optirnizauon crireria used,

requires aing aii possible combinations of these variables.

In out case, we will only rely on the variable IWI in solving the RWA/NCO problem in

the sense chat the maximum complcsity of any neovork node is absolutely a hncuon of

both 1WI and Ay(which is always a constant), as dearly shown in Figs. 3.1 and 3.2.

Accordingiy, the optimum soiution' c m be obtained bv solving the RWA problem severai

urnes for 2 I IWI I IWI,, where (WI- is the technological Mt of the fiber, as foiiows. At

-

The control circuitry consists of dnvers. Each driver is required to change the state of an optical 1x2 switch. Sometimes, a group of these switches can use a single driver. The nurnbcr of the rquired driven is a function of the switch sizc. However, if we assume that optical switches aie elccuonically conuol~ed, then we can ignore the cost of drivers since the eltctronic driver technology is significantly cheaper than the optical technology.

Keeping in mind that we arc using heuristic rncthods to approach the optimum solution of the intcgratcd RWA/NCO problem, it is important to note that the tcnn optimum always rcfcn to the term sub-optirnum.

each IWI, the least cost w n i a l topology is to be idenafied among ocher virtual topologies

&at can be built with the available hardware resources with the given IWI. We will refer to

dus levei of optimization as focail-euef optimizan'oon and the least cost vittual topology ac a

certain IWI as a locdy optimized vimial topology, b:"'. Hence, the opamum vimd

topolog-, at 1 W( = 1 WI,, is the least cost vimtal topology among the locally optimized vinual

topologies provided that diis vinual topolog can handle aii node pair uaffic demands; i.e., ir

must achieve 100% hTetwork Tbrotgbput. The nenvork diroughput is defined as the percentage

of rra& dernands that are successfully routed or mapped over the virniai topology. Thus,

the optimum solution is resuicted by the following: 1 Wlmn < 1 WI,,p, S 1 WI- Y whcre I\Vim,, is

the fewest IWI required to achieve 10O0~'o xetwork Thmughput. We wil l refer to this level of

opumitation as gfobd-hvei ophzipa~on and die optimum virtud topology ar IWI = IWl,,pr as a

globally optimized virtual topolog, ~ ~ " h u ' .

A high-level description of die algorithm used to solve the integrated

problem is given, as foliows:

RWANCO Algonthm; m;u

Input:(d,,l\,c, IWI,,,! , P , , Node ~chitecrure, RWA scheme, WDM-components cos ts) glubut Output: Least cos t Wmai topoiogy; b,

Begin Initialization:

Optkn~m Neovork COS[, C O S T ~ L ~ ~ ~ + Optimum Average Network Delay, EQV + - lwlmin=O Iwl=2

While (1 W16 1 W(,) oc (IWI f 1 WI,) (beyond 1 WIsur boih C O S T N ~ ~ ~ , and E(t) get saniratecl)

{ Use I N H O to determine the Initial (ma?Umum) Network Hardware resources Use RWAO to solve the RWA problem (the locai-level cost optimization is puformed at r h i s stage)

If Network Thmughppul=lOOO/o (Le., the resultant vLNd topology can handle aii mffic demands), then: IWI,, = IWI I f ( lwl WL")

{ Use FM40 co derermine the cosr of die Final Necwotk Hardware requiremenn, which are less than or equal die initial hardware requlements If COST;",,, S COSTihoRK, rhen:

~f C O S T : ~ ' , ~ ~ ~ c COST&tORK, dien:

- COSTNC;wORK = C O S T N ~ , , , - EW,, = E(t ) - IWI, =IWI

G$[<J>uI = ~ X t l f

- V

Eise: (coST$&,, = COST&yoRK) If E(r) < E(t)op, , &en:

- E(r)dJp , = E ( t ) - 1 wl ,Jpr = l w l G gliibul = G l,>d ,Y - 3

} /WltlWI+I

1 End.

Derded desaipaon of the used modules in the above algorithm are esplained in die

following sub-secaons, respectively.

3.3.3.1 INH Module

In dus module, the masimum hardware resources, at a certain IWI, CO be made avadable to

the RWA problem are decided. In other words, referring CO Figs. 3.1 and 3.2, the maximum

allowable size and number of WDM components at every nework node are determined, as

Demdtiplurers/Multiplexers: The masirnum complexity mode1 is given by

Number: IWI

Complexiryy = Size: L\P + 1 if single - fiber arch. is used i E {O, , . . , - 1 (3.6)

Size: 2 A: if multiple - fiber arch. is used

Transminers/Receivers: The maximum complexity modd is gwen by

IWI if single - fiber arch. is used Complexi~" = Vi E {OJ, .., N - l}

IWI - L\I if multiple - Aber arch. is used

Wavelength Converten: The maximum complesity mode1 is gwen by

if single - fiber arcfi. is used Complexity" = Vi E { 0 , L . . 7 N - 1)

multiple - fiber arch. is used

3.3.3.2 RWA

In this module,

Module

three sub-problems are solved for a certain IWI: (1) choosing a leasr cosr

v i d topology; (2) assigning wavelengths CO the virtuai knks; (3) doing staac packet routing

over die virtual topology. The fùst and the second sub-problems are solved simuitaneouslg

and will be considered as one sub-problem, we c d it the virtud topology design sub-

problerL (VTD). The T'TD sub-problem and the static padtet rouang sub-problem will be

solved sequenâdy, as shown in Fig. 3.4. We wiil explain the methodologies used in solving

the w o sub-problems as follows.

RWA 1

Design

9 Tdf ic Considend in the 8 . ... S... 8 . - . ..--:-- v inuai t opaiogy ucsign I I

Throughput

Fig. 3.4: A global view of the approach used to solve the RW\cYI:4 problem.

3.3.3.2.1 VTD Sub-Problem Solution

Most of the work that has been reported in the lirerature does not pay careful consideration

ro the network traffii demands while desigmng che vimial topolog, escept the work that

was presenced in pYCh19971. The objective of that work is ro reduce the maximum virrua!

link ualizaaon and to consider a i i nenvork trafic demands at the same urne in order co be

able to map aii uaffic demands with fewer number of virtual Links. In our view, filiing up

\*imal Li& in this way reduces not only the number of virtual links, but also the nenvork

cost. Following this path, we present here a novel approach (different from PYCh19971)

where the W N a l topology design is based on a careful consideraaon of the nemork naffic

demands. In order to impiement chis approach, we first need to clearly understand the

foiiowing three scenarios of esrablishing a comecaon benveen any source-destination pair:

Conanuou~ char ligbtpath connetton: In a dear iightparh connecaon, aii optical-sitching

mamces of the incemediate nodes dong the comection route bypass the wavelengrh

signal from its source to its d e s ~ a u o n . This comecuon is c o n ~ u o u s in the sense chat

the launched signal must use the same waveiuigrh duoughout the route, as shown in

Fig: 3 . 5 In other words, this we of connecuon must sausfy the wavelengch-continuiy

consuaint. The main advantage of rhis type of comecaon is that a packer traveling from

its source to iu destination does not encounter elecwoptic-conversion delays and

queuing delays before reaching its h a 1 destination. The main disadvancage is the cost,

because establishing such a connecrion requires not only using a new mansrnitter and a

new receiver, but also using new inpuo/oucputs of the optical space-division switches

and new LVDM demuluplexers/multipIesers channels dong the route, which, as a result,

increases the aggregate optical-switchmg matris cost.

0 Fiber Link with 3 7c's O Yetwark Node

- - Available Wavelength - Connection

Fig. 3.5: Iliusuation of the continuous dear hghtpath connection.

'ion-contzn~ous c k r Igbptb annection: Ir is a clear lightpadi connecrion that does not use

the same wavelengrh chroughouc the route, as shown in Fig. 3.6. In other words, here the

wavelengdi-con~uity constraint is not sausfied. However, since changing die signai

wavelength to anorhu wavelengch requires using an opacal wavelength converter, more

cost will be espected han in the case when the conMuous one is used.

ICg

m.A- . - L... ........... ..

II Fiber Link with 3 A's O Netwark Nade

- - Available Waveleneth - Connection

.......... Used Wavelen~th Wavelength Converter

Fig. 3.6: Illusrration of the non-conthuous d e u iightpath conneccion.

Lficfear Iightpatb conneclion: T ~ H cype takes advantage of the esisang established clear

Lightpath c o ~ e c à o n s by combining the s-d pair uaffic wirh ocher uaffic akeady cmied

on these dear lightpath connections as long as they have enough remaining capacity

resources to handle the r-d uaffic demand, as shown in Fig. 3.7. This means chat at leasr

one eleccronic-nvicching mamx of the kitennediate nodes diroughouc the connecuon

route is involved in locaily routing the wavelen,gh signal in order to add other node pairs

uaffic to another aleady established clear lighrpath en route chat utilizes che rame or

different wavelength. Of coune, the big gained advantage of using this y p e o i

connecrion is the cost, since no new opucal-hardware is needed. Nevertheless, using

such a c o ~ e c u o n involves nvo delay components: the electroop tic-conversion delay and

die queuing delay; however, these components can be tolerated in the WAX

I I Fiber Link with 3 k9s Connection

Fig. 3.7: Illusrration of the unclex lightpach connecuon.

In comparing these connections, it is clear that the use of an unclear Lightparh

connection has a sigmficant impact on reducing the rate ar which vimal links are b d t . In

order to achieve this purpose, we need ro do capacity assignment for every s-d pair granted a

connection. Tnis looks as if the scatic packet routing sub-problem is simultaneously solved

i ~ l v i t h die VTD sub-problem, as shown in Fig. 3.4. Nevertheless, h s packet-routing soiuaon

wiIl not be considered as a final solution at dus stage, but the performance of the soluuon,

duough the caiculation of the network rhroughput, will be used as a measure of die

percentage of traffic considered in the vimal topology design, as shown in Fig. 3.4.

Based on the advamages and disadvantages of chese connections, it is clear that the

locaiiy cost-oprimized vimal topology, for a cenain 1 WI, cm be achieved, if the use of these

connections foiiows a certain prioriazed order. Funhermore, the sequence in which s-d pairs

will be served needs to follow a certain policy. Ttuee priority policies are suggested here and

they are described as foiiows:

P&y 1 Where s-d pairs are sorted in the increasing order of thek fewest number of

physical hop requirements; i.e., one-hop neighbors are served &sr, then the second-hop

neighbors, then the third-hop neighbors and so on. If more han one pair has the same

number, chen sorring of these pairs is done in the decreasing order of their uaffic

demands. The idea behind dus policy is CO minimize the physical hop distance of the

corkections. This has an impact on the following: (1) reducing the aggregare opcical-

switching cost; (2) reducing the ame delay of die connecaon; (3) reducing the

wavelength requirements to establish aii connections.

Policy2 ' inere s-d pairs are sorted in the increasing order of their fewesc number of

hop (physical o r Wnid by choosing the kwer) requirements. If more chan one pair has

die same number, then sorting of these pairs is done in the decreasing order of their

traffic demands. This poiic): aaempts to further exploit the capaciy resources to be

made available while building the vimal links.

Poliy3: VC'here s-d pairs are sorred in the decreasing order of rheir traffic demands. The

idea behind this poli? is that rounng most of che uaffic in one virtual link may lower the

number of virmai links and, consequendy, lower the aggregate interfacing-pan cost.

A high-level description of the aigorithm used to solve the VTD sub-problem is given, as

follows:

VTD Aigorithm;

Input: (6,,\, c, f" , pLy , Node architecture, Prionry Poli.)

Output: Locdy optimbed WNal topology 6"' Begin lnitializa rion

The resource(hardwue, wavelength, capauy)-updatlig variables are sec to zero/$

Let M = {m,, , m, , . . .} be a set of r-d prirs whose uaffic # O Ser 1 = o, where 1 is an NxN binary m a a s whose entries indicare which of die r-d paLs are successfdy considered by the VTD algorithm

\ i ; ~ e ( M # @ ) t

Order the J--d pairs in M accordlig to the given priority poliq Route the r-d pair pointed by the kt element of M , q, using ULCO module in an

atrempr to establish an Unclear Lightpath Connection. If a connecrion is established, then:

- Remove m, from M - Y, = l

If (Ys, = O) and (wavelength converters are noc aiiowed CO be used)

Route î?~,, using CCLCO module in a n attempt to establish a Continuous Clear Lightpath Connection. If a connection is esrablished, then:

- Remove 4 from M - Yfd = 1 Else: - Removc 4 hom M

1 If (Y,, = O) and (wavelengch converters are dowed to be used)

{ Route %ushg CLC() module in an artmpt to establish a Clear Lightpath Connection (cm be either 3 continuous one if wadengch converten u e nor rcquired along die connecuon path or a non-continuous one if at Ieast one waveiength converter is cequired dong the comecàon padi). If a connecàon is established, then:

- Runove 4 from M - Y,d = 1 Eh: - Remove % fiom M

Before we proceed with the derailed description of the used modules in die above

algonthm, it is important to mention chat building the Wnial topology depends on the

avdable hardware, capacity and wavdength resources. In order to keep ûaclr of these

resources, die foiîowing resource-updating vaxîables are dehed:

8 : is the vimal comecavity between Node i and Node j carried on A,, where

1 if rhere is a clear lightpath launched on A k vk =

C, : is rhe remaining capaciq- of die Waal link Li, where

t; : is the propagation delay of fi, where

Tk t is the number of used uansmitters at Node i char operate at kk , where

0 I T~ S A: if multiple - fiber arch. is used

o ~ l 3 l i f single - fiber arch. is used

R: : is the number of used receivers at Node i that operate at A, , where

0 5 Rif S A! if multiple - fiber arch. is used

O S R : SI if single - fiber arch. is used

A: : is a binary variable that indicares whether or noc the demulupluter (which is located

at Node i and attached CO rhe physicai link $) channd that operates at A, is used, where

1 if the channel that operates at Â, is used

0 otherwise

8 Bic : is a b i n q variable that indicates whether or not the multiplever (which is located at

Node i and anached to the physical link 1;) channel that operates at Â, is used, where

1 if the channel that operates ar A, is used

0 otherwise

O!,!' : is the number of used A, -space-division swicch inputs at Node i that are direcdy

comected to the demultiplesers secuon, where

p" : iis the number of used A, -space-division switch outputs at Xode i that are drectly

comected to the iuitip~exers section, where

osp" 'A{

X , : is the number of used wavelength converter at Xode i, where

0 I 5 IWI 2 47 if multipie - Sber arch. is used

0 5 X i L IWI .(A: + 1) if single - fiber arch. is used

y, : is a set of the distinct used wavelengdis in die physical link 1;, where

8 si, : is a set of physical links chat constitue the best physical path used to establish the

dear lightpath connection beween Node i and Node j

a, : is the set that connins the wavelength-assignment information of the physical links

that belong to %, ; i.e., if 3, = {l,$ , I& , . . . ,liPh) , then a, = { K ~ ~ ~ , y Ki,i2 . . , Ki R-l(n . } ;

where &, E W , i= i , , in = j , and n is the

the physical hop distance of the path

n, : is a set chat contains the virtual links used

number of physical hops dong the path or

to establish an undear Lighcpath connecrion

benveen Xode i and Nodej.

Sow, the three modules chat are used in the VTD algorithm exhaustively rely on the

shortest-pach (SP) aigorichrn, which is due CO ~i jksua ' PIJK19591, to search for the best

parh for the connecrion using different cosr criteria which mainly depend on some of the

menrioned resource-updathg variables. A detaded descripaon of each of diese modules is

espiained as shown below.

ULC Module: In this module, an effon is made to Find the best possible route to

establish an unclear lightpath connecaon, as foLlows:

1. Find the best path for an undear lightpath connecuon using the number of virtual

hops, where a virtual hop represents an already-built virtuai Lnk, as a cost meuic for

the SI? algorithm. The reason behind using this cost memc is to reduce the

duplicaaon of the trafic demand among virtual Links as much as possible to Save the

esisang capaciy resources for other connecuons. The virrual link cost from Xode i

(00 otherwise

A shortest path, R , , whcre X , = {l&t , 1liz ?... ,Li' . } , n is the number of vinual a-i Ja

hops dong the shortest padi, i, = s, and in = d , exists if and only if it has a finite

total cost and satis fies the foilowing condition:

More cornplete description of this algorithm can be found in [SCHW 19881 [BeGaI 9921 [TANEI 9961 [STALU 9973.

Ohenvise, there is no way to route this r-d pair uaffic using an unclear lightpath

connection.

( ) ,z!J) are aitemauve shonest padis that have the same nurnber of 2. If Irxd , 7rSd , ..-

virtual h o p ~ and saris@ the above condition, then the evaluation funcuons,

E~ ..., E*, of these shonest paths, respecuvely, c m be obtained, as foilows

Consequendy, RY' is the one diac achiever the follouing:

3. If ~t, exists, then the foilowing resource-updaung variables are updated:

Cih-lib = CL,, - A, for 1 I h < n

CCLC Module: This module is used if wavelength conveiters are noc: aüowed to be

used in the node architecwe. In this module, an effort is made co find the best possible

route to cstablish a continuous dear lightpath comecuon, as foLiows:

1. .Find the shortest parh for a continuous dear Lightpath connecuon path using the

number of ~hvsical h o ~ s as a cost memic for the SP algorithm. The number of

reduce the aggregace op ucd swl tchmg-

between Xode i and Node J is initial-

L J L

physical hops is used as a cosr meuic ro

matris complexicy. The physical link cost

evduated as follows:

1 if 4, = l and H$ c W - otherwise

Then for O I k 2 I w I - 1 , where k refers to the wavelength indes, do the foliouing:

/ I - Let E = e , where C is the iniaaily-sec cost ma& and is a ternporq cost

mauix

- Set enmes of l' such as

( ~ ( i , j ) if A, E y,, = O, and R,* = O

- Fid the shortest

other wise

that sausfies the foiiowing condition:

whese dibIih is the propagation delay of the physical link IL,,* and can be obtained

from the foliowing.

where u is the speed of Lighc in the single-mode fiber; = 2 . 1 ~ 1 0 ~ m/ sec.

,If the sarne 3, is obtained at different ks, which rneans that there are many

wavelengdi-assignment soluaons for R,., , then choose the solution whose

wavelength indes has the lowest value; i.e., if A,.. and A,. are possible soluaons and

k" > k' , then choose A,. for a,, .

7. If 3 . , 3:;) ,. ..,%$) are aiternacive rhonesr paths thai have the same number ol

physical hops and saasf-y the above condition, then the evaluaaon funcûons,

Z, , T? ,. . ., r m , of these shortest pachs can be obtained, respecaveiy, as foilows:

and is the one thar achieves the foiIouing:

3. If there is %, and its corresponding wavelength assignment information is a,, ,

then the following resource-upda~g variables must be updated:

. = y ,. UA,for l r h l n b l l h h-l ll

Il if single - fiber arch. is used

= { + 1 if rnuliiple - fiber arch. is used - f if single - fiber arch. is used

BAC. J ~ - I ~ = 1 for K h l n - 1

a:' =a?'+l for K h l n

CLP Module: This module is used if wavelength converters are ailowed to be employed

in the node architecture. In this module, an attempt is made to find the best possible

path to establish a dear lightpath comecuon, whether it is conanuous or non-

continuous, as foilows:

1. Fînd the shortest path for a dear lightpath connection again using the number of

physical hops as a cost metic for the SP algorithm. The evaluation of the physical

link cost benveen Node i and Node j is evaluared, as foiiows:

1 if 4, = 1 and y, c W q,,) = {

00 otherwise

3, esists if it sausfies die foliowing conditions:

if single - fiber arch. is used

If there are many different wavelengdi-assignmenc soluaons for 3, , chen the besr

solution, a,, is the one that requires die fewest number of wavelength converrers

dong die path.

7 If %(') 3::) , . . ., 32) are aiternative shortest parhs char have die same number of -* SJ 3

phvsical hops and satisf}: the above condiaons and dieir corresponding wavelength

") (:) dm) then the evaiuation hinctions u/, , v / ? ,. . ., y, of assignments are 0 h , ,. . ., ,, ,

these shortesc paths, which represenrs the nurnber of wavelength conveners needed

dong each path, respectively, can be obtained, as follows:

h=l if singk-tikr mh. is used

1 if K,, * K i i % = { n r-r

O otherwise

(1 if Ak + K,,, and A,. = Ki ~ - 1 1 n

1 if A, = K,, and A,. * K, n-l 'n

2 if A, # K ,,,, and 1,. * K: . 4 - ibn

10 otherwise

where A, and A,. are the launching and cerrninaung wavelengths, respectively.

Then die m' sub-besc paths arnong die m paths are chosen such as

Aker thar, use the previously

thac

menuoned evduation

3. If there is %y1 and its corresponding wavelength

launching and the t e m i i n a ~ g wavelengths are

(hesr ) is a, and both the

A, and A,. , respectively (if die

mulaple-fiber architecture is used, dien A, = & ~ , and A,. = K, V - I ~ ~ . ), then the

foiiowing resousce-updating variables are ro be updated, as follows:

Wbl,h=y /el , h UK, h-l Id for I I h S n - - new old

fi if single - tiber arch. is used

T k = { + 1 if rnuiiipie - fiber arch. is used LiZ

r if single - fiber arch. is used

new

X , = w atw

oid

Xi + l - old

X , w old

Xih + 1 - otd

X , + old

X i +1 * old

R- t h

sr' old

1 for l S h < n

3.3.3.2.2 Static Packet Routing Sub-Problem Solution

The rouung solution obcained while building the virtuai topology wdi be considered as a

first-phase packer-rouang solution. P e r f o h g another phase of packer routing over the

final vimal topology, as shown in Fig. 3.4, will yield better capacity assignment. In other

words, nework traffic will be evenly dismbuted among the builc vimal links. As a resulr,

less average virrual link ualizauon, less average delay and more nenvork rhroughput can be

especred.

The packet routing sub-problem can be solved as a linear programming (LP) problem;

rhis is acceptable for small networks, however, as the nenvork size increases, the cornplesin-

of the problem increases roc. Therefore, ro saas@ Our design speed requirements, we use a

heurisac approach, which is based on a heuristic aigorithm suggested in FrCh1971]6 uith

some modifications.

A decailed descripaon of the algorichm used to solve the sracic packet routing sub-

problem is given, as lolows:

i l l u

Input: ( b p l , ~ , c , ,lP, p _ ) Output: bes t offued packet-rou~g solution; (Aietwork Tbmughput, E(t ) , g , c) Begin INtializa tion

-- - -

fi In this work, the authors have showed that thcir solution is very close to the optimum solution.

Let M be a set of r-d pals whose naffic# O SP = 1 ; this variable will be used to identie the so&g policy

*L A

Set 1 = o, where 1 1s an NxV bhaq mamv whose enmes iadicate which of the r-d paks are successhiiy considued by the Packet-Routing algorithm

L W e (SP 5 4)

Sort r-d paLs in M as folows: If SP = 1, then son in the inueaslig order of th& fewest numbu of vlnial hop requlemena. If more than pair has the s m e number, then socting of these pairs wiii be done randomiy (this policy has been used in prCh19711) If SP = 2, then sort in the increasing order of th& fewest number of vicmal hop requirements. If more than one pair has the same number, then soorrinng of these pairs will be done in the increasing order of their a t f i c demands If SP = 3, then sort in the increasing order of th& fewest number of vLtual hop requlements. If more chan pair has the rame number, then soning of these pairs wiiî be done in the decreasing order of k i r traffic demands If SP = 4, chen son in the deueasing order of th& a f f i c demands

iYh.de(M $ 0 ) {

Foilowing die sequence of die demena in M , route every elemenr accordingly using ULCO module. If the r-d pair 1s successhiiiy routed, then: - Remove the J-d pair kom M -Yd=1 Else: Remove the r-d pair Gom M

1 1 f hërivork Thmughpr<r 2 rnax , then:

If Xetwork Thmugbp~r > max, then: - rnax =Nehvork T h ~ ~ ~ g h p ~ r - min = E( t )

- %est = - Ch,, = c

Else: ( Xetwork Thmwgbpfir = ma) i f E(t) < min, chen:

- min = E(t) - E6c.r = - - c e , = c

S P + S P + l }

The best solution, then: - Nen~ork Througipur= rnax - E(t) = min - E =Eber t

- C=C,, End.

3.3.3.2.3 RWA Schernes

Five RWA schemes are suggested. The fkst duee schemes differ in the prioriry policy used

in solving the VTD sub-problem. The iourth scheme will be used for compacison pusposes

heuris tic

not give

to compare our new VTD aigorithm widi die maximizing multiple-hop traffic

algondun suggested in @ikfu1997] as an exarnple of a VTD algorithm that does

a carefui consideraaon to the nenuork uaffic demands (note: chis algorithm was

bneflv esplained in Section 2.3.2 and clearly esplained and slighdy modified here to fit our

contest). The goal of using such an algorithm is KO see the impact OF the careh1

consideration of the nenvork uaffic demands on improving the local-level o p d z a t i o n . The

fifrh scheme will also be inuoduced for comparison purposes to compare desigmng a one-

hop ( U y transparent) wavelength-routing packec-swirched nenvork, in which al1 s-d pairs

musc use dear lightpath connections whose physical lenpdis are the minimum, with a mulu-

hop @ d d y transparent) wavelength-routing packec-switched nework, in which s-d pairs

c m use both undear lightpath conneceons and clear lightparh connections whose physical

lengths are the minimum. Detailed descriptions of these schemes are given, as follows:

Scheme t Run the following sequentiaiiy: the VTD module widi Policv 1 and then the

Packet -Rou~g 31 odule.

Scheme 2 Run the following sequenaally: the V ï D module with Policy 2 and then the

Packer-Routing Module.

Scheme 1 Run the foiiowing sequuirially: the VTD module with PoIicy 3 and dien the

Packet-RouMg Module.

Scheme 4 The *al topology is built using die foiiouruig aigorithm:

Scheme 4 VTD Algorithm; Input: ( d p , l , C , fP. y p- y Node uchitecnue)

Ourput: V i copoiogp, GY'

Begin Initializaaon

The resource-updating variables are set to zero/@

Let M be a set of r-d pa l s whose mfGc # 0 Set - Y = 0, - where is an XxX b i n q mamr whose enuies indicate which of the j-d pairs are successfdy considued bu the VID algorithm

M * D )

Order the r-d pairs, in M , in the deueasing order of the multiplication of the unfric demands and heir iewest number of hop (physica.1 or Wmd; take the iewei~

If (wavAengrh converten n e not d o w d to be used)

Route m, using CCLCO module. If a connection is esrablished,

1 If (Y, = 0) and (wai-elength converters are aliowed to be used)

{ Route % using CLCO. If a connecuon is established. dien:

- Remove Q Erom M - YSI = 1 Else: - Remove 4 from M

1 End.

M e r thac the Packet-Roucing module is mn.

Scheme 5: In this dgorithm, the VTD sub-problem and die packec rouung sub-problern

are solved sknultaneously, using the foilowing algoridun7:

Scheme 5 RWA Algonthm; Input: (d,,Q, C, p- , Node architecture)

Outpur. RWA solu9on; @y, Ne~mork Thmuglput, E(t), g, g)

Begin Inîtiaiization

' This aigorithm can be used to solve the sta<ic RWA problern in circuit-switchcd nctworics.

- = , urhae 2:; is the minimum propagation delay benveen Node s and Node d

and can be obtained through the SP algorithm by using d as a cost mauk

The resource-updatlig variables are set to zero/ # Let M be a set olr-dpWs whose a f f i c# 0 Set = g, whese 1 is ui iLX'V binary maris whose entries indicate which of die r-d

pairs are successfdy roured and considered by the VTD aigorihm (i.e., - Y = - Y ) ~ h i l e ( M + @ )

0 Order die r-d pairs, in M , in die inaeasing osder of diUr hwest number of physical hops requirunena

If (waielength conrerrers are not dowed to be used) {

Route 4 using CCLCO module. If a connection is established, dien:

- Remove hrom M J

I i (Y, = 0) and (wavelengrh converters are aiiowed CO be usecl)

{ Route 4 using CLCO. If a connection is established, then:

- Remove 4 Gom M - Y,=l Else: - Remove from M

1 1 End.

3.3.3.3 FNH Module

The cost o f the final nenvork complexiry is decided h o u g h the following resource-updating

Demultiplexers/Multiplexeis: The final cost mode1 is given b y

where C, is the cost of a (de)multiplexer channel.

Optical Space-Division Switches: The &al cost model is given by

Transrniners/Receivers: T h e final cost model of the interfacing-pan is given by

where CT / CR is the fixed-wavelength transminer/'receiver cost.

Wavelength Conveners: The final cost model is given by

where C,, is the cosr of a dedicated wavelength converter.

Consequendy, die finai aggregate nework upgrading cost) COST;",,, , can be obtained by

combining equauons (3.39)) (3.40), (UI ) , and (3.12) as follows:

3.3.4 Performance Metrics Calculations

In this section, we will mathematicaliy define some performance meaics, some of which

have already been mentioned and used by the RWANCO algondun. The ochers wiii be used

for die comparative analysis in the next chapter. A

Xen~ork T b m g b w

successfully routed,

is the percentage

and it is given as

of die total applied traffic on the nenvork rhat is

s .d Network Throughput = ,,

%Trafic Conridtred in VTû: is the percentage of rhe total applied naffic on the nenvork

rhat is considered in the vimal topology design, and it is given as

% Trafic Considered in VTD = r.d

Average Network Delay it is the average deiay experienced by ATM cells in the network,

and it is gwen as

rn Average Virtuuiknk LItili~~~arion: is the virtuai link unlizaaon averaged over aii virmai links

of the vimal topologv, and cm be expressed as

rn Awrage EIcmonic H p is the average number of elecuonic hops required by die

established connections, and cm be obtained either from pAlE1988]

*

0 if A, =Oor Y, = O

1 i f v : = I V k

> 1 otherwise

Average IVaueIengih Utilp?on: is the fracaon of the used wavelength channels per fiber,

and it is expressed as

Nmber of Wavelengtb Conuerierr. is the totd required wavelength converters in the

nenvotk, and can be obrained from

Chaptei 4

Numerical Results and Analysis

4.1 Introduction

In this chapter, through numerical examples', we are aiming to clari4 and validare many

issues that have been elaborated on in the previous chapters using our new proposed

approach. Among these issues are the application of the RWANCO algorithm, the definition

of the optimum node architecture, and the defuiluon of the opumum RWA scheme. In

addition, we will address the questions of why adding a second phase of packet rouung is

important, what the sigmficance is of using wavelength converters, what the consequences

are of noc carefdly considering the nenvork traffic demands in the \'TD sub-problem, and if

it is worth designing a static "fully-transparent" wavelengrh-rouang packet-switched

In ail esamples, we assume that aii WDM componenrs and 1 / 0 pom of the electronic

switches can operate up to IOGbit/sec PORTEL]. This is die opacal bandwidth of any

wavelength channel; c = 1 Wbit / sec (2358Mcell l sec ), using any of the 32 wavelength

channek avdable in the single-mode fiber PORTEL]; Le., Iwlrnx = 32. Furthemore, the

following 1999 +ces (in US dollars) of the WDM components are used':

Fixed-wavelength nansmitter: C, = $9,799 [[NORTEL]

7x2 or 2x1 electronicdy-connolied optical switch: CIx2 = $525 [JDSRTU]

The programming of the RWANCO algorithm was implemcnted using UC++ Language and c h e d out using MICROSOFT VISUAL CM (version 6) on WNDOWS 95/98/NT platform.

Here w assume that the cosrc of sirnilar WDM componenrs operating at difkrent wavelengths are the same.

Average cost of (de)mdtiplexer per charnel: Cc, = $1,160 UDSFITEL]

Tunable-wavelength converter: C,, = $30,000 LUCU'EL].

4.2 Application of the RWANCO Algorithm

In this section, we demonstrate the application of the RiVANCO algorithm through the

sud! of the loiiowing esample:

Phvsical topology: ?-node wide-area necwork, as shown in Fig. 4.1, where the distances

(in kms) benveen nodes are gwen by the foliowing manis3:

Fig. 4.1: The 7-node wide-area network euample.

The physicai conneetivity matrix. f , can be obrained frorn by following this logic:

Traffic requirement: given by the following matsix:

where ma& elements (in M ceil/sec) are randornly and uniformiy chosen from the

range (0,11.792) wCD1987] [PTVF1992]

?;ode architecture: single-fiber architecture withour wavelength conveners

No-consuainr on the delay requiremenr of al1 s-d pairs

No consaaint on die vimal link capaciry utiiizacion

RWA scheme: Scheme 2.

The results of solving chis esample are shown in Table 4.1. The table is divided into nvo

parts: the first pan. shows the results of the siruarion if only the first phase of packet roucing

(see Fig. 3.4) is considered as a final solution to the packet rouang sub-problem. This

situation represenrs an anempt to solve the vimial ropology design sub-problem and packer

routing sub-problem simuitaneously. In this case, the nenvork throughput is equal to the

percencage of traffic considered in the virmal topologÿ design. The second pan shows the

results of adding another phase of packer routing upon deciding the final Wnial ropology. In

dis situation, the nvo mentioned sub-problems are solved sequenady. In dus case, the

nenvork duoughput obtained from die &SC phase of packet roucing is considered as a

measure of the amount of aaffic considered in building the virtual topology, and die

nerwork rhroughput is obtained fiom the second-phase solution.

Table 4.1: Resdts ofusing the RWMCO aigorithm to sobe the 7-node network esample. RWA % T M c Nliwor(r

Approrch Iw Conrldrnd m u t E([" ~ ( f ) E(r) ~ ( p ) ~ ( h ) CO- ., CO-.. coq,. c o n , i n n d [SI [ m m ] [mru] [mru) (US$] [US$] [US$) [USSI

2 60.26 60.26 0.0009 1.6488 1.6497 0.81 15 1.6883 $13,920 $159,240 $50,400 $223,560 n D 3 80.56 80.56 0.0009 1.5088 1.5097 0.7018 1.5472 $37,120 $225.590 $96,600 $359.310

VTD . 2 60.26 69.79 0.001 1.433 1.434 0.8069 1.4497 $13.920 $159.240 $50.400 5223.560 tnen 3 80.56 87.82 0.0013 1.6262 1.6275 0.7402 1.4971 537.120 $225.590 596.600 $359.310

Rouring . ! - - @ f ~ ~ - ; : * ~ . ~ L-- .-&--A .-.- L -

$278,670 $96,600 3437.910 VTD stands tar vinurl 1 apaiogy Design

Now, Born the above table, it is clear diat as IW( increases, the nenvork throughput

increases too, since more WDM-hardware resources, which are function of I w I , become

available for solving the RLVA problem in such a way that more v i d Links can be builr to

handie die naffic demands. Moreover, as espected from Chapter 3, solving the cwo sub-

problems sequenuaiiy improves the network diroughpur. This eventualiy can cause the

nework chroughput ro reach 100°/o with fewer I w I than would bc die case if the nvo sub-

problems were solved simultaneously.

To cleaxly esplain the sipficance of addmg a second phase of packet rouung, let us rake

a close look at the resultant vimal topolog design at IWI= 4 . Table 4.2 shows a detailed

descripaon of diis v i m d topology. The description includes the comecrivity, the physical

parh of virtual links, and die wavelength assignrnent of die used physical links. The virruai

topology graph is shown in Fig. 4.2, where every node in the graph represents an elecuonic

switch. Now, Table 4.3 shows the solurions of the packer routing problem over the resultant

wnial xopology, where part (a) shows the tirs<-phase solution and pan (b) shows die

second-phase solution. From Table 4.3, ir is dear that the second-phase soiuaon is the better

solution, since 111 r-d pairs are served; that is why ~ N e ~ o r k Tbmugbpw~100% in this case,

whereas in the fïrst-phase solution some s-d pairs uaffic cannot be routed; this explains why

Nerivork Tbmugbpfit ~97.49%.

Table 4.2: A complere description of the Wtual topology at IWI= 4.

From\To Nod8 O Nod* 1 Node 2 Node 3

Node 4 PP:4-> 1 WA: 1

O O O 1

Node 6 PP:6->4-> 1 PP:6-a3 WA:O->O - WAA - PP stands for the Physical Paih ot the vinual link

"WA stands for the Wavelength Assignment of the physical links

Fig. 4.2: 'The Faode 4 m i a l topology p p h at IwI = 4 .

- 7 3 -

Tabk 4.3: Packet-routing soluaon for ail 1-d pain at IWk 4 . (a) The &sr-phase solution @) The second-phase solution.

3->6 4 - 4 5->4 4->1 1 ->O 1 ->2 3->4 1->2->3->4 4->6 0 - 4 6->3 O->5->4-> 1 4->6->3 6->3->4 5->4-> 1 -->O 2->3->4-> 1 3->4-> 1 ->2 6->4-> 1 3->6-> 1 -->O-->5 2->4 3-> 1 3->O 0->4 O--A-26->3 1 ->3 4->1 ->&->O 1 ->2->4->6 6->3->4-->5 0-2 2->6 O->2-->6 1 ->O->5 4->1->3->0-->2 NO way through No way through 6->1 ->O 6->1->2 5->3 5->3->1 5->3->O-->2

The global-level cost-optimizaaon process commences at I w ~ mtn ; lwlrnn = 5 if the cwo

RIVA sub-problems are solved simultaneousl~ and lWlmin = 4 if they are solved sequenually.

The final nenvork cost at any IWI is detehned upon solving the RWA problem, using the

FNH module. To explah how d i i s c m be decided, let us, for example, look at Node 5

before and a h solving the RWA problem at IW( = 4 . Before solving the problem, the initial

(maximum) hardware rcsources chat can be made available to the RWA problem, using the

LNH module, are deuded based on the foUowing: A: = 2 and I w I = 4 . Therefore, the initial

complexity is as follows: 2 demuluplexers of size 7x4, 2 mulaplexers of size 4x7, 4 opucal

space-division suritches of size 4x4, 4 uansminers, and 4 receivers. Upon solving the RL'iZ

problem, the &al hardware complexity is to be decided based on the utilizauon of these

initiai resources by the vktuai links chat are launched/terminated/opucally bypassed

from/aE/by Node 5, as shown in Table 4.2. Accordingly, the final WDM-hardware

complesiry, using the FNH module, as shown in Fig. 4.3, is as follows: 2 demulaplesers of

size 7x2, 1 multiplexer of size 3x7 (noce: there is no need to use a mulripleser at the

outgoing iiber iink, since only one wavelength channel is needed), 2 uansmitters, and 2

receivers. Accordingly, die cost of Node 5 is the cost surnmaaon of all these used \S'DM

components. The same hing applies for other nodes, and the final nework cost, therefore,

is the aggregate cost of the final WDM-hardware comp1ex.i~ of aii nodes, as shown in Table

4.4.

Fig. 4.3: Detait of the final hvd-e requirement at Node 5 at IWI = 4 .

It is interestkg to note that the optimum network cost (at the highlighted rows in Table

4.1) can be obtained at lWlopr = 1wlmin in both cases; however, dus is not always the case, as

we will see in the next section. Comparing the achievable optimum nenvork cost in both

cases, ic is, therefore, not surprising that the second case can achieve a lower network cost,

since, in die first case ar I WI= 4 , the nework chroughput is less dian 100%. This means thar

he final nenvork cost cannot be considered by the global-levei cost-opumizaaon process.

Table 1.4 shows the opamum hardware requirement, which is the final hardware

requirement at IWI = 4 . This hardware requjrement fields an aggregace cost of S 121,220.

Table 4.4: The optimum hardware requiremenc, which is die fmal hardware requkemenr ar I C V ~ = 4 .

In order for this WDM-hardware requirement to W the shape or the connectivity of

die vimiai topology besides realizing the static packet routing solution, ail nodes swirches

musc be configured as shown in Table 4.5. For the elecuonic switches pemutations, the

shown permutations are the receiver-nansmitter ones, which are important for esrablishing

undear bghtpath connections. For esample, at Node 5, as shown in Fig. 4.3, the input port

of die elecwnic switch chat is comected to the A,receiver has to be comected to the

output port that is connected to uansmitter so that an unclear lightpath that is used bu

the 0-7 pair (note: in order to trace t h s conneccion, see first Table 4.3(a) then Table 4.2) can

be established as follows: from Node O to Node 5 using the vimal link chat operates at A,

and then from Node 5 CO Node 3 using the virtual link that operates at A,.

Table 4.5: Swirches permutations for aii network nodes ar I w I = 4 .

It is worth rnentioning that even if so ldg the RWA sub-problems sequenady and

simuitaneously yields the same optimum nenvork cost, die former stdi c m achieve iess

average network delay and average vktual link utilization as the necwork chroughput in both

cases reaches 100%.

It is interesring to note thar, as I W I inaeases, whue I w I 1 I w ~ ~ ~ ~ , the avexage nework

dday deutases. This is happming because as ( ~ 1 incrcases, the avaihbility of wavelengths

inueases ac every physical Iink; cherefore, the building of a vimial h k can be accomplished

dirough a shoner physical path. Thus, ac a certain point, a M e r increase Li I w I wiii not

have any effect on the delay and any other parameters, because the shortest path will be che

choice for d Wnial U s . This happens at IwI 2 I w I SUI ( I w I Sur = 5 in ehis example).

4.3 Cornparison of Node Architectures

In this section, the nvo suggested node architecnues with and wichouc using wavelength

conveners will be invesagaced. The following input-data is used for ths example:

Physical topolog- 19-node European Opacal Nenvork @ON) [GSMa199;1, as shown

in Fig. 4.1, where the lengths of physical links are the distance (in krns) becwecn nodes

measured on the map and are given as shown below

Traffic

where mamx elements (in M cell/sec) are randomly and uniformly chosen [rom die

range (0,11.?92)

Node architecture: borh architectures with and widiout wavelength conveners

No consuaint on the delay requirement of ali r-d pairs

No consnainc on rhe Wnial link capauty utilization

RWA scheme: Schemes 1-4.

Resulrs of uskig the RWAEjCO algorithm with the suggested RWd4 schemes employing

the nvo suggested node uchitecmres with and wirhouc using wavelength converters OVCs)

are shown in Figs. 4.5-4.8. Derailed results are provided in Appendix A.

Ir is dear fiom part (a) of Figs. 4.5-4.8, as expected from Chapter 3, that using the

muiaple-fiber architecture requires fewer lwlmin than using the single-fiber architecture due

to the fact that the former has bener spatial-reuse property of wavelengdis. This esplains

whv E(w) is higher with che former than the latter, as dearly demonstrated in part (b) of

Figs. 4.3-4.8. Moreover, emplo+g wavelength conveners in both architectures c m further

d u c e lwlmin. This is because of the fact that relaxing the wavelength-conunuiv constraint

can increase the uulzaâon of some LV'DM-hardware resources (by establishing non-

conanuous clear lightpaths) chat can be available at a cenain IWI and, on the other hand,

cannot be utilized in die absence of wavelength converters. However, employing war-elength

conveners does not necessarily mean that E(w) c m usuaiiy be higher, as shown in part (b)

of Figs. 4.5-4.8. This is happening because, sometimes, che physical hop distance of a non-

conunuous dear lighcpath can be less chan a conanuous clear Lightpath. Tnis mems that the

former'needs to occupy fewer wavelengths dong its parh. On the other hand, a virmal link

established using the single-fiber architecture and the one established using the mulaple-fiber

architecnire are expected to have dose physical hop distance. That is why E(w) is always

higher with rhe multiple-fiber architecture.

Based on these hdings, using the multiple-fibex architecture wich wavelength converters

will be the besc reùpe to reduce ( ~ 1 , ~ . In gencral, factors diat can conaibure to the inuease

in l ~ l ~ ~ ~ a r e the nework size, the connectivi<y of the network (the average physical nodal

degree of the network, E(AP)) , and the aaffic applicd on the necwork.

On the other hand, in comparing parts (c) / (d) and (e) /(O of Figs. 1.5-4.8, it is quite clear

chat using the single-fiber architecture leads to a lower optimum nenvork cost than using the

multiple-fiber architecnue. ï h i s difference, as expected from Chapter 3, is mainly due to the

greater optical-swicching complexity requirement in the latter. This situation becomes quite

noticeable ac I w ~ # ~ ~ , where using both architectures can achieve the same COST&,,,,,w,

and COSTT,, . For example, cornparhg Figs. 4.5(c) and (e) at I w ( = 15 and 12, respecavelÿ,

it is dear rhat the cost difference benveen the w o architectures is mainlv due to the

difierence in COST, .

.hother observation worrh menaonkg from pans (d) and ( f ) of Figs. 4.5-1.8 is thac the

need for wavelength converters vanishes as I w I increases, and at I w I = IwlYu, the nurnber of

converters becomes zero. This is happening because, as IWI increases, the choice of building

a virtual link using a continuous clear lightpath radier than a non-conunuous clear Lighcpadi

tvill be more likely. Furthemore, ic is inceresung to observe chat ac I w I , , ~ , , the nurnber of

wavelength converters is zero. 'This is d w ~ s the case provided thac IwI,, is achievable with

die given IwI-. However, this does not apply for Scheme 3 since the rate ar which virtual

Links are built as IWI increases is higher chan orha schemes. Therefore, in Scheme 4, it is

aiways expected that 1 WI, = IWI,, < 1 WIsuI.

It is also interesthg to see from parts (ci) and (e) of Figs. 1.5-4.8 rhat using die single-

fiber architecture with wavelength converters is stiU a cheaper choice dian using the

mulaple-fiber architecture without wavelengrh converters, provided thar both architectures

can achieve 100% x e ~ o r k Tbmughput and the former c m o t achieve 100% Network

Thmvghput without waveluigth converters. This is happening because COSIGR plus

C O S T D ~ I I X + ~ X in both architecnues are quite dose and COS&, plus COS& in die

single-fiber architecture Mth converters is lower than COS?& in the mulaple-fiber

architecture without converters. It is clear chat both the number of wavelength converten

and the ratio benveen the wavelength converter cost and the optical swicch crosspoint cost,

C,,/C,,, , are c o n m b u ~ g to the decision. Thus, one musc keep in mind that if this number

or ratio is high enough, we c m espect that using the mulapiedber architecture without

converters will be the cheaper option. Factors that can conaol the number of wavelength

converters are the nenvork size and the nework connecthlty.

It is also interesting to note fiom Tables A.1-16 that at a certain IWI the pcrcenrage of

trafic considered in the Wtual topology design is equal to the nenvork throughput Beyond

d ù s point, die number of virmal links remains unchanged. This saniration in the number of

vimial links can be observed {rom the foiiowing: obselving E(h) as lWI increases, where it is

clear chat ~ ( h ) remains unchanged after this point, or observing COSTT,, , which is direcdy

proportional co the number of virmal links, as IW( Licreases. For example, ac

IWI = 13,12,9, and 9 , in parts (c), (d), (e), and (O of Fig. 4.5, respecuvely, COST;,R remains

unchanged after this point We u,-di refer CO this point as lWIs,-ju, throughout the rernainder

of this chapter.

However, beynd lwlsub phgsical paths used to establish vimal links mighc be

altered, and r h i s depends on whether or not it is possible to use shorter physical paths.

Therefore, it is expected that the aggregate cost of the optical-nvitching mauis

( C ~ ~ ~ m u x + ~ m + COST,,) decreases util it is sanuated at certain (wI; I w ~ = ~ w I .fut .

However, a k d y sceiilrio woidi mentionhg occun in Figs. 4.5(c) and (d) (or Tables A.1-2)

where COSTw is unexpectcdly increased from 61,755,600 at [ w I = 13 to $1,766,100 ar

I w I = 14 while the number of physical hops is decreased, which can be implied fiom the

decrease in COSTDm,,wm . This inaease is due to the consrraint imposed on the used

switch architecture CO be non-blocking which, rherefore, requires the size of the switch to be

a multiple of two. For esample, if the usable switch size upon sohing the RWA problem is

9, dien .the switch size must be 76x76 instead of 9x9.

Fig. 4.5: Rcsults of cornparhg the node uchitecnues ushg Scheme 1.

Fig. 4.7: Results of cornparhg rhe node architecnues using Scheme 3.

Fig. 4.8: Resulo of cornparhg the node architecnucs using Scherne 4.

4.4 Cornparison of RWA Schemes

In this section, we investigate the relative cost evaluation of the proposed RWA schemes via

simulaaon using the foLlowing input-data:

Physical topology: EON nework (Fig. 4.4)

Traffic patterns are generated as follows [Rasil 995bI [Rasil9961 [BaMu1997]

[BYChl997] P U K H I 9971:

- (100-F)% of the uaffic mamx elements are uniformiy and randornly distributed over

the range (O, x), where x is the maximum offered traffic load per s-d pair and x 5 c .

- F O/O of elements are uniformly and randomly distnbuted over the range (O, y), where

y S x .

- Traffic pattern parameters: P = x / c (uaffic intensity measure), R = x 1 y (the ratio

benveen the upper lirnits of the two ranges), F (uaffic pattern density measure if

R > N ; increasing F means that the traffic becomes more concentrated among a few

s-d pairs and decreasing F means that the traffic becornes distributed more evedy

among s-d pairs).

- Traffic patterns are generated for d possible combinations of the foiiowing

parameters: F=O, 25, 50, and 75%; E0.25, 0.50, 0.75, and 1; and R=100. If F=O0/0,

then a uniform-uaffic pattern is generated; othenvise, a non-uniform-uaffic pattern

is genera ted.

Node architecture: single- fiber archi teccure without wavelength converters

Time constraint: the simulations are conducted first without imposing restrictions on

J-d pairs delay; Le., lmU -t - 00, and then with imposing strict consuaints; i.e., lm = tv (by

ignonng the queuing delay component)

No consaa.int on the Wntal h k capauty utilization

RWA schemes: Schemes 1-5; Scheme 4 is used here to show the consequences of

designing the virtual topology without carefdy considering the network traffic demands.

Scheme 5 is used co design a M l y transparent wavelength-rouung packer-switched

nenvork. This scheme yields the lower bound of the following metrics: E ( t ) , E(h) , and

m- The cosr results and other performance meuics versus traffic pattern vaxiacions are

shown in Figs. 4.9-4.17 (soiid and dashed h e s represent the no-rime-consna.int case and the

suict-he-constlainc case, respectively)' and are based on averaging 10 simulation results

where each cime different seeds are used for random number generators that generate both

(O, x) and (0, y) ranges and deude which of the r-d pairs to be considered in the F% pair set.

Detailed results with die 95% confidence interval pLKDl987l P(u\fol988] are provided in

hppendk B.

Overail, as shown in Fig. 1.9, it is relauvely clear that increasing the naffic amount by

either increasing P and fixing F or deueasing F and fising P results in an increase in the

optimum nenvork cost, because more vimial links are needed to increase the capacinr of the

nenvork to handle the increasing uaffic amount. This increase in the nurnber of virtual links

is directly propomonal to the increase in the aggregate interfachg-part cost, as shown in Fig.

1.10. Consequently, rhe minimum nurnber of wavelengths per fiber required to do

wavelengch assignment of these links increases mo, as shown in Fig. 4.12.

Moreover, compared with the no-the-consuaint case, imposing time consnaints on all

s-d pairs delay reiativeiy yields an increase in the opcimum network cost since more Wnial

h k s are required. This is not because, for a certain r-d pair, the available clear lightpaths that

cm constitute an undear lightpath do not have enough remainîng capauties to handle the s-d

' This does not apply for Scheme 5, because it always insures that the conneetion delay of al1 s-d pain is the minimum.

uaffic d a a n d , but because the aggregate delay of this undear lighrpadi does not saüsfy the

tirne-consuaint requirement. This relative increase in the number of wnial links can be

observed in Fig. 4.10. Fig. 4.16 gives a dear indication that the residual capauaes in the

established Wnial links are underutilized compared with the no-tirne-conscraint case. Due to

this relative increase in the number of virtual links, lwlmin reiatively increases too, as shown in

Fig. 4.12.

In comparing the RWA schemes, the foilowing expected observations cm be made [rom

Fig. 1.9. First, in the no-ame-consrraint case, when the traffic panem is much denser, chere

is no dear winner benveen Schemes 1 and 2. However, Scheme 2 in the majorin* of diese

generated uaffic patterns is slighdy the wimer. As the uaffic panern densiq decreases,

Scheme 3 becomes a contender and, in fact, ic is the winner when F=?jO/f' and P=l , as

ciearly indicated in Table B.1. Now, whether Schemes 1 and 2, on one side, or Scheme 3 is

the winner depends on die combination of the foilollowing three trends: (1) As shown in Fig.

4.20, at a certain P, the optimum aggregate interkingpart costs, COST;:;. using Schemes

1-3 are quite close when the traffic pattern is much denser, but as F increases, the cost

becomes greater with Schemes 1 and 2 dian with Scheme 3. (2) As shown in Fig. 4.1 1, ac a

certain P, Scheme 3 provides a greater opamurn aggregate optical-switching matris cosr,

c o S T ~ & ~ ~ + ~ ~ plus COST;;, rhan do Schemes 1 and 2 when the aaffic pattern is much

denser. However, as F kcreases, this ciifference starts to shrink. (3) With increasing P, at a

certain F, these already mentioned cost differuices start to increase in the former and

deaease in the latter. Thus, based on diese trends, it is expected that at certain values of P

and F Scheme 3 would emerge the winner.

The question now is why these trends are happening. The h s t trend is due to the fact

that with Schemes 1 and 2 virtud W<s are granted ro 1-d paks based mainly on the physical

comectkity of the network Alrhough a care is caken to establish these Wnial links which

cm reduce the rate at which chey are built, s d some are built to achieve comecuviry arnong

one-hop neighbors, whose wffic demands might be very low, radier than lackmg remaining

capauues in some already established vutual links. On the other hand, with Scheme 3, wnid

Links are granted to the r-d pairs that have the highest uaffic demands takmg care to b d d

these vimial h k s as well. By following Scheme 3 priority policy, these vimal links cm

ulrimacely provide the required connecaviry for the rest of s-d pairs. However, when the

uaffic pattern is much denser, we expect that the difference in the number of vunial

hnks/COSTTf:, to be dose, as shown in Fig. 4.10. This is happening because when the

uaific pattern is more unifom, d r-d pairs tend to have equal chance of having a vinual iink.

As result, the priori? poiicy will not have a sigmficant impact on changing the number of

vimal links that c m support di naffic demands. In conuast, increasing F increases the

significance of the priority policy to be more naffic dependent, as it is the case with Scheme

3. As a result, the difference in the number of Wnial Links dramaucdy grows as F increases,

as shown in Fig. 4.10. It is important to menuon in dus regard that the increase in the

nurnber of virtual links in Schemes 1 and 2 provides extra capauaes that ailow more unclear

iightpachs CO span mmy virtual links, while, with Scheme 3, vimal links are effiuendy

unlized; Therefore, undear lightpaths span b e r vinual links. Thus, as F increases, spanning

of virtuai l u i k s is espected CO be comparably more widi Schemes 1 and 2. This dearly explain

why E(h) is greater in Schemes 1 and 2 than Scheme 3, and why the diffesence in E(h)

increases as F increases, as shown in Fig. 4.17. It is also important to mention that

sornehes E ( p ) , as shown in Fig. 4.16, does not give a dear picture of the capacity

utilkation of virn;lai links. This is due to the fact that the nuniber of virtual links is not

exacdy the same with aU schemes besides the fact chat wich Schemes 1 and 2 E(h) 1s ' more

which means that traffic is duplicated among many vknial links.

Tne second uend is due to the fact that vimal links in Scheme 3 are physicdiy longer

than the ones obtained with Schemes 1 and 2, since Scheme 3 prionty policy is a physical-

tapology independent. This also explains why E ( t ) is greater wirh Scheme 3 chan with

Schemes 1 and 7, as shoun in Fig. 4.15. Thus, as v i r ~ a l links gec longer, the agregate

opucai-switching matris cosr increases. For dus reason, when the number of iimial links is

close at uniform traffic patterns, Scheme 3 tends ro achieve greater aggregare oprical-

swicching mamv cosr, as shown in Fig. 4.1 1 (a). Because increasing F leads ro fewer virnial

links with Scheme 3 than with Schemes 1 and 2, the difference in the aggregate opucal-

swirching matrix cosr tends to decrease.

The third uend is the result of the following. Increasing the naffic intensity makes ic

difficulc for unclear lightpachs to span more vimd links thar saasfy the remaining-capaciq

consmaint. Therefore, the nurnbu of r-d pairs thar are forced to use dear lighcparhs

increases. Hence, this explains the following observations. (1) the increase in boch the

aggregate interfacing-part cost and, accordingly, the aggregate opticai-switching mauix cosr

as P increases, as shown in Figs. 4.10 and 4.1 1, respectively; (2) the decease in E (h ) as P

increases, as shown in Fig. 4.17; (3) the decrease in E ( t ) as P increases, as shown in Fig.

4.15, in the sense that the physical hop distance of a dear lightpath is less or equal CO the

physicai hop disrance of an undear iightpath chat failed to sans@ the remaining-capacity

consa%t. Now, given the fact that sparuiing virtud iinks that saasfy the remainuig-capaciv

constraint is generdy reduced w i h Scheme 3, we expect chat chance of using undear

lighcpaths will be greater and uaffic duplication will be less. As a result, the remainuig-

capaay constraint can be easiiy satisfied. Therefore, the rate a whidi the number of WNal

links increases as P inaeases tends to be less with Scheme 3; consequently, the same dÿng

applies for the rate at which the aggregate opacal-switchng ma& cost increases as P

inueases.

The rate of these trends depends on wo factors. (1) The raao benveen the cost of the

WDM components that consutute the optical-switching mams and the cost of both die

cransrnitter and the receiver that consritute the interfaung part. Increasing this ratio can lead

to a higher value of F at a certain P that makes Scheme 3 to be the winner, whereas

decreasing dus raao cm lead to less F at a certain value of P. (2) The physical topology of

the network'; for example, by comparing the resulo of the EON nenvork example,

where E(A") = 4 , with the PYSFNET nenvork example menaoned in ~a\Io1999], where

E(@) = 3, it is d e s thar increasing the connectiviq of the physical topology leads to the

increase in the value of F, at a certain value of P, rha t makes Scheme 3 the winner. This is

expected to happen because with low network connecuvity spanning more v i m d links chat

c m achieve the remaining-capauty constraint becomes more difficult with Schemes 1 and 2.

Therefore, more Wnial links are built co achieve comecuviy.

The second observation that c m be made from Fig. 4.9 is thac in the no-urne-consuaint

case, SCheme 2, in the majoriq of these generated naffic patterns, slighdy oucperfoms

Scheme 1, as deady shown in Table B.1. This is happening because the used priorig poliq

in Scheme 2 is intended to reduce the duplicaaon of the traffic demands among the already

established vLniai links, therefore, the rate at which wnia l Links are built cm be reduced. As

a result, a slight reducaon in the optimum nenvork cost can be expected wherever diere is an

In [NaMo1999], a similar sudy W ~ S conducted using the 14-node 1991-NSFNET physical topology ( E ( A , ) = 3 ) where Schernes I and 3, among otfrer RWA schcmcs, wcre investigated. It has ken shown thar Scheme 3 is the clear winncr at F=50% and P>0.25. This proofs that the physical topology is one of the factors that dtcide which values of traffic dcnsity and vaffic intcnsity make Scheme 3 the winner.

improvement in ~ ( p ) . This observation can be done by companng Figs. 4.9 and 4.16.

However, not following the pnonty policy of Scheme 1, by going a head of line for some 1-d

pairs, can increase the network cost. This could stem from the foiiowing scenario. A certain

J-d pair, whose minimum vimial-hop requirement, according to the used pnority policy of

Schemé 2, is fewer than the minimum physical-hop requirement, f ' l ed to establish an

unclear lightpath because some or al1 of the already established virtual links dong any of the

possible paths benveen the source and the destination do not have enough remaining

capaùues to handle the s-d uaffic demand. As a result, a virtuai link wiil be granted for this

pair. O n the other hand, this scenario could have been avoided, if Scheme 1 pnority policy

had been used and the s-d pair had used an unclear lightpath instead.

Third, in the strict-urne-consuaint case, Scheme 1 is the clear winner, and as the trafic

becomes more concenuated among a few s-d pairs, Scheme 2 brcomes a contender, as is

clearly shown in Fig. 4.9(d). We expect Scheme 1 to outperform Schrme 2 and both schemes

to outperform Scherne 3, simply because it is more likely with Scheme 1 to establish unclear

lightpaths whose virtual links saas$ not only the urne consuaint but d s o the remaining-

capacity constra.int for many s-d traffic demands. Whereas with Schemes 2 and 3 it is more

likely and even much more likely with the latter (because Scheme 3 priority policy is totally a

p hysical-topology independent) chat unclear lightpaths wiil not sa tis fy the ame consuain t

and sail have enough remaining capaciaes in their intended virtuai h k s ; consequendy,

building more vimal links becomes more likely. This dearly explains: (1) why with Scheme

3, unlike the no-time-consuaint case, ~ ( h ) decreases as F increases, as shown in Fig. 4.17;

(2) why the rate nt which the aggregate interfacing-part cost increases is more with Scheme 3,

as shown in Fig. 4.10; (3) why E ( P ) is the iowest with Scheme 3, as shown in Fig. 4.16. It is

expe&d char Scheme 2 will be a contender when the traffic pattern densi. decreases and

the naffic intensicy decreases, because one-hop vimal links will mostiy be sufficient to

handle aii uaffic demands.

Fourth, neediess CO Say, Scheme 4 is out of the contest in both tirne-consnaint cases. Its

iailure to obtain the least cost locally oprimited vktual topology is due to the fact that the

vimal topology is built without a careful considerauon of the nenvork traffic demands, as

shown in Fig. 4.14. Tlvs is happening because of the folowing: (1) Since buildmg Wnral

Links is based on the availabilicy of WDM-hardware resources rather than the necessity to use

them (as is the case with Schemes 1-3), the rate ac whch the number of virtual links are built

is expected to be the highest with Scheme 4 (see Fig. 4.8). This erplains why the aggregate

interfacing-part cosr, is shown in Fig. 1.10, is always the highest, encepr at low values of F

and P in the no-ame-consuainc case. For this reason also, Scheme 4 comparably

underutilizes die available capauaes in the estabiished vimai link, as shown in Fig. 4.16,

except at low values of P and F in the no-cime-consuaint case. (2) In the no-urne-consuainr

case, virmal links do not have the chance CO be shonened. In other words, the physicai hop

distance of virtuai links c m exceed die minimum requirernents. This results in an increase in

the aggregate optical-switching maaiv cost, as rhown in Fig. 4.1 1, even when the number of

the estabiished Wnial links is the fewest, as is the case at low values of F and P. This also

explains the increase in E ( t ) , as shown in Fig. 4.15. Virtual links c a ~ o t be shorcened

because, unlike Schemes 1-3, it is difficuit to obtain the leasc cost beyond lwlrnin in the sense

that increasulg IWI increases rhe number of wnid links rarher than shortens them. This

esplains why I w ~ , , ~ ~ = [wII,, by c o m p a ~ g Figs. 4.12 and 4.1 3. (3) In the smct-timetonstrainr

case, shonening of vknid links must occur to sausfy the time conscraint. However,

shortt@~g begins when the nurnber of v h a l links is sanuated, i.e., at I w I = IwI,-~~, , and,

herefore, 1 WI,, = 1 WI,, > PL-rn* In this case, the percentage of uaffic considered in the

\*al topology design is expected to be dose to 100% (but s d i less dian other schemes, as

dearly shown in Table B.2) in the sense that mosr r-d pairs will be granted wnia l linlis.

Because of this, we can approach the 100% nansparency (dues:E(p) = E(p),wcrB,, , , as

shown in Fig. 4.16, and E(h) - 1, as shown Fig. 4.17). It is interesting to see from Fig. 4.9

that the obtained opamum nework cost evceeds even the cost of a fuliy uansparent

nenvork (using Scheme 5). Trus is due to the increase in the aggregate opacd-switcirching

matris cost, as shown in Fig. 4.11, although the aggregate interfacing-part cost is close to

each other, as s h o w in Fig. 4.10. This is happening because, wich Scheme 4, virmal links, ar

a certain node, use fewer opacal space-dicision switches which means that die sue of every

switch is expected to be more and 11ce versa with Scheme 5. This observaaon is direcdy

related to the fewer wavelength requiremenrs with Scheme 4 than Scheme 5 , as shown in

Figs. 4.12 or 4.13.

Findy, in response to the question whether it is wonh using a

wavdengrh-rouang packet-switched nenvork, the answer is "no" based

fuiiy transparent

on the foiiouing

reasons. (1) The cost of a partialiy uansparent wavelength-rouang packet-swrched nework,

using Scheme 1 with a strict t h e delag constrainc, is significantiy lower h a n the cost OF a

fùiiy uansparent necwork, using Scheme 5, as shown in Fig. 4.9. This is happening because

the involvement of the elecuonic-switchhg maaices bg using undear lightpaths, as is the

case with the former, can improve the capacity utilization, as shown in Fig. 4.16, and,

consequendy, ~cduce the number of Wnial links, as shown in Fig. 4.10. (2) Bo& nerworks

c m achieve aimost the same average delay by ignoring the queuing delays, as shown in Fig.

4.15. (3) ALthough a fully uansparent EON network is achievable with lWlmU =32, as

shown in Fig. 4.12, th is might not be the case with othcr larger topologies or those wirh less

connecriviry. However, with a partiab transparent nenvork, die wavelength requiremencs are

significandy fewer, as shown in Fig. 4.12. This is due to the fact that fewer nurnber of virtual

links requires fewer wavelength r equiremena .

Fig. 4.9: Optixnum necwork cost vs. traffic pattern variarions for RWA Schemes 1-5 with and without imposing a thne-consuaint F is the uattc dmsity and P is the aaf6c intensiy.

Fig. 4.10: Optknum aggregate interfachg-pazt cost m. affic pattern variarions for RWX Schemes 1- 5 Mlh and wirhout imposing a Orne-constraint F is the mffic density and P is the traffc intensity.

Fig. 4.11: Optimum aggregate opticd-mitchiag mamx cost vs. a f 6 c panem vaxiaaons foc RLVA Schmies 1-5 andi and widiout imposing a tirne-cons train^ F is die traffic densi? and P is

. the craffic htensiy.

Fig. 4.12: h&n.imum number of wavelengchs required to adiieve 100°/o Nefwork Thmughp~t vs. affic pattern variations for RWA Schemes 1-3 wich and without imposing a tirne-consauit F is the aaffic densicg and P is the traffic inraisic);.

(4 (4 Fig. 4 3 : Numbu of wavdaigths required to achieve the optimum network cost vs. affic panun

variaaons for RWA Schemes 1-5 with and without imposing a time-consaint F is the rnffic densi y and P is the affic intensity.

% Traffic Considered in VTD % Traff ic Considered in VTD .

O B B 8 e E ) g

% Traff ic Considered in VTO

Average Cell DelavJmse$ o h ) * Q > -

Fig. 4.16: Average vircual link utiiizaaon at the optimum newok cost m. traffic panun variations for RWA Schanes 1-5 Mth and without irnposing a tirne-constra.int. F is the aff ic densiry and P is the craffic intensity.

Fig. 4.17: Avenge elecmnic hops obtaiued at the optimum neovorli variations for RWA Schemes 1-5 witb and without imposing a a f k daisity and P is the traffic intensiy.

(4 cost vs. traffic the-consaaint

pattern F is die

Chapter 5

Conclusions and Future Research

5.1 Conclusions

In this thesis, a novel heurisac aigondun, RWANCO, has been proposed as a cool CO optimdy

design the WDM-segment to be added to the esisang static opucal wide-area packet-swirched

nenvork in order ro increase ia capacicy to handle the growing aaffic demands and delay

requiremenrs of aii nenvork node pain.

It has been shown chat the cost-optimizauon process in the RWANCO algorithm takes

place at NO levels. (1) The local-level: whch occurs when the RIVA problem is solved for a

ce& I w I , where we c m have many solutions. Therefore, the opamizaaon goal here is CO

h d the best soluaon chat leads to the least cost vimal topology a t a certain IWI. (2) The

global-level: which happas when the optimum WNal topology is chosen among the locaily

opemized virmd topologies obtained in the range [2, I w I - ] , provided that these topologies

can achieve 1 OOO/o 3'etwork Thmngbpwt.

It has also been shown that the local-level ophizauon cm be irnproved by the following:

hst, s o h g the RLVA sub-problems sequentidy rarher chan simulraneously; second, carefdly

considering the n e m k traffic demands whde building the WNd topology; third, choosing

the right prioriry poliq for building the WNal topology.

In compzuing the suggested node architectures, the foilowing has been demonsaated.

Fust, using the singledber architecture achieves lower nenvork cost han using the mulaple-

fiber architeetue. Second, the multiple-fiber architecture needs fewer wavdength requirements

co achieve 100Y0 Ne~ork Thmug@ivt. Third, as an answer to the debate on the ualiry of opricai

wavelength conversion in staac wavelength-routing network, it nuns out that employing

wavelength converters in both node architectures c m reduce the wavelengrh requirements to

achieve 100°/o Netul~tk Thmugbpt. However, unfortunately, if there is no resmction imposed

on 1 WI (i.e., 1 WI,, S IWImU), then using wavelength converters has no impact on reducing the

optimum nemork cost Fourch, when 100% Network Tbroughpwt is unachievable midi the

single-fiber architecture without waveiength converters, it rnight be cheaper to add wavelength

converters rather than employ the multiple-fiber architecture, provided that using wavelength

conveners c m achieve 100°/o Xtwork Tbmgbput. Fifth, die best combinarion to reduce the

wavelength requirements is to use the mu1 ti pie- fiber architecture wi th wavelengrh converters.

The evaiuauon snidy of the proposed RWA schemes suggests that under a no-ame-

consmaint condition', Schemes 1 and 2 should be used when die aff ic pattern is much

denser. Further, under a no-time-constra.int condition, Scheme 3 should be used when the

uaffic is concenaated among a few s-A pairs and the naffic intensity CO be beyond certain

value. However, based on the sirnularion conducted on the EON topology and a similar study

wr conducted on the NSFNET topology in Fjah.I01999], it has been shown that the physicd

connectiviiy of the nework has a significant impact on defining which values of die tnffic

incensiy and the uaffic density make Scheme 3 the winner. Accordingly, we evpect char wich a

high nenvork physical connectivity, Scheme 3 wdi never be the winner. Findy, under a smct-

cime-consuaint condition, Scheme 1 shouid be used regardess of rhe traffic pattern densicy

and the' uaffic intensity.

1 lht: no-timr-consnint condition is rccommcndcd whcn thc physiui topology gcognphiuiiy covcrs a s m d ;rra (cg. EON copology covas the Eusopan con~cnt). in conmur. thc smct-turicconsmint condiaon is cccommcndcd whrn thc physid topoIogy g c o p p h i d y covcrs a 1- m (cg. NSWkT topology covcrs thc Unitcd Sotc o f Amcria) sincc undcar lighpth connections without a timc consaaint cm spm a mulrinidc of phpicd iinks.

ZlIoreovu, ic has been shown that a My transparent (one-hop) packet-switched EON

n e ~ o r k , in which 5-d pairs use dear lightpaths, is possible to b d d with the cunent

achievable technological limit of the number of wavelengrhs p u fiber, even by using the

single-fiber architecnue and without employing wavelength converras. However, we have also

shown that a partidy transparent (muki-hop) packet-switched nework, in which man)- s-d

pairs use undear lightpachs, achieve much lowe. necwork cost and fewer wavelength

requirements and at the same t h e achieve the same nerwork delay givm the fact that queuing

delays are negligible in the WAN environment.

Given the facc that these calculauons c m be done off-line, the foliowing design scheme is

recomrnended for any uaffic pattern, physical topology, and prices of NDM components:

S cart with the single- fiber architecture widiout wavelength converters

Solve the integrated RWA/NCO problem using Schemes 1-3

If the opamum necwork cost is less than infiniry ( i . . 100% Scn~ork Tbroughput is

achievable) with any of the RWA schemes (if more dian one scheme yields a nenvork cosc

less than infuuty, then choose the leasr cost one), then go to step 9

If the optimum nenvork cost is infini., aliow the use of wavelength converters in the node

architecture and repeat steps 2-3 and then go to step 5

Use the multiple-fiber architecture without waveiength convexters and reDeat stem 2-3 and

then go to step 6

Choose the least cosrly architecture: either the single-fiber architecture

the multiple-fiber architecture without convarers

A A

with converters

If die optimum nenvork cost is infinity ushg both architectures, use the multiple-fiber

architecture wich waveiength convenus and repeat seps 2-3 and dien go ro step 8

8. If the optimum nenvork cost is sd infïnity, this means that not sufficient to

design the network; i.e. 1 WI,, > 1 WI,, . Then, adduig exua fibers wili be the only choice

9. End.

5.2 Future Research

-4s an extension to chis work, we finalize diis thesis with a lirt of open problems:

More effort c m be chected at improving the local-level optimization. This can be done by

developing new prions. policies and vimal topolog). design approaches and ~ l n g to find

the exact optimum solution of the RWA problem at a certain IWI, at least for smaii-sized

nenvorh, to check the effecuveness of our heuristic approaches.

The nenvork cost model can be enhanced by considenng the Coiiowing cost models: (1)

Opücal amplifier cost model, which depends on the exact placement of diese amplifiers

based on the power-budgethg calculations of the wavelength signals. ?bis in nim depends

on die lengths ofdear lightpadis and die used optical technology. (2) Optical switch dnver

cost model, which depends on the used optical switch size, switch archirecnue, and switch

technolog)-. (3) Elecnonic-switching matris cost model, which depends on the used packet

suitch size, the used switch architecture, the amount of buffering required w i h n the

nvitching fabric, and the switch technology. Tius model will be considered if packet

switches do not udst in the fiber-layout, in contrast to our assumpaon in this regard, or if

the! do eus6 but cheir sizes need CO be increased to handle more nansminers/receivers.

(4) Fiber link cost model, which is direcdy proportionai to the physical lengrh of the link.

This model will be considered if die fiber-layout origkially does not exist (this innoduces

the so-cded physicai ropology design problem), or the fiber-layout exïsts and we need to

add exrra fiber links to increase the necwork comectivity and/or die nenvork reliability.

Good referaices for such a work can be found in FTGC19941 [SPkN1987] ~aMo1995].

The soluaon to the integrated RWA/NCO problem c m be eurended to consider the

bihircated-aaffic case (eg. IP traffic). This requires a change in the undear lightpath

connection module (ULC module) to use several paths to establish a connection.

Furthemore, if we evtend the problem by dowing the use of more than one clear

iightpath benveen a node pair, changes need CO be made in the dear lightpath modules

(CCLC and CLC modules) as weii. Good references CO solve the bifurcaccd packet-routing

problem can be found in [CaGeI 9741 [ScCh1976].

The nenvork design depends cruuaiiy on the forecast of the ualfic pattern and if dus

forecast is inaccurate (note: predicting the hmre traffic pattern becomes a r i s k y business

nowadays due CO the dramatic changes in die necworking business) or the average value

does n a dearly reflect the traffic behavior (as is die case with the bus. traffic), it c m be

especred that inemciencies in performance will occur. For instance, if packet ssltches are

equipped with veq large-sized buffers, then excessive queuing delays will be especred. If

rhev are equipped with smd-sized buffers, then packet losses will be espenenced. In order

to reduce the neonrork sensiâviy to the dynarnic craffic variations, die resulrant virtua.1

topology needs to undergo a sensitiviq investigation under a real uaffic model. ï h e

controiling variable in th is invesagaaon will be the maximum Wmal link utdiration, p,, .

Decreasing P, will keep some extra remaining capaciv in die vimal link for uaffic

variaaons but, on the other hand, results in more nenvork cost. Thus, reducing the

network sensiriviqr will be a trade-off problem. It wiii be a good opportuniv as weil to test

m q dynarnic packet r o u ~ g schemes besides the staac packet-routing solution as an

altekative way to cope with the traffic variation. In otha words, by doing that, we are

simply estendmg the solution of the sratic-static in teped RWAINCO problem (in the

contcvt of the RWA problem dassification we made in Section 2.2.2.3) to the soluaon of

static-dynamic RWA/NCO problem by considering the resultant wnial topology of the

former as the solution of the &st sub-problem of die latter. Then, the solution of the

packet routing sub-problem over the resultant W d topology is to find a "good" dynunic

packet routing scheme. h good srart for this work c m be found in FrCh19711

[ZMc1994] [ZMc1995].

The same approach used to soive the staac-srauc RWA/NCO problem can be estended to

solve the adapave RWA/NCO problem, where the problem is soived for many uaffic

patterns. One idea for solving this problem is to obtain all locaily optirnized \lrtual

topologies in the range [I WI,,, , 1 W I , ~ ~ , ] for eveT traffic panem. Then, End ali possible

combinations of vimiai topologies, where eveq vinual topology in the combinauon

corresponds to a different uaffic pattern. After that, for every combination, combine the

complesities of its vimial topologies and h d the cost of the resultant complesiry.

Thereby, the combination whose resultant complsity cost is the minimum will be the

optimum combination that compromises ail uaffic patterns. Cseful references for such

work cm be found in wc1991] W c 1 9 9 4 1 [BaMu1997] wKH1997].

To improve the WDM nenntork reliabilicy, the failure of a single iink or node m u t not

b ~ g down the entire nemork Therefore, designing the WNal ropology must check for

nodes whose fdure would break the network into two or more pieces. The opamization

process m u s then redesign the Wnial links to improve rehabiliy. One of the chLigs that

c m be done to inuease the reliabiliry is to lùnit the number of allowable hops between any

two nodes. Anotha possibilicy is CO provide rnany alternative paths for aii node pairs; the

more paths we provide, rhe more reliable the network will be with the consequence of

inaeased neouork cost. Moreover, we can add extra fiber links CO achieve dus purpose.

Good refuuices to s r a r t with can be found in [CWDe1997] [GSMal997] FSi19981.

- 113 -

Appendix A

Results of Node Architectures Cornparison In rhis appendiu, we present the derailecl results obtained in section 4.3. In the tables below,

the highlighted rows represenr the optimum solution of the integrated R\X'A/NCO problem.

Table A.1: Results of unplopng the single-fiber architecrure - withour wavelengh conveners and usine Sdieme 1 in die RWiWCO algorithm o v e the range [2,I ~ l ~ , ] .

Tabk k2: R e d t s of employing the single-fiber architecnuc wich waveiength convenus and using

Scheme 1 in the RWANCO algoiitûm over the range [ 2 , 1 ~ 1 , ] . %TWk n*n*i

IWl ,- ~ ( r " E(I" &(r) E(p) E ( h ) E ( w ) Y Ca\7DOU,.e C ~ ~ T T + * CUJT. CU.T,+ CO-,, [KI [mwc] (maoc] [mec] [ U s q [usq [USSI [ u s q [USS]

2 21.6584 23.7345 0.0036 5.4526 5.4m 0.8032 1.426r 0.2885 7 13920 490990 163800 21000a 878710

Table A.3: Resuln of anploying the multiple-fiber ardiitecture without - wavelaigth convurus and

Table A.): Resulrs of employing the multiple-fiber architecture - with wavdength converters and ushg

74.9604 88.2726 98.6458

T a o 100 100 loa ldd

Table 115: Results of unploying the single-fiber architecture without wavelength converten md using - - Schune 3 in the R\V.WCO algorithm over the range 12.1 ~ l , , ~ , 1.

T Wihr* IWI --w &(tu) ~ ( r ~ ) E( t ) E(p) E ( I ~ ) E ( w ) \Y C0~wnwi.rsCi)'7r-r Clj+sT, C(J57., COST,,,,

h m [W [mmq [ I ~WJ r-1 LUSI rusr1 tuss] [usa [USSI 2 22.3483 22.5185 O.ûû41 5.9% 5.9605 0.8163 1.5223 09821 O 9280 490990 140700 O 640970 3 33.916 35.7926 0.0017 7.417 7.4187 0.8545 1.5174 0.3333 O 88160 743120 331800 O 1163080 4 44.9564 47.5953 0.0047 8.2939 8.2986 0.8993 1.587 0.3782 O WS6OO 981980 615300 O i7û2800 5 56.5498 59.3591 0.0173 9.8958 9.9131 0.9331 T.&14 0.4333 O 35a320 1220840 995400 O 2566560 6 61.0276 69.0946 0.0073 10.2939 10.3012 0.9435 1.6503 0.4551 0 454720 14lQegO 1314600 O 3189210 7 75.0132 81.6176 0,0007 10.5345 10.5432 0.9573 1.624 0 .463 O 570720 t618940 17094M O 3899060 8 83.9667 92.7922 0.0069 10.4069 10.4938 0.9375 1.5824 0.4728 O WUCI 1031260 2205CQO 3 4713700

Table A.6: Results of employing the single-fiber archirecrure with wavclengdi converters and using Scheme 2 in the RW.WCO algorithm over the nnge [2,1 WI,.~,].

%Trillk Nlhir* - E t E ( r r ) E ( i ) E(p ) E(h) E( w) Y C('.QiipiIIBlT ClLVr., <W. COS., CO^-^ m WD Ixl [-] [ M l imwtl lusr) fusq [usq [US] [usq

2 21.9659 23.7945 0.0036 5.4526 5.4563 0 . m 1.4264 0.2865 7 $3920 490990 163600 210000 878710

Table k7: Rcjults of employing the multiple-fiber ardutecture without wavelmgth convaers and using Schane 2 in the RWANCO aigorithm over die range [î, 1 w I , ] .

Ilihir. IK'I - - &(tu) ~ ( r ~ ) E(t) E(p) E(h) E ( w ) Y C'7%nz1- CfA-r., C L CILV., COS^^,.,,

Table k8: Resdn of ernploying the multiple-6bu architecture - - with wavelength converters and using

Scheme.2 in the RWANCO algorithm over the range [2,I w I , ~ ] .

Table kg: Results of employing the single-fiber uchirecrure without wavelength convenus and using - . Scheme .3 in the RWANCO aigorithm over die range 12,l wIiur].

*TW* - 1 - - E t ) E(I" E ( t ) E(p) E(h) &( W ) C".PT~. i .~~ CfLq.n '31x7- CfJ.i7., COSTrn*III

hm 13;1 [muc] [rmrc] [mu] [USQ [USSI [usq [US$] [USSI 2 24.6746 27.582 0.0032 10.7m 10.7236 0.9023 14109 0.6282 O 167040 504260 804300 O 1475600 3 36.5733 sO.1&9 O.Wt 11.4S2 11.4512 0.8902 14332 0.6538 O 315520 756390 1236900 O 2308810 4 46 2645 49.0887 0.0008 11.1852 11.186 O 8634 1 4173 0.5801 O 382800 942170 1417500 O 2742470 5 61.05% 65.2844 0.0082 71.1937 11 2018 0.952 1.5392 0.5718 O 496480 1234110 1@0100 O 3370690 6 68.9M6 75.9733 0,0088 11.5418 11 5506 O 9487 1 5732 O.%& O 603200 1472970 2041200 O JI17370 7 80.W6 85.9637 0.0059 12.3338 12.3397 0 9505 1.5939 0.5751 O 721520 1685290 2536800 9 4943610 8 80.4421 96.9666 0.0059 11.7053 11 7112 0.923 1.5233 0.5529 O 784160 1871070 2618700 O 5273930

9 - - 2 . l ~ 8 ~ _ j ~ o p 5 1 0 ~ ~ ~ F z ~ 0 . ~ ~ - ~ ~ ~ - + ~ O ~ ~ 1 4 2 + ~ - ~ 2 5 ~ O T 2 o - o . - ~~~ 0 54791 30 J.. -- -&- e 2" -10' -1 ~~ ._ O 51909S0

1 1 7 0.7251 1.3579 04406 O 867600 218955û 23562ûû O 5413430 :2 99.7196 100 0.0002 9.3ôôd 9.38ôô 0.6947 13483 0.4103 O 874640 2269170 2194500 O 5338310 13 100 100 0.0002 9.4338 9.434 0.684 1.343 0.3846 O 893200 2295710 2037000 O 5225910

Table A.10: Resulrs of employing the single-fiber ~dutecnire with wavelmgth converters and using Schane 3 in die RWrWCO algorithm ovu die range [2,I wI,].

Table bll: Resdts of employing die mulaple-fiber architecture without wavelength converten and using Scheme 3 in the RWANCO algorithm o v u die range [2,1 WI,, 1.

Table 1112: Results of anploying the multiple-fiber architecture - with wavdength convenus and using

Table 1113: Results of employing the single-fiber architecture Mthout wavelength convaers and using Schexne.4 in the RW-WC0 algorithm over die range [ 2 , 1 ~ 1 , ] .

Table k14: Results of emplo$.ng the single-fiber architecture uirh waveiength converters and using - -

Tabk AU: Resulü of employing the multiple-fibu architecture - widiout - wavelength convuters and

Table A16 Resdts of anploying die multiple-fibu archtecnire with ~ v e l e n g t h converters and using - - Scheme J in the RW-WC0 algorithm over the m g e [2,1 WIJur].

klnnk - iW1 ~hroullyil &(lu) E( I " ) E ( t ) E (p ) & ( h ) E ( w ) J . . C U S I , C O S - ,

1% [mrrcl [mu] [mwc] [US] [Usq tusq [US] [USSI 1

3 39.9892 62.1738 0.0036 11.9512 11.999 0.9379 1.558 0.97ô6 14 528960 1207570 2801400 420000 4957930 4 52.6947 81.487 0.W97 l l . W 9 11.495 0.9273 1.5756 0.9487 19 ôûUûû 1618WJ 3822000 570000 669534 5 63.1417 98.Mô9 0,001 10.8796 10.B806 0.8194 1.4255 0.959 30 865360 2003TIO 5514600

7 02.1896 lûû O.QQa1 8.3564 8.3565 0.4606 1.1787 0.8993 19 1139120 2-20 7660WO 8 87.8056 100 0.0001 8.1561 8.1542 O.W5 1.1219 0.88s 26 1287600 3211340 8158500 9 91.5095 100 0.0001 7.7149 7,7149 0.3621 1.0049 0.8519 29 1385û40 3503200 8005200 10 94.7031 1Cû 0,0001 7.4229 7.4229 0.3313 7.053 0,0051 17 1458960 3715600 8425200 t t 96.5006 1W 0.0001 7.3511 7.3511 0.3i12 1.035 0.764 14 1521920 3888110 8339100 12 97.7244 100 0.0001 7.2293 7.2294 0.2964 1.0228 0.7254 9 1575280 4034080 8481900 13 98.7181 100 0.0001 71144 7.1145 0.2824 1.0128 0.7012 11 1649520 4193320 85P7WO 14 99.3191 100 0.0001 7.0321 7.0322 0.27t3 1.0068 0 . 6 W 9 1723760 4339290 8509200 15 99.7665 100 0.0001 6.9617 6.9897 01644 1.0023 0.- 5 1737680 4432180 8528100 16 99.9082 100 0.0001 6.993 6.9523 0.2609 1 . W 0.605 2 17516Oû U S 2 6 0 8345400 17 100 100 0.OOOt 6.93ô6 6.9366 0.2576 1 0.962 2 17M48a 4530340 8227800 78 100 100 0.0001 6.9095 6.9096 0.2576 r 0.5399 1 t758580 4538340 8127000 19 100 100 0.0a01 6.9055 6.9056 01576 1 0.5108 O 1758240 453634 8003tCû 20 tû0 . lm 0.0001 6.8964 6.8965 0.2576 1 0.484 O t7516W 4538340 7889700

Appendix B

Results of RWA Schemes Cornpanson

In diis appendix, we present the detaded results obtained in section 4.4 using the single-fiber

architecture without wavdength converters. Table B.1 shows the average results with the

95% confidence interval when no time consuaint is imposed, and Table B.2 shows die

results when a strict time consuaint is imposed.

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