Traffic Grooming, Routing and Wavelength Assignment in

Metropolitan Transport Networks

Ana Catarina Pacheco Pais Martins

Thesis to obtain the Master of Science Degree in

Electrical and Computer Engineering

Supervisors: Prof. Dr. João José de Oliveira Pires

Dr. João Manuel Ferreira Pedro

Examination Committee

Chairperson: Prof. Dr. Fernando Duarte Nunes

Supervisor: Prof. Dr. João José de Oliveira Pires

Members of the Committee: Prof. Dr. Amaro Fernandes de Sousa

October 2014

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Acknowledgments

First and foremost, I would like to thank Professor João Pires for his guidance, patience and

support throughout all the stages of this Thesis. To João Pedro, of Nokia Siemens Networks, for his

availability, his insight, for the knowledge provided and the precious inputs and suggestions that

allowed me to always follow a well-planned line of work. To everyone at Nokia Siemens Network, for

the kindness with which they welcomed me in their workspace, always providing a great environment

to work in.

To all my friends at IST with whom I had the pleasure to share 5 incredible years making the

journey more memorable and amazing.

To everyone at work who supported me to end this journey and to Pedro who spent many

after work hours with me, each wrapped up in our respective thesis, struggling to balance them with

the projects at hand. To João Gomes for the friendly pressure to end this work so I could finally

dedicate myself fully to the wonders of the Microsoft and Oracle technologies.

Finally, I would like to thank my parents for always believing in me and driving me to aim

higher. For those late night talks and the valuable life lessons they taught me and for allowing me to

broaden my horizons and my views on the world. To my brother Ricardo for always bringing fun into

my life, for the way he continuously amazes me and shows me how special and unique one can be

(also for lending me his computer putting breaks on his Breaking Bad marathons in the process).

ii

Abstract

The Optical Transport Network’s delivery on the promise to supply high bandwidth availability,

OAM&P support, accommodation of multiple client signals and efficient capacity utilization when in

combination with WDM’s technology has stirred service providers’ attention. As is the case whenever

new network technology is deployed, capital expenditures are required. The scope of this work is the

optimized planning of such networks so as to minimize the acquisition costs and drive down the

operational costs for maximum return.

The current document focuses on the study of the characteristics and associated equipment

of WDM and OTN technologies. An overview of selected existing planning methodologies targeting

such networks is conducted and results are extracted from simulations implementing the models

described, some with further original adaptations.

Ilp and heuristic RWA approaches are presented and simulations are pursued in scenarios

comprising networks with distinct topologies under varying traffic conditions. The benefits of combining

wavelength and sub-wavelength switching are analyzed in networks with services mix by application

of formulations to the GRWA problem.

Based on the studies conducted, the work culminates with the development of a heuristic and

ILP methodologies making use of traffic grooming to attain the lowest costs in serving traffic demands

with distinct bit rates. Both are compared regarding the quality of the solutions and the computational

times required. Distinct cost models and network configurations are used. Conclusions are drawn in

favor of using intermediate traffic grooming and on the benefits of mixed line rate networks over single

rate ones.

Keywords

OTN/WDM, grooming, ILP, heuristic, cost

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Resumo

A promessa da Rede de Transporte Óptica em fornecer elevada largura de banda, suporte a

OAM&P, acomodação de múltiplos clientes e eficiente utilização da capacidade quando combinada

com a tecnologia WDM captou o interesse dos prestadores de serviço. Como é norma sempre que se

instala nova tecnologia de rede são necessários investimentos. O âmbito deste trabalho é o

planeamento optimizado destas redes de forma a minimizar os custos de aquisição e baixar os custos

operacionais para máximo retorno.

O presente documento foca-se no estudo das características e equipamento das tecnologias

OTN e WDM. São conduzidas análises de metodologias existentes de planeamento destas redes e

extraídos resultados de simulações implementando os modelos descritos, alguns com adaptações

originais.

Abordagens heurísticas e em ILP ao problema de RWA são desenvolvidas e simulações em

cenários com diferentes topologias de rede em condições de tráfego variáveis apresentadas. Os

benefícios de combinar comutação ao nível do comprimento de onda com outra mais granular são

analisados em redes com diversidade de serviços aplicando formulações ao problema de GRWA.

Baseado nos estudos conduzidos, o trabalho culmina com o desenvolvimento de uma

heurística e uma metodologia ILP usando agregação de tráfego para servir pedidos com diferentes

débitos ao custo mais baixo. São apresentadas comparações tendo em conta a qualidade dos

resultados e tempo computacional dispendido. Diferentes modelos de custo e configurações de nós

da rede são usados. As conclusões pesam a favor da utilização de agregação de tráfego intermédia e

da utilização de canais ópticos com diferentes débitos binários.

Palavras chave

OTN/WDM, agregação, ILP, heurística, custo

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Table of Contents

1 Introduction ........................................................................................................................................... 1

1.1 Introduction to Transport Networks ................................................................................................ 2

1.2 Motivation ....................................................................................................................................... 4

1.3 Dissertation Layout ......................................................................................................................... 5

1.4 Original Contributions ..................................................................................................................... 5

2 OTN: Background and State of the Art ................................................................................................. 7

2.1 Rationale for OTN .......................................................................................................................... 8

2.2 OTN’s layered model .................................................................................................................... 10

2.2.1 OTN’s Optical Layer: WDM-network definitions ................................................................... 11

2.2.2 OTN’s Electrical Layer .......................................................................................................... 13

2.2.3 OTN over DWDM: ODU/DWDM switch ................................................................................ 14

2.3 Network design and planning ....................................................................................................... 18

2.3.1 DWDM layer planning methodologies: RWA in transparent networks ................................. 19

2.3.2 OTN planning methodologies: traffic grooming .................................................................... 21

2.4 Conclusions .................................................................................................................................. 24

3 Routing and Wavelength Assignment in transparent DWDM networks ............................................. 25

3.1 Introduction ................................................................................................................................... 26

3.2 General Problem Statement ......................................................................................................... 26

3.2.1 RWA node-link formulation applying asymmetrical routing .................................................. 27

3.2.2 RWA node-link formulation applying symmetrical routing .................................................... 28

3.2.3 RWA link-path formulation applying asymmetrical routing ................................................... 29

3.2.4 RWA link-path formulation applying symmetrical routing ..................................................... 30

3.3 Results of simulations applying Ilp methodologies....................................................................... 30

3.3.1 Node-Link and Link-Path Comparison ................................................................................. 30

3.3.2 Running times’ sensitivity to network’s dimensions ............................................................. 32

3.3.3 Symmetric and asymmetrical routing comparison ............................................................... 33

3.3.4 Results for networks with distinct mean nodal degrees ....................................................... 35

3.4 Heuristic Methodology .................................................................................................................. 36

3.4.1 Traffic Selection Schemes .................................................................................................... 36

3.4.2 Routing and wavelength Assignment Algorithm ................................................................... 38

3.4.3 Integrated and Iterative algorithm ......................................................................................... 38

3.5 Ilp and Heuristic methodologies comparison ............................................................................... 39

3.6 Applying the heuristic to networks of greater reach ..................................................................... 43

3.7 Conclusions .................................................................................................................................. 44

4 OTN/WDM network planning: GRWA methodologies ........................................................................ 45

4.1 Introduction ................................................................................................................................... 46

4.2 Mathematical Models in resource scarcity scenarios ................................................................... 47

4.2.1 Ilp model for translucent networks ........................................................................................ 49

4.2.2 Ilp model for transparent networks ....................................................................................... 51

v

4.2.3 Ilp model for opaque networks ............................................................................................. 51

4.3 Applying the Ilp methodologies .................................................................................................... 52

4.3.1 Sensitivity to resources’ variation in translucent scenarios .................................................. 52

4.3.2 Translucent scenarios with selected hub nodes .................................................................. 55

4.3.3 Translucent, transparent and opaque networks comparison ............................................... 56

4.4 Heuristic Approach ....................................................................................................................... 59

4.4.1 MST and MRU heuristics...................................................................................................... 60

4.4.2 Graph Heuristic ..................................................................................................................... 61

4.5 Ilp and heuristic comparison ......................................................................................................... 62

4.6 Applying the heuristics to networks of larger dimensions ............................................................ 64

4.7 Conclusions .................................................................................................................................. 66

5 Cost Minimization Methodologies ....................................................................................................... 67

5.1 Introduction ................................................................................................................................... 68

5.2 Ilp Model for symmetrical traffic .................................................................................................... 69

5.2.1 Translucent Networks ........................................................................................................... 70

5.2.2 Opaque Networks ................................................................................................................. 71

5.2.3 Transparent Networks .......................................................................................................... 71

5.1 Applying symmetrical traffic Ilp models ........................................................................................ 72

5.1.1 Comparing Translucent, Opaque and Transparent Networks.............................................. 72

5.1.2 Comparing Single and Mixed-Line Rate Transparent Networks .......................................... 74

5.1 Heuristic for symmetrical traffic .................................................................................................... 75

5.2 Comparing the Heuristic to the Ilp Methodologies ....................................................................... 81

5.3 Applying the heuristic to networks of larger dimensions .............................................................. 83

5.4 Ilp Models for asymmetrical traffic ................................................................................................ 85

5.4.1 Model for bidirectional line cards using symmetrical optical connections ............................ 87

5.4.2 Model for bidirectional line cards using asymmetrical optical connections .......................... 87

5.4.3 Model for unidirectional line cards using asymmetrical optical connections ........................ 87

5.4.4 Formulation using unidirectional and bidirectional line cards using asymmetrical optical

connections.................................................................................................................................... 88

5.4.5 Asymmetrical and symmetrical bidirectional line cards using asymmetrical optical

connections.................................................................................................................................... 88

5.5 Applying asymmetrical traffic Ilp models ...................................................................................... 89

5.6 Conclusions .................................................................................................................................. 91

6 Conclusions and Future Work ............................................................................................................ 92

6.1 Conclusions .................................................................................................................................. 92

6.2 Future Work .................................................................................................................................. 94

Appendix A ............................................................................................................................................ 98

A 1. Via Network ............................................................................................................................ 98

A 2. Abilene Core Network ............................................................................................................ 98

A 3. Czech Education and Scientific Network (CESNET) ............................................................. 99

A 4. National Foundation Science Network (NFSNET) ................................................................. 99

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A 5. Very-High Performance Backbone Network Service (Vbns) ............................................... 100

A 6. Italy Network (ITALY) ........................................................................................................... 100

A 7. Slovenia Academic and Research Network (Arnes) ............................................................ 101

A 8. Optosunet (Sweden) ............................................................................................................ 101

A 9. Arpanet ................................................................................................................................. 102

A 10. Cost37 .................................................................................................................................. 102

A 11. Germany Network (Gbn) ...................................................................................................... 103

A 12. Italian Backbone Network (IBN) ........................................................................................... 103

A 13. Metrona Network .................................................................................................................. 104

A 14. Bulgarian Research and Education Network (BREN) .......................................................... 104

A 15. European Optical Network (EON) ........................................................................................ 105

Appendix B .......................................................................................................................................... 106

B 1. K-shortest paths algorithm ................................................................................................... 106

B.2 Algorithm for generating traffic matrixes .................................................................................... 107 Appendix C .......................................................................................................................................... 109

C 1. Comparing the network’s throughput applying translucent, transparent and opaque models 109

C 2. Applying the heuristics to the Bren Network considered in 4.3.3 ........................................ 110

Appendix D .......................................................................................................................................... 113

D 1. Description and example...................................................................................................... 113

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List of Figures

Figure 2.1: Optical Transport Hierarchy ................................................................................................ 10

Figure 2.2: Optical Layers demarcation points with OCh between OTMs ............................................ 12

Figure 2.3: Optical Layers demarcation points with OCh between ROADMs ....................................... 12

Figure 2.4: OTN's digital frame .............................................................................................................. 13

Figure 2.5: Selected OTN multiplexing options ..................................................................................... 14

Figure 2.6: Network's topology and traffic demands. Example of intermediate grooming ................... 15

Figure 2.7: Example of end-to-end grooming for the transparent scenario .......................................... 16

Figure 2.8: Architecture of an OTN/WDM Switch .................................................................................. 16

Figure 2.9: Opaque node configuration ................................................................................................. 18

Figure 2.10: Transparent node configuration ........................................................................................ 18

Figure 3.1: Physical topology and traffic matrix used for comparative example ................................... 34

Figure 3.2: Symmetrical routing (left) and asymmetrical routing (right) results ..................................... 34

Figure 3.3: Effect of the mean nodal degree on the required number of wavelengths ......................... 35

Figure 3.4: Comparison for networks with distinct mean nodal degrees .............................................. 35

Figure 3.5: Step by step description of the heuristic algorithm ............................................................. 39

Figure 4.1: Example of the transport of an end-to-end connection request .......................................... 49

Figure 4.2: Throughput attained against wavelength and transponder availability variations .............. 53

Figure 4.3: Selected nodes with integrated OTN switches ................................................................... 55

Figure 4.4: Variation of the network's throughput in opaque and translucent schemes ....................... 59

Figure 4.5: Comparing the heuristics' performance for the Germany Network ..................................... 65

Figure 4.6: Comparing the heuristics' performance for the Arpanet ..................................................... 65

Figure 5.1: Six nodes network's physical topology ................................................................................ 72

Figure 5.2: Cost obtained for transparent, translucent and opaque models ......................................... 73

Figure 5.3: Seven nodes network's physical topology .......................................................................... 73

Figure 5.4: Cost obtained for transparent, translucent and opaque models ......................................... 73

Figure 5.5: Cost obtained for single and mixed line rate networks ....................................................... 74

Figure 5.6: Cost obtained for single and mixed line rate networks ....................................................... 74

Figure 5.7: Algorithm to obtain the graph inputs ................................................................................... 77

Figure 5.8: Algorithm to select the candidate lightpaths for elimination ................................................ 79

Figure 5.9: Description of the overall heuristic ...................................................................................... 81

Figure 5.10: Distance on the cost of the heuristic to the Ilp (mixed translucent) .................................. 81

Figure 5.11: Distance on the cost of the heuristic to the Ilp (mixed opaque) ....................................... 81

Figure 5.12: Distance on the cost of the heuristic to the Ilp (single rate) .............................................. 81

Figure 5.13: Distance on the times of the heuristic to the Ilp (mixed translucent) ................................ 82

Figure 5.14: Distance on the cost of the heuristic to the Ilp (mixed translucent) .................................. 82

Figure 5.15: Distance on the cost of the heuristic to the Ilp (mixed opaque) ........................................ 82

Figure 5.16: Distance on the cost of the heuristic to the Ilp (single rate) .............................................. 82

Figure 5.17: Distance on the times of the heuristic to the Ilp (mixed translucent) ................................ 83

Figure 5.18: Cost obtained for transparent, translucent and opaque models ....................................... 83

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Figure 5.19: Cost obtained for single and mixed line rate networks ..................................................... 84

Figure 5.20: Cost obtained for transparent, translucent and opaque models ....................................... 84

Figure 5.21: Cost obtained for single and mixed line rate networks ..................................................... 84

Figure 5.22: Comparing asymmetrical (top) and symmetrical (bottom) line cards................................ 85

Figure 5.23: Using bidirectional optical channels to satisfy demand..................................................... 86

Figure 5.24: Using asymmetrical optical channels to satisfy demand .................................................. 86

Figure 5.25: Advantages of combining unidirectional and bidirectional line cards................................ 86

Figure 5.26: Comparing symmetrical and asymmetrical cards using bidirectional connections ........... 89

Figure 5.27: Comparing the establishment of bidirectional and unidirectional optical channles using

bidirectional line cards ........................................................................................................................... 89

Figure 5.28: Comparing either bidirectional or solely unidirectional line cards using asymmetrical

lightpaths ............................................................................................................................................... 90

Figure 5.29: Comparing asymmetrical lightpath schemes: bidirectional and symmetrical line cards vs

symmetrical + asymmetrical line cards vs bidirectional + unidirectional line cards............................... 90

Figure A. 1: Via Network’s physical topology ........................................................................................ 98

Figure A. 2: Abilene Core Network’s physical topology ........................................................................ 98

Figure A. 3: Cesnet Network’s physical topology .................................................................................. 99

Figure A. 4: Nfsnet Network’s physical topology ................................................................................... 99

Figure A. 5: Vbns Network’s physical topology ................................................................................... 100

Figure A. 6: Italy Network’s physical topology ..................................................................................... 100

Figure A. 7: Arnes Network’s physical topology .................................................................................. 101

Figure A. 8: Optosunet’s physical topology ......................................................................................... 101

Figure A. 9: Arpanet’s physical topology ............................................................................................. 102

Figure A. 10: Cost37 Network’s physical topology .............................................................................. 102

Figure A. 11: Gbn Network’s physical topology................................................................................... 103

Figure A. 12: IBN's physical topology .................................................................................................. 103

Figure A. 13: Metrona Network's physical topology ............................................................................ 104

Figure A. 14: Bren's physical topology ................................................................................................ 104

Figure A. 15: EON’s physical topology ................................................................................................ 105

Figure B. 1: Description of the k-shortest paths algorithm .................................................................. 106

Figure B. 2: Network's physical topology............................................................................................. 107

Figure B. 3: Results obtained applying the k-shortest path algorithm to node-pair (1,7) .................... 107

Figure B. 4: Description of the Algorithm for generating traffic matrixes ............................................. 108

Figure D. 1: Description of the algorithm to update the auxiliary graph's state ................................... 115

Figure D. 2: Network topology (left) and initial graph state ................................................................. 116

Figure D. 3: Path used to route the first request (left) and updated graph's state .............................. 116

Figure D. 4: Path used to route the second request (left) and updated graph's state ........................ 116

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List of Tables

Table 2.1: OTU and ODU signals and data-rates ................................................................................. 14

Table 3.1: Network Parameters ............................................................................................................. 31

Table 3.2: Required number of wavelengths employing link-path and node-link formulations ............. 31

Table 3.3: Running times employing link-path and node-link formulations ........................................... 31

Table 3.4: Required number of wavelengths employing link-path and node-link formulations ............. 31

Table 3.5: Running times employing link-path and node-link formulations ........................................... 32

Table 3.6: Network Parameters ............................................................................................................. 33

Table 3.7: Computational time’s sensitivity to traffic load and network’s dimension............................. 33

Table 3.8: Via Network results applying symmetric and asymmetrical routing ..................................... 33

Table 3.9: Vbns Network results applying symmetric and asymmetrical routing .................................. 34

Table 3.10: Network Parameters ........................................................................................................... 35

Table 3.11: Traffic Selection Schemes and associated cost metrics .................................................... 37

Table 3.12: Network Parameters ........................................................................................................... 39

Table 3.13: Number of required wavelengths applying Ilp models ....................................................... 39

Table 3.14: Comparison on the required wavelengths applying Ilp and heuristic models ................... 40

Table 3.15: Comparison on the number of used optical links applying Ilp and heuristic models .......... 40

Table 3.16: Observed running times ..................................................................................................... 40

Table 3.17: Comparing the Traffic Selection Schemes for the Vbns Network ...................................... 41

Table 3.18: Comparing the Traffic Selection Schemes for the Cesnet Network ................................... 42

Table 3.19: Comparing the Traffic Selection Schemes for the Nsfnet Network .................................... 42

Table 3.20: Comparing the Traffic Selection Schemes for the Vbns Network ...................................... 42

Table 3.21: Comparing the Traffic Selection Schemes for the Arnes Network ..................................... 43

Table 3.22: Network Parameters ........................................................................................................... 43

Table 3.23: Results applying the heuristic to networks of large dimensions ......................................... 44

Table 4.1: Simulation Parameters ......................................................................................................... 53

Table 4.2: Medium Lightpath Length ..................................................................................................... 53

Table 4.3: Number of established lightpaths ........................................................................................ 54

Table 4.4: Volume of sattisfied connections in multi-hop virtual routes ................................................ 54

Table 4.5: Medium Lightpath Occupation .............................................................................................. 54

Table 4.6: Comparison of the throughput obtained for both scenarios ................................................. 56

Table 4.7: Comparing the required resources to satisfy all demand in scenarios with hub nodes and

where all nodes are translucent ............................................................................................................ 56

Table 4.8: Performance of the transparent solution in regards to throughput ....................................... 57

Table 4.9: Performance of the opaque solution in regards to throughput ............................................. 57

Table 4.10: Resources required in opaque and transparent networks against translucent ones ......... 57

Table 4.11: Comparing the lightpaths' occupation in transparent and translucent scenarios .............. 58

Table 4.12: Comparing the lightpaths' occupation in opaque and translucent scenarios ..................... 58

Table 4.13: Throughput attained by the MRU heuristic compared to the Ilp model .............................. 62

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Table 4.14: Throughput attained by the MST heuristic compared to the Ilp model .............................. 63

Table 4.15: Throughput attained by the Graph heuristic compared to the Ilp model ............................ 63

Table 4.16: Resources required to satisfy demand for the three heuristics .......................................... 63

Table 4.17: Running Times observed applying the Ilp model ............................................................... 63

Table 4.18: Comparing the running times for the Ilp and the MRU heuristic ........................................ 63

Table 4.19: Comparing the running times for the Ilp and the MST heuristic ......................................... 64

Table 4.20: Comparing the running times for the Ilp and the Graph heuristic ...................................... 64

Table 4.21: Resources required to satisfy demand for the three heuristics .......................................... 65

Table 4.22: Resources required to satisfy demand for the three heuristics .......................................... 65

Table 5.1: Conditions common to all simulations .................................................................................. 72

Table 5.2: Number of established lightpaths in translucent mixed rate configurations ......................... 73

Table 5.3 - Lightpath Selection Schemes and associate weight calculations ....................................... 79

Table 5.4 - Virtual Path Selection Schemes .......................................................................................... 80

Table A. 1: Via Network's relevant parameters ..................................................................................... 98

Table A. 2: Abilene Core Network's relevant parameters ..................................................................... 99

Table A. 3: Cesnet Network's relevant parameters ............................................................................... 99

Table A. 4: Nfsnet Network's relevant parameters ................................................................................ 99

Table A. 5: Vbns Network's relevant parameters ................................................................................ 100

Table A. 6: Italy Network's relevant parameters .................................................................................. 100

Table A. 7: Arnes Network's relevant parameters ............................................................................... 101

Table A. 8: Optosunet’s relevant parameters ...................................................................................... 102

Table A. 9: Arpanet's relevant parameters .......................................................................................... 102

Table A. 10: Cost37 Network's relevant parameters ........................................................................... 102

Table A. 11: Gbn Network's relevant parameters ............................................................................... 103

Table A. 12: IBN’s relevant parameters .............................................................................................. 103

Table A. 13: Metrona Network’s relevant parameters ........................................................................ 104

Table A. 14: Bren's relevant parameters ............................................................................................. 104

Table A. 15: EON’s relevant parameters ............................................................................................. 105

Table C. 1: Simulation Parameters ..................................................................................................... 109

Table C. 2: Throughput attained applying the translucent model........................................................ 109

Table C. 3: Performance of the transparent solution in regards to throughput ................................... 109

Table C. 4: Performance of the opaque solution in regards to throughput ......................................... 110

Table C. 5: Comparing the resources required by transparent and translucent solutions .................. 110

Table C. 6: Performance of the MRU heuristic in regards to throughput ............................................ 110

Table C. 7: Performance of the MST heuristic in regards to throughput ............................................. 110

Table C. 8: Performance of the Graph heuristic in regards to throughput .......................................... 111

Table C. 9: Resources required to sattisfy demands for the three heuristics ..................................... 111

Table C. 10: Computational time for the Ilp formulation ...................................................................... 111

Table C. 11: Comparing the running times for the Ilp and the MRU heuristic ..................................... 111

Table C. 12: Comparing the running times for the Ilp and the MST heuristic ..................................... 111

xi

Table C. 13: Comparing the running times for the Ilp and the Graph heuristic ................................... 112

Table D. 1: Weight Assignments for each Grooming Policy ............................................................... 115

xii

List of Acronyms

AMP Asynchronous Mapping Procedure

ATM Asynchronous Transfer Mode

BMP Bit-synchronous Mapping Procedure

CapEx Capital Expenditures

CBR Constant Bit Rate

CWDM Coarse Wavelength Division Multiplexing

DWDM Dense Wavelength Division Multiplexing

FC Fiber Channel

FEC Forward Error Correction

GbE Gigabit Ethernet

GFP Generic Frame Procedure

GMP Generic Mapping Procedure

GRWA Grooming, Routing and Wavelength Assignment

ILP Integer Linear Programing

IP Internet Protocol

MPLS Multiprotocol Label Switching

OADM Optical Add and Drop Multiplexer

OAM&P Operations, Administration, Management and Provisioning

OCh Optical Channel

ODU Optical Data Unit

OMS Optical Multiplexing Section

OpEx Operational Expenditures

OPU Optical Payload Unit

OTM Optical Terminal Multiplexer

OTM Optical Transport Module

OTN Optical Transport Network

OTS Optical Transmission Section

OTU Optical Transport Unit

OXC Optical Cross Connect

PDH Plesiochronous Digital Hierarchy

PoP Point of Presence

QoS Quality of Service

ROADM Reconfigurable Optical Add and Drop Multiplexer

RWA Routing and Wavelength Assignment

SAN Storage Area Network

SDH Synchronous Digital Hierarchy

SLA Service Level Agreement

SONET Synchronous Optical Networking

TCM Tandem Connection Monitoring

xiii

TDM Time Division Multiplexing

VPN Virtual Private Network

WDM Wavelength Division Multiplexing

1

1 Introduction

This introductory chapter presents a brief overview on the main concepts of the transport

infrastructure of telecommunication networks. Core technologies are enunciated as the focus is laid

upon those relevant to the present work. The motivations supporting this thesis, its structure and

layout are outlined as are the original contributions.

2

1.1 Introduction to Transport Networks

Telecommunication networks feature as a highly complex and heterogeneous agglomerate of

systems that administrate, control and perform the operations behind the exchange of information

among a multitude of users. In aim to simplify design, development, management and processes, it is

common to stratify network functionality into layers. Ideally independent, these layers provide for a

fully functional network interacting on the basis of a client-server relationship. The divide and conquer

approach concedes for a gradual evolution of the networks as each individual component may be

designed and developed autonomously and transparently. Furthermore, the approach lies as an

enabler for interoperability supporting the elaboration of layer-specific protocols and components.

On a larger scale, telecommunication networks are usually broken down into two layers: the

service and the transport one. The service layer features on top of the hierarchy, lying closer to the

users to whom it provides utilities in the form of telephone, cellular or internet services among many

others. As a client of the transport layer, it collects, aggregates and inserts information onto that lower

layer, delegating it the task of the transparent, reliable and service-agnostic transfer of such user

streams. To provide for the aforementioned functionality, transport networks handle tasks such as the

transmission, multiplexing, routing, protection and supervision of client signals as well as capacity

provisioning.

Transport networks consist of network elements and the transmission links that connect them

in accordance to a given physical topology, most commonly mesh or ring. Together, these elements

provide paths to the client service networks, interconnecting the upper layer nodes in a logical

topology that creates for the illusion that the service network elements are physically linked.

Figure 1. 1: Example of the interaction betweem the service and transport layers

Figure 1.1 depicts an example of a stratified network showcasing the interaction between the

service and transport layers. The DWDM transport network is laid out in a ring topology composed of

3

five ROADMs, devices that allow for wavelength signals to be added, dropped or switched, connected

by means of optical fibers. Connectivity among the four routers that constitute the IP service network

is assured by means of the transport infrastructure. The connection between routers S1 and S3 is

established via a path through ROADMs T1-T2-T3 as goes for the router links S0-S2 and S2-S3,

secured by the lower layer paths T0-T1-T2 and T2-T3, respectively. Together, they provide for the IP

network’s perspective of a meshed logic topology.

Besides the horizontal partition in layers, it is possible to split network functionality into three

vertical planes that are common to all the composing layers. The entities are designated as data,

control and management plane. The data plane takes charge of transferring user information

throughout the network making use of terminal equipment, network elements and transmission lines.

The control entity complements the former plane with the means to dynamically act upon and fulfill

user inputs by providing the necessary signaling to establish, supervise and terminate connections.

Lastly, and perhaps most relevantly, the management plane is responsible for conceding networks

with high levels of reliability and flexibility. Loosely speaking, the first term refers to the capability to

detect and correct faults in small time frames while the second poses as the ability to react to changes

in traffic patterns with the prompt reconfiguration of network elements. Among the tasks carried by the

management plane, one can refer fault detection and correction, network performance monitoring,

network configuration management and access control. All these functions fall within the scope of a

network related acronym, OAM&P, standing for Operations, Administration, Maintenance and

Provisioning.

In yet another perspective, telecommunication networks are commonly partitioned into one of

three levels of a hierarchic structure and ranked based on their dimensions and resulting dissimilar

technical and operational requirements. Lying at the bottom of the scale, the smaller reach access

networks stand closest to the users. Comprising a Central Office or Point of Presence PoP where the

provider equipment is located, they carry the role of providing connectivity to residential and corporate

users whose premises are linked to that central point. A level above, the metropolitan portion

interconnects groups of PoPs in a region or city and establishes the bridge between the access and

core or long-haul networks. These last ones span the largest distances, covering hundreds to

thousands of kilometers carrying bulky aggregates of traffic among a number of metropolitan

networks.

As one moves from access to metro to core networks, the following hierarchical stratums hold

the task to transport the aggregated traffic from the previous ones. Consequently, the requirements

concerning bandwidth increase proportionally to the networks’ dimensions. Given the high

expenditures associated with signal transmission (physical links, transmitter/receiver equipment and

regenerators), transport of client signals is realized by means of multiplexing techniques in which

multiple streams are combined into a composite one for transmission over a shared medium. The two

most common flavors of multiplexing go by the name of Time Division Multiplexing TDM and

Wavelength Division Multiplexing WDM. The first approach concerns the cases where a number of

connections share a communication channel in the time domain, each periodically assigned a time-

slot in which the exclusivity of the access to said channel is owned. In the case of WDM, the light

4

spectrum is sliced such that multiple streams can be carried over non-overlapping wavelengths in a

single fiber. According to how far apart adjacent channels are, WDM technologies are categorized as

either Coarse WDM with channel spacing of 200 GHz or Dense WDM with channel spacing of 50

GHz. The mismatched wavelength windows result in a distinct number of optical channels supported

by each optical fiber.

To accommodate the traffic growth trend in telecommunication networks, the Optical

Transport Network OTN protocol arouse and evolved over the WDM network enabling the efficient

convergence of legacy SONET/SDH and emerging data services. Fitting the bill as the modern

transport technology of choice, its bandwidth granularity, enhanced OAM, multi-carrier network

support and transparent client signal transport had operators migrate their infrastructure to OTN over

WDM solutions. The technologies synergy enabling for wavelength and sub-wavelength switching with

ROADM and OTN switch equipped nodes is being seized as a cost-effective approach to maintain and

upgrade terabit mixed service networks. These networks will be the focus of the current work with

concerns settled on planning methodologies for increased performance and lowest capital

expenditures.

1.2 Motivation

The incredibly volatile telecommunications environment marked by high competitiveness, data-

centric applications, services convergence trend over transport infrastructures, escalating traffic

demand and stricter quality requirements has operators struggling with the design, development,

maintenance and upgrade stages of their networks. Current availability of 100 Gbps transponders and

the prospect of 400 Gbps equipment entering the market are propelling research and posterior

application of network design and planning techniques to optimize the ways in which the dominant

client signals in the order of a few tens or lower Gbps are carried in high capacity optical pipes in

metro and long haul networks.

Of pivotal importance, the minimization of the acquisition and operational costs stand as key

issues as operators work on strategies to scale and future proof their networks to intake a plethora of

bandwidth hungry applications. As the convergence of services onto one same transport platform with

unified management appeals to the cost-minimization challenge, it is also crucial to drive down the

cost per transported bit. In what concerns to such aim, equipment cost has historically been a variable.

WDM equipment has evolved over time to tame the capacity strand problematic and reduce the cost

of transport by increasing system capacity with higher rate channels, allowing expenditures to be

shared over a larger number of clients. As one moves to optical pipes of greater bulk, the wavelength

filling ratio’s weight on the cost sheets becomes more significant. This would not be an issue if the

service data rates and wavelength bandwidth were a match but that is not the scenario in today’s

networks where a good percentage of sub-wavelength traffic is transported over the WDM

infrastructure [1].

The Optical Transport Network OTN standard allows for a variety of service technologies to be

concurrently multiplexed onto a common network with the offer of a hierarchical wrapper structure and

fitting DWDM rates, supporting seamless transport over wavelength channels [2]. The multiplexing

5

process allows for the decoupling of the services data-rates from those of the optical channels that

carry them. In OTN networks, the number of Optical Transport Units, the electric signal before

conversion to the optical domain, is a major cost factor in that it implicates a pair of optical

transponders at each end-node. While all-optical networks still maintain their appeal, the possibility to

groom sub-wavelength connections by means of electric switching at intermediate nodes serves as an

approach to minimize the number of optical channels.

Next-generation OTN/WDM transport networks feature nodes with integrated optical switching of

wavelength channels with finer grained electrical switching of Optical Data Units. The mentioned

synergy allows for the efficient multiplexing of ODUs into OTUs in improvement of wavelength channel

utilization while counting on ROADMs to perform optical bypassing saving on costly opto-electric

conversion gear. A great planning focus is being laid on strategies to optimally combine wavelength

and sub-wavelength switching in alignment with cost minimization targets. This is the main issue

addressed in the current thesis where a primary sweep is performed on DWDM networks and

associated RWA methodologies. Posteriorly, grooming techniques are included to the problem in

relation to OTN/WDM networks. While an initial goal is drawn on throughput maximization in resource

scarcity scenarios, the final chapters address GRWA methodologies to achieve the lowest network

expenditures.

1.3 Dissertation Layout

The current work is organized as follows: the following chapter is devoted to the technologies and

equipment subjacent to DWDM and OTN networks. Design and optimization strategies scoping the

aforementioned systems are outlined and complemented with a literary review on relevant published

works. Chapter 3 focuses on the RWA problematic pertaining to transparent DWDM networks,

encompassing integer linear programming approaches and an original heuristic algorithm.

Grooming technologies are added to the planning purpose in Chapter 4 and made use of to

approach network’s throughput maximization challenges in transparent, translucent and opaque

networks. Literature adapted Ilp and heuristic formulations are pursued in such aim. The cost-

minimization challenge is eventually targeted in Chapter 5 where the intent is laid on the application of

GRWA models to achieve the least-costly configuration of deployed resources able to satisfy an

inputted traffic demand. Expenditures are accounted on the installed line cards. Again, original Ilp and

heuristic formulations are presented with applicability extended to transparent, translucent and opaque

mixed rate networks. The scenario of unidirectional optical channels is included and the cost

effectiveness of models applying a series of disparate line card configurations in scenarios with

asymmetrical traffic patterns are examined. Finally, the conclusions and prospects for future work are

revealed in the closing chapter.

1.4 Original Contributions

The contributions arising from the development process of this thesis are outlined below,

discriminated by chapter:

6

Development of further RWA Ilp models for Chapter 3, extending the one used as basis. The

referenced work included an integer linear formulation applying a link-path approach and

symmetric traffic routing. The scope was widened to include new formulations to tackle the

asymmetric routing scenario and a node-link approach intended for comparison purposes. A

heuristic algorithm is presented as a result of the studies performed on first-fit wavelength

assignment and shortest path routing strategies;

Incorporated in Chapter 4, the analysis of a published Ilp formulation concerning the GRWA

throughput maximization problem in translucent SONET/SDH network lead to the design of new

problem variants. The work that served as reference was remodeled to fit the DWDM/OTN

scenario and diversified to encompass opaque and transparent networks as well. The ability to

select which nodes were equipped with electric ODU switching fabrics was also added as an

input to the problem. The MST and MRU heuristics found in the research over alternatives to the

mathematical approach were also adapted with intents to reach increased performance;

Elaboration of integer linear programming formulations for the cost-minimization problematic in

transparent, translucent and opaque mixed rate networks incorporating DWDM/OTN

technologies. Inclusion of models for both asymmetric and symmetrical traffic patterns and study

of a set of distinct transponder line card configurations targeting the scenario with unidirectional

traffic requests. Post to that, and as was the norm during the execution of the current

dissertation, a heuristic algorithm was designed to target networks dealing with symmetric traffic

patterns.

7

2 OTN: Background and State of the Art

The current chapter’s focus lies on the OTN technology that features today at the core of

transport networks. Its most relevant aspects to this thesis work are outlined and the planning

methodologies pertaining to such networks attended. On that last topic, the state of the art on selected

network design problems is presented with a review on researched publications.

8

2.1 Rationale for OTN

The Optical Transport Network OTN standards as defined by ITU-T in 2001 in recommendations

G.709 [3] and G.872 [4] came out of the need to have a transport protocol rightly suited for multi-

wavelength networks. As is the norm, the standards picked up on the relevant points of the preceding

SDH/SONET technologies in intent to magnify its most relevant features and to fill in the gaps left void.

Built out of experience and of a lessons learned process, the protocol has evolved to meet the needs

of the data intensive, bandwidth demanding and service mixed networks of today. The encompassing

of both optical as well as electrical considerations and the regards towards the underlay and overlay

layers exigencies [5] provide it with a rich set of features that are enticing to operators while they plan

the evolution towards next generation networks. A true carrier’s technology, OTN holds as a cost

effective platform that concedes service providers with the tools to deliver profit assured services while

leaving room for new opportunities. Furthermore, the technology enables the engineering and scaling

of networks towards increased life cycle and enhanced responsiveness to the accommodation of new

services.

The developments in the optical industry that culminated with the appearance of DWDM

technologies into the market place disrupted the world of telecommunications on the promise of

virtually unlimited capacity, cashing in on the existing fiber plant investments by permitting taking in

extra traffic and/or adding new services onto the deployed fiber links. Having eventually integrated the

multi wavelength technology as an underlay layer, the SDH/SONET network that eventually grew to

be the backbone of most modern telecommunications in the nineties inherently presented the

limitations of a standard that had been conceived for optical interfaces that used a single wavelength

per fiber [6] [7].

The vision that DWDM would settle as the lowest layer for the transport network ingrained the

desire for a protocol that could meet its requirements and that would be conceived from the scratch

with such acquired perception. As the sketches for a new generation of optical networks started to be

outlined, many envisioned a fully transparent optical network supporting the direct mapping of client

signals onto wavelengths. The handover of all intelligent switching and routing functionality to the

optical domain appealed to many on the prospect of allowing to significantly avert the costly and delay

inducing equipment necessary to conduct opto-electric conversions [8]. While client signals could be

directly transported over a wavelength, the over barring complexity of management, monitoring and

regeneration of signals in the optical universe and the protocol and format dependency that sending

the signals in their native format required for [8], put strains in the all-optical solutions and moved the

scope towards a balanced and complementary digital and optical synergy.

The works carried by ITU-T that culminated in the standards for the Optical Transport Network

focused upon the definition of a new signal format complemented with the overhead channels for the

added functionality to perform OAM&P on the WDM network. The need for a tradeoff between the

desired all optical network and having the required functionality to maintain and improve the pattern of

reliable, flexible and scalable networks resulted in a compromise that involved making use of the

9

necessary opto-electric-opto conversion at 3R regeneration sites [5] or at domain boundaries to

provide per-wavelength and client-agnostic OAM&P capabilities in the electric domain.

In what is referred to as the “digital wrapper” approach, client signals are transparently mapped

onto the frame’s payload and overhead bytes added for capabilities such as alarm indication,

performance monitoring, defect detection and reporting and client signal identification. The

encapsulated signals can be either aggregated with a mix of other signals or directly mapped onto a

wavelength. Thanks to the multiplexing techniques, the services bit-rate can be decoupled from that of

the wavelengths and each channel’s capacity can be shared among a number of clients for optimized

bandwidth utilization [9].

As networks evolve to higher line rates, the limitations of the physical transport medium, the

optical fiber, accentuate the degradation of the transmitted light pulses, becoming an issue of critical

concern [10]. The option of increasing the number of 3R regeneration points and decrease the optical

spans to maintain the same level of quality provided to the end-users comes at a greater expense and

is, therefore, to be avoided. With such mindset, OTN defines a standardized forward error control FEC

block to be appended to the trailing portion of the frame structure that achieves improved error

performance and enables for longer optical spans in between 3R regeneration sites.

Defined at a time where voice circuits were the primary accountable for the traffic flooding

telecommunications networks, SDH/SONET was conceived targeting the efficient support of the

dominant DS1/E1 and DS3/E3 signals. As data-rates escalated and aggregation moved towards a

greater bandwidth bundle, the requirement that each intermediate network node switch down to those

signals’ granularities proved to be costly, inefficient and complex due to the amount of switching logic

involved and to the requirement that services demanding higher switching rate had to be transmitted

by means of contiguous or virtual concatenation [11]. The understanding of such limitations and the

sketches of a path towards the Gigabit signals’ era lead to OTN defining a lowest granularity some

orders of magnitude higher, initially settled at 2.5 Gbps and eventually lowered down to a grainier slot

of 1.25 Gbps. The less granular envelope allows to lessen the expenses per Gbps of switching

capacity and facilitates the scaling and management of multiterabit networks.

OTN is structured on a well-defined signal hierarchy that may not always be able to support the

seamless accommodation of new emerging signals. The option to upgrade the specified hierarchy for

the admission of every incoming signal that cannot be fitted onto the existing payloads comes out as

costly and complex and may even raise interoperability issues. To overcome the matter, OTN brought

along a pair of relevant features in the form of a variable sized container, ODUflex and a new mapping

procedure, Generic Mapping Procedure to, in a way, tame the unpredictability of the future by

responding in a prompt manner to the accommodation of new protocols.

Optical networks evolved into a complex and intelligent system that provides worldwide

connectivity and the transport of a diverse set of services. Often times, such networks need to

interoperate among many different carrier domains to offer end-to-end connectivity. To support for

multiple domains, OTN offers six Tandem Connection Monitoring fields that allow for operators to

monitor a signal in up to six configurations along its path coping with nested, overlapping and

10

cascaded network sections [12]. In such a way, each operator can monitor their network individually

and troubleshooting is facilitated as is checking SLA fulfillment.

Only recently, the recognition and adoption of OTN as a transport technology has become a

reality. The large investments and wide deployments of SDH/SONET networks caused resistance

against the evolution towards new standards given the necessary capital investments and the need to

cash in on the expenditures made. First remitted to the task of providing point-to-point transmission to

SDH/SONET networks, these days OTN is being demanded by operators worldwide as a new entire

network layer to squeeze out the most of the evolved underlay DWDM layer that has been greatly

upgraded with the progresses made on ROADMs and optical transponders. The standards are now

one of the major contenders to support the transition towards the next generation packet optical

network that operators require has to rely on a technology not only robust, but also functional for many

years holding the future proof trait not to be quickly outdated and to support evolution [9].

2.2 OTN’s layered model

OTN works on both the optical and electrical domains to ensure the reliable and QoS compliant

transport of its client signals. A separation is usually established with the definition of a layered model

where the electrical layer pertaining to the “digital wrapper” approach resides on top of the DWDM

layer responsible for the transmission and management of optical carrier signals through the fiber

optic lines. Encompassing both layers, the Optical Transport Hierarchy OTH represented in the Figure

below defines the signals’ flows in the OTN domain.

Figure 2.1: Optical Transport Hierarchy

The electric layer is the point of contact of the client signals to the OTN network. Based on the

concept of a transparent container, the user streams from a variety of overlay networks are

sequentially mapped onto a series of structures according to the defined Optical Transport Hierarchy.

At each level of the hierarchy inside the electric confines, specific OTN overhead bytes built into the

signal format are added to support OAM functionality. The client signal is first mapped onto the

11

payload area of an Optical Payload Unit. The OPU layer adds blank bytes to adapt the signals’ debts

and introduces its own overhead. Posteriorly, the OPU is converted to an Optical Data Unit with the

addition of the ODU overhead. At the final stage, the Optical Transport Unit that modulates a carrier

wavelength is built by means of the addition of the OTU overhead and of a trailing FEC field. Prior to

mapping onto an OTU frame, the ODU wrapped client signals can be subjected to multiplexing in

achievement of greater wavelength utilization.

The separation between the electrical and optical layer is made at the point where the electric

signal whose rate is a match to one of the transmission line rates is converted to the optical domain.

From then on, the task of routing the wavelength signals onto their destinations is of the responsibility

of the DWDM network. Provided with transmission, regeneration, multiplexing and switching devices,

this optical layer is responsible for the transport, management and monitoring of optical carriers. As

according to Figure 2.1, the Optical Channel carries an OTU signal over a color and is provided with

an appropriate optical overhead. The addition of further optical overhead for the management of

multiple colors in the optical transport network gives room to the Optical Multiplexing Section and to

the Optical Transmission Section. The first is demarcated in between multiplexing sections and the

second between amplification stages.

2.2.1 OTN’s Optical Layer: WDM-network definitions

At the optical layer, an OTN network is composed of WDM transmission links and WDM

network devices. The elements that constitute the WDM network include the Optical Amplifier OA, the

Optical Terminal Multiplexer OTM, the Optical Add and Drop Multiplexer OADM and its reconfigurable

variant ROADM and lastly the Optical Cross Connect OXC. These network elements are connected by

means of optical fibers according to a given physical topology, most commonly mesh, ring or multi-

ring.

The entry point to the WDM network is made by means of transponders or muxponders. While

both are in charge of receiving and transmitting the optical signals over the fiber lines, the muxponder

has the additional functionality of multiplexing multiple sub-rate client interfaces onto the line interface

according to a fixed configuration. An Optical Terminal Multiplexer is composed of transponders, WDM

multiplexers and optical amplifiers and is used at the end-points of point-to-point WDM links to

multiplex/demultiplex multiple non-overlapping wavelengths. The optical line amplifier lies as a device

deployed along the fiber link at selected locations to provide for amplification of the optical signals.

OADMs are employed in ring networks at locations were a portion of the wavelength carriers is

required to be terminated. These devices demultiplex the WDM signal from an incoming fiber,

selectively extracting wavelengths while letting others pass through. Specific wavelengths added at

local ports can also be multiplexed with the cut-through lightpaths onto the outgoing fiber.

Traditionally, simple static filters were employed for adding or dropping predefined wavelengths, any

further changes requiring local and manual intervention, eventually disrupting network service. To

overcome this lagging and costly job, Reconfigurable OADMs entered the market allowing for the

remote and dynamic configuration of wavelengths in real-time in response to changes in traffic

patterns.

12

Granting for mesh topologies to be deployed, the Optical Cross Connect allows for the switching

of wavelengths from multiple incoming to outgoing fibers. Nowadays, ROADMs can be referred to as

OXCs as well, consequent of the technical advances that have scaled up in recent years. In fact, the

state of the art ROADM is characterized by its multi-degree, contentionless, colorless and

directionless features. Composed of optical multiplexers, local ports, optical switching fabrics and

multiple WDM network ports, these devices allow for tunable transponders to have transparent and

non-blocking access to all WDM network ports. Furthermore, same wavelengths carrying different

information can be received/sent simultaneously from/to different input/output fiber ports [13].

An Optical Transport Network offers an optical-circuit connectivity service by setting up

lightpaths or synonymously optical channels. Each lightpath features as a point to point connection

between two transponders/muxponders in the network: it can optically bypass in transit ROADMs in its

span and requires a wavelength channel per crossed link. WDM multiplexing devices aggregate

bundles of optical channels for transmission over the same fiber link. Every path in the network

between multiplexing elements, OTMs and/or ROADMs, is to as an Optical Multiplexing Section. In

turn, every OMS is segmented into a series of Optical Transmission Sections, demarcated in between

amplification stages. The figures below provide examples on the exposed concepts.

Figure 2.2: Optical Layers demarcation points with OCh between OTMs

Figure 2.3: Optical Layers demarcation points with OCh between ROADMs

To each demarcation point defined above corresponds one of three layers in the optical stage of

the Optical Transport Hierarchy as defined in Figure 2.1. The OCh layer is responsible for the

accommodation of the channel’s dispersion, channel identification and protection switching. The OMS

layer manages optical multiplexing, protection switching of multiplexed signals and wavelength

assignment, identification and conversion. In turn, the OTS layer is accountable for optical

amplification and dispersion compensation by means of optical line amplifiers. The optical overheads

13

pertaining to each hierarchic level are transmitted out of band in the non-associated Optical

Supervisory Channel OSC.

2.2.2 OTN’s Electrical Layer

OTN operates on the electrical stage on the foundations of a “digital wrapper” that transparently

encapsulates client signals. Those tributaries follow through a specified hierarchy that successively

adds overhead bytes to the point a fixed length frame is formed. The layers in which the electrical

domain is partitioned are, from the top down, the Optical Payload Unit OPU, the Optical Data Unit

ODU and the Optical Transport Unit OTU.

The tributary signals are mapped onto the payload area of the Optical Payload Unit at the

primary stage and their debts adapted to the OPU structure with the addition of bytes with no

information and with the performance of negative or positive justification. The OPU overhead contains

information to identify the transported payload, bytes for justification purposes and additional reserved

fields. The addition of the ODU overhead converts the OPU structure into an Optical Data Unit. The

overhead bytes built into the ODU signal format support functionalities such as path performance

monitoring, fault type and location reporting and automatic protection switching. Also present are two

generic communication channels and protection communication channels. Like the OPU, the ODU is

formed when the tributary signal enters the optical network and both are preserved intact throughout

the network with the ability to span more than one Optical Channel.

The final layer in the digital hierarchy is attained by adding overhead fields to the ODU and a

FEC block at the trail. The overhead bytes carry the functionality for frame and multi-frame alignment

and include support for monitoring the Optical Channel end-to-end providing for connectivity fault

detection, alignment and payload errors detection and reporting. The FEC block is a feature of great

deal for long-haul optical networks where the effects of the optical impairments are most felt given the

long distances spanned. Its present is justified as a means to increase the optical reach. The OTU

shares its demarcation points on the optical network with the Optical Channel. The fully composed

digital frame is described below.

Figure 2.4: OTN's digital frame

Defined OTN payload structures and mapping schemes allow for a wide variety of client

protocols to be accommodated. Thanks to OTN’s flexible TDM hierarchy, sub-wavelength streams can

be multiplexed to share a common optical channel’s bandwidth, a feature of great deal in its ability to

increase wavelength utilization and to reduce the number of required wavelengths and transponders

to support traffic demand. In addition, operations can be simplified due to the OTU’s signal overhead

that allows for the aggregated ODUs that compose it to be managed as a single transport entity. To

14

date, the standard’s defined ODU and OTU signals relevant to the current work are as presented in

the tables below. OTN containers are defined to have a fixed number of bytes and a varying frame

duration.

Table 2.1: OTU and ODU signals and data-rates

Signal Data-rate

[Gbps]

Signal Data-rate

[Gbps] OTU-1 2.666 ODU-0 1.244

OTU-2 10.709 ODU-1 2.499

OTU-3 43.018 ODU-2 10.037

OTU-4 111.810 ODU-3 10.399

To detail OTN’s multiplexing process one first must refer two auxiliary concepts, that of the

Low Order ODU and of the High Order ODU. The first pertains to the structure that is composed of the

client signal’s payload and of the OPU and ODU overhead. The second respects to the ODU signal

onto which the OTU overhead and FEC code are added. If at times a Low Order ODU can also feature

as a High Order ODU, that is not always the case. Groups of Low Order ODUs can be multiplexed

onto the payload area of a High Order OPU that in turned is converted to ODU with the additional

overhead fields. Given OTN’s allowance of both single and multi-stage multiplexing, the process can

be repeated prior to the mapping of the final multiplexing structure onto the payload are of an Optical

Transport Unit. The High Order containers are broken down into n time-slots of either 1.25 or 2.5

Gbps, each assignable to a single Low Order structure that may span one or more slots. This partition

allows for a mix of ODUs of distinct rate to share the bandwidth of a higher rate signal without the

need for more than one multiplexing stage. An extensive list of selected available multiplexing options

in the OTN domain is showcased below.

Figure 2.5: Selected OTN multiplexing options

2.2.3 OTN over DWDM: ODU/DWDM switch

The commercial availability of 100 Gbps transponders posed serious challenges to operators

that needed to find an efficient way to fill the bulky optical pipes regardless of the services’

15

granularities, typically only a fraction of those values. In the absence of a sub-wavelength layer, static

muxponder solutions proved valid in escaping the cost escalation associated with having client

equipment directly connected to the DWDM layer at raw wavelength capacity. Despite the appeal in

their simplicity, in a time where operators focuses lied on the challenges of bandwidth monetization

and minimization of the cost per transported bit, the prospect of sub-wavelength switching at the

transport layer served more fitting to the purpose. By switching at the ODU layer, the switching fabrics

can be made transparent to the client protocols and end-to-end optical performance and signal

monitoring can be maintained. Most importantly, sub-wavelength traffic grooming at the transport layer

holds the means to maximize wavelength channel utilization for reduced costs.

Grooming techniques attempt to form highly packed wavelengths between two grooming sites

as opposed to between the source and destination of the sub-rate demands as is the case when

applying muxponder solutions. Employing intermediate grooming strategies, sub-wavelength streams

can share a common optical channel’s bandwidth despite having mismatched end-points. Not only

that but the demands with which a given stream is aggregated with may change at multiple sites along

its path [14].

A practical grooming example is showcased in Figure 2.6 where the network’s physical topology

and traffic demand are presented. A 40 Gbps (OTU-3) line rate is assumed. Also displayed is a

possible grooming strategy: assuming nodes 3 and 7 are equipped with ODU-switches, a single

wavelength is used to carry all of node 0’s demands to node 3 and another to carry all of node 1’s

demands towards node 3. The grooming equipment at that node allows for wavelengths to be “broken

apart” and later reconstituted using different groupings. By means of OTN Mux/Demux and switching

fabrics, nodes 0 and 1 demands for node 10 are aggregated and routed over an optical channel

towards their final destination. Similarly, all demands destined to node 7 and 8 are aggregated into the

same optical channel to node 7, regardless of their origin. At that grooming site, streams intended for

that node are locally dropped and the remaining ones are packed into a wavelength and transmitted to

node 8.

Figure 2.6: Network's topology and traffic demands. Example of intermediate grooming

In comparison with the transparent strategy presented in Figure 2.7 where an optical

channel must be established between any end-points with traffic demands and multiplexing

is restricted to streams with the same source and destinatio, the solution employing ODU

16

switching at intermediate nodes requires for a lesser number of lightpaths: 5 as opposed to

6. Also, the groomed wavelengths are on average 72.5 % filled as opposed to the 27.1% for

the multiplexed wavelengths. Finally, in regards to the consumption of wavelength links (a

wavelength assigned to an optical channel at a fiber link constitutes a wavelength link),

grooming is accounted for 9 units whereas multiplexing is accounted for 26.

Figure 2.7: Example of end-to-end grooming for the transparent scenario

By optimally combining wavelength and sub-wavelength electrical switching by means of

ROADMs and ODU switches, either as a multi-granular integrated device or as standalone solutions

connected by short reach interfaces, traffic grooming can be complemented with optical bypassing to

drive down the cost per transported bit. One could have, for instance, close to completely or

completely filled 100 Gbps optical channels bypassing all intermediate nodes on path to destination

and poorly filled 100 Gbps optical channels terminated at intermediate nodes and aggregated onto a

better filled outgoing wavelength with locally collected traffic sharing a common path.

Figure 2.8: Architecture of an OTN/WDM Switch

17

A possible OTN/WDM switch architecture is depicted in Figure 2.8. The client cards

insert/collect streams from a variety of services and protocols into/from OTN frames. At the ODU

switch, locally added signals are routed alongside in-transit demultiplexed signals from terminated

wavelengths onto the line cards’ ports. Incoming signals from the DWDM network also surpass the

ODU switch to be delivered to the rightful client cards. The line cards, as detailed in the figure, are

composed of OTN Multiplexer/Demultiplexers and of Optical Transponders. These devices multiplex

the groomed signals from the ODU switch and convert the composite signal to the optical domain and,

in the reverse direction, convert the optical signal into the electric domain and further demultiplex the

carried ODU signals. At last, the multi-degree ROADM not only allows for wavelength channels to be

added or dropped but also performs optical bypassing by switching wavelengths from incoming to

outgoing fibers.

The presence of OTN/WDM switches at the network nodes makes for translucent networks. In

the spectrum of network configurations, two other solutions can be deployed:

Opaque [Figure 2.9]: Each network node is equipped with a standalone OTN switch connected to

the WDM network via line cards and WDM mux/demux devices. Only sub-wavelength switching is

allowed and the WDM network’s purpose it to provide for point to point connections among OTN

nodes. Optical channels can only span a single fiber line and the number of virtual hops a

connection must endure from source to destination is lower bounder by the physical hop count of

the shortest path between such endpoints;

Transparent [Figure 2.10]: Signal switching is restricted to the optical domain. Locally added

streams are mapped onto OTN frames at the client cards. These cards are connected to line

cards that convert the electrical signal to the optical domain. The resulting wavelengths surpass

the ROADM that performs the switching required to route them towards the appropriate fiber

ports. Client streams are carried in a single direct lightpath from source to destination as

intermediate nodes are always optically bypassed. On the matter of line cards, Figure 2.10

displays three possible configurations: one composed of an ODU multiplexer/demultiplexer and of

a transponder, a configuration featuring a muxponder device and yet another approach with a

single transponder. While the first two configurations have the ability to multiplex sub-rate

streams onto a higher bandwidth signal that is later converted to the optical domain, the static

muxponder solution generally restricts the client side signals to only a subset of the possible

service rates (for instance,10x10 Gbps aggregation into 100 Gbps signal or 4x2.5Gbps

aggregation into 10 Gbps signal). In turn, the ODU mux/demux with transceiver solution allows for

any combination of sub-rate signals to be aggregated onto a composite channel so as long the

channel’s bandwidth is not surpassed. Lastly, the configuration featuring a single transponder lies

appropriate for the cases where the client signal’s rate is a match to the transmission line rate.

18

Figure 2.9: Opaque node configuration

Figure 2.10: Transparent node configuration

2.3 Network design and planning

In order to introduce design and planning methodologies targeting Optical Transport Network,

some auxiliary concepts have yet to be introduced. Both the physical and virtual topology are often

times, and in the scope of planning, represented by means of graphs or matrixes, the interchange

from one model to the other easily achievable. A graph is a set of non-empty vertices and a collection

of edges corresponding to pairs of vertices among which there is a connection. In the context of the

physical topology of a networks, a vertex represents a network element and an edge a fiber link

uniting any two vertexes. Regarding the case of virtual topologies, a vertex stands for a network node

where optical channels are added or dropped and an edge corresponds to a lightpath.

A directed graph is that where the edges have an orientation, where it is applicable the

terminology “a connection from 𝑎 to 𝑏”. In such cases, vertex (𝑎, 𝑏) is not the same as (𝑏, 𝑎). A

19

lightpath’s route can be mapped onto the graph representation of the network’s physical topology as a

path, an ordered collection of vertices {𝑣𝑖 , … , 𝑣𝑛}, such that 𝑣𝑖 and 𝑣𝑖+1 are neighbors, that is, there is

an edge among them. The degree of a vertex is calculated as the sum of its neighbors. It is usual to

refer to a network’s mean nodal degree so as to have a perception of its connectivity.

As mentioned, matrixes and graphs are strongly related. Given a graph with 𝑛 nodes, it is

possible to construct a direct representation in the form of a 𝑛 𝑥 𝑛 matrix where each entrance 𝑒𝑖𝑗

assumes a value corresponding to the number of graph edges from 𝑖 to 𝑗. Both terminologies will be

used from this point on.

In the scope of planning methodologies, it is common to recur to linear programming models. As

a subclass of Programming problems, they constitute mathematical optimization strategies. Widely

employed in scientific and economical fields to modulate real life situations, these methodologies are

taken as a means to reach a measurable target under problem specific constraints. The statement of

a linear programming problem comprises a set of linear equations and/or inequations specifying the

problem’s constraints and bounding the space of feasible solutions and a linear function subjected to

either maximization or minimization expressing the goal to achieve. A solution that simultaneously

complies with the imposed conditions and satisfies the given objective is referred to as an optimal

solution. In the particular case where the variables are limited to integer values, the problem is said to

be an Integer Linear Programming one. A comprehensive set of algorithms was developed with the

intent to solve such problems and currently, software-implemented solvers are also commercially

available [15] [16] [17].

Often times the mathematical models prove to be inefficient despite their promise of optimality.

The associated heavy and untraceable computational effort make it so that alternative approaches are

searched for the optimized design of real life networks. Based on either an underlying theory and/or on

the study of experimental results, heuristic algorithms are employed to seek solutions as close to the

optimum as possible at the cost of low or moderate computational times.

2.3.1 DWDM layer planning methodologies: RWA in transparent networks

All optical wavelength-routed WDM networks are comprised of wavelength routing nodes

interconnected by optical fibers. Traffic is transferred from one point to the next by means of all-optical

circuits called lightpaths, unidirectional connections between two end-nodes without intermediate

O/E/O conversion. These networks are inherently tied to the clash constraint that specifies that no two

lightpaths can share the same wavelength at a common link. However, spatial wavelength reuse is

allowed as multiple optical channels can be assigned the same carrier over distinct fibers. In

transparent networks with no wavelength converters, a lightpath must be assigned the same

wavelength over all spanned optical transmission lines. This restriction is known as the clash

constraint and can be lifted for systems where the ROADM switching devices are equipped with

wavelength converters that allow for a lightpath to be setup with disparate wavelengths on different

links along its path.

A lightpath is uniquely identified by a physical route and a particular wavelength. The problem of

determining the set of links crossed by a lightpath and the claimed wavelength at each segment of

20

said path is referred to as Routing and Wavelength Assignment RWA. Due to limitations on the

number of wavelengths per fiber and to the wavelength continuity constraint when in the absence of

wavelength converters, the network may not be able to accommodate all requests. For this reason, it

is desirable to apply efficient RWA algorithms to establish the requested connections with high

indicators of network performance.

Typically, there are two types of network traffic: static and dynamic. For static traffic, a set of

time-invariant connection demands are known in advance. The problem’s goal is to accommodate all

requests at the expense of the minimum resources, typically the number of required wavelengths. In

concerns to the dynamic scenario, requests arrive over time and are released post a random time

frame. Lightpaths are required to be establish dynamically, seizing the available resources at each

moment. Existing circuits cannot be re-routed for the accommodation of new ones and it so may

happen that connections are blocked over unavailability of free wavelengths along the source-

destination paths. The objective drawn in such cases is the minimization of the blocking probability.

In currently deployed networks, connections are routed over bidirectional optical circuits with

identical capacities in the direct and reverse directions. The direct direction is considered, in this

scope, the one from the lower to higher numbered node. To implement bidirectional lightpaths, either

symmetric or asymmetric routing approaches can be pursued according to whether the inverse

lightpath’s route is the same as the direct lightpath’s, although in the reverse direction, or not.

Symmetric routing methodologies allow to reduce the problem’s dimension and execution time by

considering only the direct requests. The attained results can then be seamlessly mirrored to the

reverse connections. On the other hand, the asymmetrical routing approach is presented with a larger

solution space which may prove more efficient in the utilization of network resources as explored in

latter chapters.

Integer Linear Formulations are commonly pursued to solve the RWA problem. On that note,

mathematical programming methodologies for mesh, ring and multi-ring topologies applying

bidirectional routing can be found in [18]. The author considers time-invariant demands and sets a

goal for minimizing the number of wavelengths. Though left out of the scope of the present work, the

reader is remitted to [19] for static RWA Ilp formulations for networks with wavelength conversion

capabilities.

The integer linear programming formulations presented on the aforementioned works are

merged RWA methodologies in that they integrate the routing and the wavelength assignment

problem. The Ilp combined RWA approach has proven to be NP-Hard thus making it computationally

difficult to track [20]. To work around that trait, the problem can be made easier to handle by

decoupling into two separate sub-problems of routing and wavelength assignment. However, by

making the sub-problems independent, the individual optimization of each sub-problem is not

guaranteed to provide an optimized solution to the overall problem of routing and wavelength

assignment.

On the study of decoupled methodologies, [20] presents a well-known methodology involving an

Ilp algorithm to solve the static routing problem and a graph coloring problem for the remaining

wavelength assignment problem. The methodology makes use of the routing sub-problem’s

21

determined routes for the connection requests, to create an auxiliary graph where each vertex

corresponds to a calculated lightpath’s path. The vertexes are connected such that if two paths share

a common link on the physical topology, the corresponding vertexes are united by means of an

unidirectional edge. In the end, the wavelength assignment problem comes down to assigning

wavelengths to the auxiliary graph’s nodes compliant with the restriction that no two neighbor nodes

share the same wavelength and with the goal of minimizing the wavelength count.

On the matters of dynamic RWA decoupled algorithms, the same work presents a compilation of

representative methodologies for each individual sub-problem. Selected algorithms from among those

listed for the routing sub-problem are described below:

Fixed shortest-path routing: A single static path for each source-destination pair is calculated

offline. The path corresponds to the shortest-path among the two nodes such that there is one

common wavelength on all links;

K shortest-path routing: A set of k shortest-paths is calculated offline for each source-destination

pair. Incoming connection requests are assigned the first shortest-path, from the one comprising

the lowest number of physical hops to the highest, such that a common wavelength is available

over all spanned fiber lines.

Least-congested path routing: A given incoming request is served with the least- congested route

among all possible candidate paths uniting the source and destination nodes. A route’s

congestion is calculated as the number of wavelengths available on the fiber link with the highest

number of assigned wavelengths, the most congested link.

In regards to the wavelength assignment problem, the authors list the following methodologies:

Random: A random wavelength is selected over the set of wavelengths common to all fiber links

of the determined route;

First-fit: Wavelengths are indexed and searched in a fixed order according to their index number.

The assigned wavelength for a given calculated route is the one with the lower index from among

the candidate wavelengths available over all links of the path;

Least-used: This algorithm requires global network state and information storage in order to

determine the wavelength that is least used in the network. A selected route is served with the

least used wavelength common to all spanned links.

Most-used: The opposite to the previous methodology, the chosen wavelength is the most used

in the network.

2.3.2 OTN planning methodologies: traffic grooming

The OTN/WDM switch presented in 2.2.3 allows for multi-granular signal handling, providing not

only for optical bypassing but also for traffic switching and aggregation at intermediate network nodes

as opposed to the all-optical or transparent solution where sub-wavelength signal aggregation is

restricted to the multiplexing of same source-destination streams. The variant of the previously

introduced network topology design problem concerning the combination of low-speed streams onto

high capacity channels is referred to as the traffic grooming problem. Given a set of connection

requests with different bandwidth granularities and the network’s configuration comprising the

22

network’s physical topology, number of transponders per node, number of wavelengths per fiber,

wavelength channels’ capacity and each node’s electrical and optical switching capabilities, the traffic

grooming problem concerns the establishment of lightpaths in satisfaction of the connection requests.

Given the sub-wavelength granularity of the requests, one or more connections can be multiplexed

onto the same optical channel.

As was the case in 2.3.1, traffic can be deemed static or dynamic whether the requests are

time-invariant or distributed over a time-line, respectively. Traffic grooming in static scenarios is a dual

optimization problem. In cases where the available resources are prohibitive to the satisfaction of the

entire traffic demand, the objective is to maximize the network’s throughput, that is, the volume of

successfully attended connections. On the other hand, in cases where there are enough resources to

expedite all traffic, the grooming problem is aligned with cost-minimization goals such as the

minimization of the number of optical line cards or of wavelength-links.

The throughput maximization problem is addressed in [21]. Assuming the presence of optical

cross connects and electrical switching fabrics with multi-granular traffic handling capabilities, a set of

SDH/SONET sub-wavelength requests of different bandwidths is to be attended under constraints on

the number of available wavelengths and transponders. The fibers’ optical impairments are despised.

The authors present formulations for multi and single hop traffic grooming corresponding to

translucent and transparent networks, respectively. The attained results prove increased network

efficiency for the translucent case, the ability to groom traffic at in-transit nodes allowing for higher

wavelength utilization and network throughput.

As a variant of the RWA problem, the Grooming, Routing and Wavelength Assignment problem

inherits its NP-Hard trait. On that note, in [21] the authors introduce two heuristics targeting the

throughput maximization problem in meshed SDH/SONET networks where all nodes are equipped

with both optical and electrical switching fabrics. The presented Maximum Single Hop Traffic and the

Maximum Resource Utilization Heuristics are both conceptually similar. Supported on the assumption

that carrying the most volume of traffic in direct lightpaths from source to destination is an enabler for

maximum throughput, the authors break the problem down to the sub-problem of lightpath selection

and RWA and into the sub-problem of aggregation and routing of sub-wavelength streams over the

achieved virtual topology design. Subjected to constraints on the number of wavelengths and

transponders, the algorithms select node-pairs in turn and try to establish lightpaths among such pairs

using shortest-path routing and first fit wavelength assignment. Once no more lightpaths can be set-up

over unavailability of wavelength and transponder resources, the heuristics satisfy all connections that

can be routed on direct lightpaths respecting the channels’ bandwidth constraint. In the end, the

remaining connections, if any, are routed in multi-hop virtual paths if enough spare capacity exists on

the deployed lightpaths. The algorithms diverge on the order imposed on the lightpath selection and

on the order of selection of the connections that cannot be routed in single-hop virtual paths.

A more complex and elaborated methodology to the traffic grooming problem of throughput

maximization is presented in [22]. Making use of an auxiliary graph, the manipulation of its edges

(weight assignment and placement) allows not only for the achievement of different grooming policies

(minimization of the number of lightpaths, wavelength links or traffic hops), but also for the

23

accommodation of several network scenarios. It enables the specification, for each individual network

element, of the number of transceivers and wavelengths supported as well as of its grooming and

wavelength conversion capabilities. Unlike previously mentioned algorithmic approaches that start by

creating the virtual topology and later route the connections, the graph model defines the virtual

topology simultaneously to allocating the traffic demands: requests are selected in turn and carried

over the shortest path over the graph that may comprise already established lightpaths and/or demand

the creation of new lightpaths. Distinct solutions for the same problem can be attained by combining

different grooming policies and traffic selection schemes, the latter ones defining the order in which

connections are allocated.

On the other end of traffic grooming problems lies the cost minimization challenge. According to

a given cost model, the objective is to employ traffic aggregation at source and eventually at

intermediate nodes in combination with optical bypassing to attain the lowest network expenditures.

For a detailed multi-layer cost model (IP/MPLS, OTN and WDM layers) the reader is remitted to [23].

In [24], the authors present an Ilp and a heuristic model for the cost minimization problem in

optical impairment aware networks assuming expenditures to be related to the use of line, client,

regenerator, transponder and grooming cards. The work compares three distinct models: an all-optical

network scenario where only transponder and regenerator cards are employed, a translucent

configuration where grooming cards are employed for both traffic grooming and signal regeneration

and finally, a translucent scheme where the previous configuration is extended by allowing the use of

regenerator cards as well. Results conducted applying the developed models for each individual

scenario prove the grooming and regenerator card approach to be the enabler for the lowest

expenditures with the grooming card only solution coming closely behind.

In [25], the authors model the costs of the WDM and OTN layers and propose two network

configuration approaches: one where muxponder cards aggregate same source destination pairs and

another where OTN switches provide for traffic grooming at intermediate locations. The results of

simulations applying each model reveal that the use of OTN switches allows to reduce the number of

transponder cards significantly. The multi-layer optimization strategy employs optical bypassing when

intermediate grooming would only allow for marginal gains. By doing so, the number of regenerations

and OTN ports is lowered. In the end, the intermediate grooming approach is proven to provide for the

lowest overall costs, the expenditures associated with OTN switches offset by the cost savings in

transponder cards.

The introduction of mixed line rates in an optical network is analyzed in [26] as a means to

minimize network cost. With a primary objective of minimizing the total cost of optical line cards and a

secondary one of minimizing the average number of wavelengths used per link, the authors develop a

heuristic and recur to the previously introduced graph model. Traffic grooming is employed at

intermediate nodes and 10 and 100 Gbps line cards are considered. A test case applying single rate

models with either 10 or 100 Gbps line cards and a mixed rate model where both line cards are

allowed to coexist proved that the mixed line rate solution conceded for the lowest expenditures.

24

The greatest portion of the load that falls upon the optical transport network nowadays is traced

back to IP traffic, the accountable for the data services outgrow of voice. Though the links in IP

networks are unidirectional, IP streams are currently routed over symmetrical optical connections.

Under the assumption that savings could be attained if the two directions could be treated

independently, the authors of [27] model an asymmetrical traffic demand for an optical network based

on the quantification of the asymmetry of traffic of a real large IP backbone network. The referenced

work compares an approach where traffic is routed over bidirectional lightpaths and bidirectional

optical line cards are employed, and another where asymmetrical optical connections are established

and unidirectional line cards are used. The multi-layer cost model used included transponder, OTN

ports, router ports and regenerators and took the cost ratios between unidirectional and bidirectional

equipment in consideration. The simulations performed against the IP backbone network and optical

underlay network proved the asymmetrical optical connection approach to provide for the lowest

expenditures.

2.4 Conclusions

The current chapter focused on the Optical Transport Network standards and laid

considerations on both the electrical and optical layers defined in the Optical Transport Hierarchy. The

electrical layer signal’s formats, rates and overheads were discussed and the WDM network elements

and their association to the OTN optical layers exposed. Finally, the relevant OTN/WDM switch was

presented and its ability to provide for multi-granular management of the signals surpassing the optical

network highlighted.

Also presented in this chapter was the state of the art regarding the optical layer design and

optimization. On that topic, two approaches can be pursued when considering network optimization

models: the mathematical programming approach where linear programming formulations are used to

attain exact solutions and heuristic algorithms where the optimal results may not be achieved but

savings can be attained in regards to running times. The network optimization problems discussed in

this chapter comprised the Routing and Wavelength assignment in all-optical networks and the traffic

grooming problem in translucent networks.

On the matters of RWA methodologies, static Ilp formulations presented in the literature were

referenced and a listing on decoupled algorithms for the sub-problems of routing and wavelength

assignment were exposed.

In regards to the traffic grooming problem, two dual objectives were considered: throughput

maximization in resource scarcity scenarios and cost minimization in environment with resource

availability. A published Ilp model and three heuristics for the throughput maximization problem were

briefly discussed. In regards to the cost minimization challenge, works pertaining to comparative

studies on translucent and transparent configurations and single and mixed line rate networks were

presented. To finalize, a study on the cost benefits of employing asymmetrical optical circuits in

networks served with unidirectional traffic requests was mentioned. The study’s conclusions proved

that the asymmetrical lightpath solution was the most fit for the undertaken scenario.

25

3 Routing and Wavelength Assignment in

transparent DWDM networks

This chapter delves on Dense Wavelength Division Multiplexed Networks addressing planning

methodologies intended for their optimization. On that note, Routing and Wavelength Assignment

formulations are pursued as a means to minimize the number of wavelengths required to satisfy time-

invariant traffic demands in all-optical networks. A range of Integer Linear Programming formulations

applying distinct Ilp and traffic routing strategies are presented and scrutinized. Lastly, a heuristic

algorithm is pursued and put to test against the mathematical methodology in intent to draw

conclusions on its performance in regards to the quality of the solutions attained and running times.

26

3.1 Introduction

Dense Wavelength Division Multiplexed networks stand as a branch of optical networks

supporting the delivery of multiple signals over a single fiber by means of non-overlapped tightly

spaced wavelength channels. Multi-degree ROADM equipped DWDM network nodes have the ability

to switch wavelength signals from multiple incoming to outgoing fibers ports, enabling for mesh

configurations to be deployed. In cases where digital signal processing is restricted to the end-points

of wavelength channels, that is, no O/E/O conversion takes place at intermediate nodes, the networks

are said to be transparent or all-optical. In such scenarios, the routing of traffic demands falls upon

direct lightpaths.

The design of an all-optical network revolves around the resolution of the Routing and

Wavelength Assignment problem as addressed in the previous chapter. The following sections feature

Ilp formulations taking into account the static, time-invariant nature of the traffic requests. The

developed formulations derive from the study of the methodologies presented in [18]. The referenced

work presents a comprehensive set of static RWA ILP formulations for the cases of ring, multi-ring and

mesh topologies. The author follows a symmetrical routing approach taking into account solely the

requests in the direct direction. In the current chapter, the scope was widened to include asymmetrical

routing as well.

Further adaptations were performed in regards to the studies presented in [18]. Seeking for a

wider volume of comparison criteria, node-link methodologies were included to conduct studies

against the link-path approach followed by the referenced work. In the case of link-path formulations,

the set of paths between any two nodes with traffic demands is calculated in advance. In order to

diminish the problem’s complexity it is usual to consider only a subset of paths, common practice

being on settling for the k-shortest paths, k a pre-defined value. A review and comparative study of k-

shortest path algorithms is available at [28]. The link-path approach takes a globalized perspective

over the whole of the network, as opposed to the latter case of node-link methodologies in which there

is a localized approach. In such enunciations, there is no knowledge whatsoever on the possible

routes a lightpath can take. The problem takes into consideration units of flow (optical channels)

leaving and entering nodes and traveling specific links, complying with flow conservation laws.

3.2 General Problem Statement

The RWA problem can be defined as follows: given a graph 𝐺(𝑉, 𝐸) where 𝑉 corresponds to the

network nodes and 𝐸 stands for the bidirectional fiber links connecting them, a traffic matrix 𝑇

corresponding to the requested optical connections and a maximum value for the number of

wavelengths supported per fiber 𝑊, the goal is to establish the requested optical connections at the

expense of the minimum number of wavelengths. This measure is perceived as the total number of

distinct wavelengths assigned over all fiber links. The objective set lies as an enabler for better

distributing the load over the wavelength links such that the network can be prepared to undertake

further traffic demand. Subjected to constraints regarding the impossibility that two or more channels

are assigned the same wavelength in a common fiber, and the requirement that each optical channel

27

has the same wavelength reserved to it over all spanned fiber links (derived from the absence of

wavelength converters), the expected outcome is a virtual topology composed of the deployed

requested lightpaths.

The assumed bidirectional trait of the optical connection requests leaves room for two routing

approaches according to whether the reverse lightpaths are dependent or not on the direct ones. A

direct lightpath is considered a connection from a lowered indexed to a higher indexed node. The

symmetrical routing approach considers only the requests in the direct direction and mirrors the

attained results to the reverse direction. In turn, the asymmetrical methodology treats each direction

separately, allowing for a lightpath in the reverse direction to follow a different route than the one of

the direct lightpath in the opposed direction.

In the next sections, the node-link and link-path formulations applying both symmetric and

asymmetrical routing are presented. In common, the methodologies share the problem’s inputs and

notation as presented below.

Problem inputs:

A physical topology 𝐺 = (𝑉, 𝐸), consisting of a bidirectional graph, where 𝑉 is the set of

network nodes and 𝐸 the set of fiber links connecting the nodes. The number of arcs uniting

any two nodes is the same in both directions in results of the graph’s bidirectional trait.

Number of wavelength supported per fiber 𝑊;

Traffic matrix 𝑇 corresponding to the lightpath demand.∀ 𝑖, 𝑗 ∈ 𝑁, 𝑡𝑖𝑗 denotes the number of

optical channels to establish among source-destination pair (𝑖, 𝑗).

Assumptions:

The network is laid out in a mesh topology;

The network nodes have no wavelength conversion capabilities: lightpaths must be assigned

the same wavelength on all physical links spanned;

The transceivers featured in the network nodes are tunable to any of the available

wavelengths on the fiber;

The fibers’ optical impairments are despised removing the need for regeneration of the optical

signals thus assumed to be able to travel any considered distance;

Optical connection requests are bidirectional.

3.2.1 RWA node-link formulation applying asymmetrical routing

As previously mentioned, the node-link approach is centered on each individual node and the

traffic flows that enter or leave them in compliance with flow conservation laws. In this particular case,

the node-link formulation comprises asymmetric routing disjoining the direct connections from the

reverse ones. This routing scheme can be applied to problems considering both bidirectional or

unidirectional traffic requests. The notation, problem inputs and variables used within this scope are

outlined below:

Notation:

𝑚 and 𝑛 denote the endpoints of an unidirectional fiber link;

28

𝑖 and 𝑗 denote the origin and destination of a lightpath. These endpoints may not be adjacent

for an optical channel can traverse more than one fiber link on its route.

Variables:

𝐿𝑖𝑗𝑚𝑛,𝑤

: Number of lightpaths originated at node 𝑖 and terminated at node 𝑗 traversing fiber

link (𝑚, 𝑛) on wavelength 𝑤. 𝐿𝑖𝑗𝑚𝑛,𝑤 ∈ [0, 𝑃𝑚𝑛], 𝐿𝑖𝑗

𝑚𝑛,𝑤 ∈ 𝛮0;

𝑍𝑤: Denotes whether wavelength 𝑤 is assigned to at least one of the lightpaths in the

network (𝑍𝑤 = 1 ) or otherwise (𝑍𝑤 = 0). 𝑍𝑤 ∈ {0,1}.

Parameters:

𝑃𝑚𝑛: Number of fibers interconnecting nodes 𝑚 and 𝑛. 𝑃𝑚𝑛 ≥ 1 if 𝑚 and 𝑛 are physically

adjacent and 𝑃𝑚𝑛 = 0 otherwise. The fiber’s bidirectional feature makes it so that 𝑃𝑚𝑛 =

𝑃𝑛𝑚 , ∀ 𝑛, 𝑚 ∈ 𝑉.

Formulation:

Objective function:

(3.1) 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 ∑ 𝑍𝑤

𝑤 ∈𝑊

Constraints:

(3.2) ∑ ∑ 𝐿𝑖𝑗𝑖𝑛,𝑤

𝑛∈𝑉𝑤 ∈ 𝑊= 𝑡𝑖𝑗 ∀ 𝑖, 𝑗 ∈ 𝑉

(3.3) ∑ ∑ 𝐿𝑖𝑗𝑚𝑖,𝑤

𝑚∈𝑉𝑤 ∈ 𝑊= 0 ∀ 𝑖, 𝑗 ∈ 𝑉

(3.4) ∑ ∑ 𝐿𝑖𝑗𝑚𝑗,𝑤

𝑚∈𝑉𝑤 ∈ 𝑊= 𝑡𝑖𝑗 ∀ 𝑖, 𝑗 ∈ 𝑉

(3.5) ∑ ∑ 𝐿𝑖𝑗𝑗𝑛,𝑤

𝑛∈𝑉𝑤 ∈ 𝑊= 0 ∀ 𝑖, 𝑗 ∈ 𝑉

(3.6) ∑ 𝐿𝑖𝑗𝑚𝑘,𝑤

𝑚 ∈ 𝑉= ∑ 𝐿𝑖𝑗

𝑘𝑛,𝑤

𝑛 ∈ 𝑉 ∀ 𝑖, 𝑗, 𝑘 ∈ 𝑉 ; 𝑘 ≠ 𝑖, 𝑗 ; 𝑤 ∈ 𝑊

(3.7) ∑ ∑ 𝐿𝑖𝑗𝑚𝑛,𝑤

𝑗∈𝑉𝑖 ∈ 𝑉≤ 𝑍𝑤𝑃𝑚𝑛 ∀ 𝑚, 𝑛 ∈ 𝑉; 𝑤 ∈ 𝑊

Equation (3.1) states the objective function of minimizing the number of wavelengths used.

Restrictions (3.2) to (3.5) assure that all traffic requests are satisfied. The wavelength continuity

constraint is accounted for in equation (3.6) and inequality (3.7) makes sure that one wavelength is

assigned to at most one optical channel on every fiber link in compliance with the clash constraint.

3.2.2 RWA node-link formulation applying symmetrical routing

When dealing with bidirectional traffic requests it is common, as a means to reduce the

problem’s dimension and subsequently its complexity, to restrict the problem to a single direction. The

drawback, however, is that by doing so, limitations are placed upon the space of possible solutions,

bounded to those where the routing and wavelength assignment is the same for both directions. Given

such scenario, it must be guaranteed that if an optical channel in the direct direction between node

pair (𝑖, 𝑗) is assigned wavelength 𝑤 on physical link (𝑚, 𝑛), the same wavelength is reserved for the

optical channel between pair (𝑗, 𝑖) on link (𝑛, 𝑚) and therefore cannot be assigned to any of the

remaining traffic requests. The formulation for this particular case is very similar to the one presented

in section 3.2.1 and only the differences will be stated below:

29

Where ∀ 𝑖, 𝑗 ∈ 𝑁 feature in constraints (3.2) to (3.6), it must also be stated that 𝑗 > 𝑖;

Constraint (3.7) must become:

(3.8) ∑ ∑ 𝐿𝑖𝑗𝑚𝑛,𝑤

𝑗∈𝑉,𝑗>𝑖𝑖 ∈ 𝑉+ 𝐿𝑖𝑗

𝑛𝑚,𝑤 ≤ 𝑍𝑤𝑃𝑚𝑛 ∀ 𝑚, 𝑛 ∈ 𝑉; 𝑤 ∈ 𝑊

3.2.3 RWA link-path formulation applying asymmetrical routing

The link-path approach requires some previous computation in order to determine the set of

available physical routes in between any two nodes with traffic requests. These offline computed paths

are taken as an input to the problem and allow, when in comparison with the previous formulations, to

reduce the formulations’ complexity. The notation, problem inputs and variables to the formulation

applying asymmetrical routing are as described below.

Notation:

𝐾 denotes the set of node pairs (𝑠(𝑘), 𝑑(𝑘)) among which there is at least one traffic

demand;

𝐴 denotes the set of unidirectional network arcs such that there is at least one physical link

with starting point 𝑠(𝑎) and ending point 𝑑(𝑎).

Variables:

𝑃𝑘: Set of available directed paths uniting nodes 𝑠(𝑘) and 𝑑(𝑘). These routes are to be

calculated in advance, prior to the problem’s execution. The arcs crossed by each path on

route from source to destination are denoted as 𝑎𝑝𝑘;

𝑃𝑘𝑎: Set of possible paths between node pair 𝑘 that traverse arc 𝑎, that is, such that 𝑎 ∈

𝑎𝑝𝑘 ∀ 𝑝𝑘 ∈ 𝑃𝑘;

𝐿𝑝𝑘𝑤 : Number of lightpaths between the end-points of request 𝑘 routed over path 𝑝𝑘 on

wavelength 𝑤. 𝐿𝑝𝑘𝑤 ∈ [0, min(𝐹𝑎)] , 𝑎 ∈ 𝑎𝑝𝑘

;

𝑍𝑤: Denotes whether wavelength 𝑤 was or not assigned to any of the established

lightpaths. 𝑍𝑤 ∈ {0,1} .

Parameters:

𝐹𝑎: Number of fiber links on arc 𝑎.

Formulation:

Objective function:

(3.9) 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 ∑ 𝑍𝑤

𝑤 ∈𝑊

Constraints:

(3.10) ∑ ∑ 𝐿𝑝𝑘𝑤

𝑝𝑘 ∈ 𝑃𝑘

𝑤 ∈𝑊

= 𝑡𝑘 ∀ 𝑘 ∈ 𝐾, 𝑤 ∈ 𝑊

(3.11) ∑ ∑ 𝐿𝑝𝑘𝑤

𝑝𝑘∈𝑃𝑘𝑎𝑘∈𝐾

≤ 𝑍𝑤𝐹𝑎 ∀ 𝑎 ∈ 𝐴, 𝑤 ∈ 𝑊

Equation (3.9) states the objective function. Constraint (3.10) assures that all traffic requests are

satisfied and restraint (3.11) assures that the clash constraint is respected. By defining variable 𝐿𝑝𝑘𝑤

the wavelength continuity constraint is implicitly accounted for.

30

3.2.4 RWA link-path formulation applying symmetrical routing

For the particular case where symmetrical routing is applied, only the required changes to the

above formulation will be stated. To reduce the problem to a single direction it must assured that set 𝐾

complies with 𝑠(𝑘) < 𝑑(𝑘). To account for the fact that wavelengths assigned to a lightpath in one

direction must be reserved to the lightpath in the opposite direction in all segments of the shared path,

equation (3.11) must be changed to:

(3.12) ∑ ∑ 𝐿𝑝𝑘𝑤

𝑝𝑘∈ {𝑃𝑘,𝑎 𝑃𝑘

𝑎′}𝑘∈𝐾≤ 𝑍𝑤𝐹𝑎 ∀ 𝑎 , 𝑎′ ∈ 𝐴, 𝑤 ∈ 𝑊

, where 𝑠(𝑎) = 𝑑(𝑎′) 𝑎𝑛𝑑 𝑑(𝑎) = 𝑠(𝑎′).

3.3 Results of simulations applying Ilp methodologies

The current section presents the results obtained by running simulations with the developed ILP

models for a number of real life transport networks for which physical topologies and network

parameters can be found in [29] and in Appendix A. The link-path model is compared against the

node-link one not only in terms of the quality of the solutions but also in regards to the computational

effort required for their achievement. Post to such analysis, network and traffic traits are explored and

their impact on the solutions considered. Conclusions are drawn for every analysis performed.

When applying link-path Ilp formulations, 𝑃𝑘 was calculated according to the k-shortest path

algorithm described in Appendix B.1, and the value chosen for 𝑘 fixed to 7. It was assumed, unless

stated otherwise, that 160 wavelengths were available per fiber link. For every test case, a set of traffic

matrixes was randomly generated according to a uniform discrete distribution. Hence, a finite number

of integer values ranging from 0 to a top value M were equally likely to feature as the requested

number of lightpaths among any two nodes. To subject the networks to distinct traffic loads, parameter

M was increased in unitary steps, 𝑀 ∈ [𝑀𝑚𝑖𝑛 , 𝑀𝑚𝑎𝑥] to attain traffic matrixes with varying traffic

volumes. The algorithm responsible for generating the traffic matrixes is described in Appendix B.2.

3.3.1 Node-Link and Link-Path Comparison

In order to study how the two methodologies performed against each other, it was chosen to

conduct simulations on two real life networks of different dimensions, the Via Network and the Abilene

Core Network. The most relevant aspects of these networks are described in the Table 3.1. The

criteria used for comparison was the computational effort measured in units of time required to attain

the exact solution for the static RWA problem and the solutions themselves. The bidirectional traffic

requests were attended with asymmetrical routing approaches due to expected higher computational

times. All tests were performed by a Mac Book Pro (processor 2.53 GHz Intel Core 2 Duo, memory 4

GB 1067 MHz), using the Cplex [15] libraries for C++. The complete set of results is presented in the

tables below where 𝑛𝑙 refers to node-link simulations and 𝑙𝑝 to link-path ones.

31

Table 3.1: Network Parameters

Network Via Abilene Core

Number of Nodes 9 10

Number of bidirectional links 12 13

Mean Nodal Degree 2.67 2.60

Via Network

Table 3.2: Required number of wavelengths employing link-path and node-link formulations

M 𝜆𝑛𝑙 𝜆𝑙𝑝 ∆𝜆 = 𝜆𝑛𝑙 − 𝜆𝑙𝑝

1 5 5 0

2 9 9 0

3 12 12 0

4 17 17 0

5 21 21 0

6 26 26 0

7 29 29 0

8 34 34 0

9 38 38 0

10 42 42 0

11 46 46 0

12 49 49 0

Table 3.3: Running times employing link-path and node-link formulations

M 𝑡𝑛𝑙 [𝑠] 𝑡𝑙𝑝 [𝑠] 𝑡𝑙𝑝 𝑡𝑛𝑙 ⁄ [%]

1 588.6 11.4 1.9

2 295.9 41.6 14.1

3 684.9 31.5 4.6

4 527.3 41.5 7.9

5 981.3 30.0 3.1

6 710.9 24.9 3.5

7 602.8 27.2 4.5

8 1036.2 31.7 3.1

9 425.4 23.9 5.6

10 542.8 23.8 4.4

11 311.8 23.3 7.5

12 587.5 18.1 3.1

Abilene Core Network

Table 3.4: Required number of wavelengths employing link-path and node-link formulations

M 𝜆𝑛𝑙 𝜆𝑙𝑝 ∆𝜆 = 𝜆𝑛𝑙 − 𝜆𝑙𝑝

1 7 7 0

2 14 14 0

3 21 21 0

4 26 26 0

5 33 33 0

6 40 40 0

7 47 47 0

8 54 54 0

9 60 60 0

10 67 67 0

11 74 74 0

12 80 80 0

32

Table 3.5: Running times employing link-path and node-link formulations

M 𝑡𝑛𝑙 [𝑠] 𝑡𝑙𝑝 [𝑠] 𝑡𝑙𝑝 𝑡𝑛𝑙⁄ [%]

1 5119.83 30.41 0.6

2 2605.18 31.21 1.2

3 3241.1 41.99 1.3

4 5252.95 56.5 1.1

5 4115.11 82.08 2.0

6 4480.27 39.59 0.9

7 3281.23 68.58 2.1

8 4674.36 61.04 1.3

9 2026.18 36.9 1.8

10 5314.12 47.22 0.9

11 2691.4 46.97 1.7

12 3196.34 37.35 1.2

The tables above show that, for the test cases conducted, the results attained applying both

formulations converge, at all times, to the same results concerning the minimum number of

wavelengths necessary to satisfy traffic demand. In regards to the computational effort required, the

ones observed for the link-path methodologies are always considerable lower. Furthermore, as the

networks’ dimension increases, the differences become more accentuated: for the 9 nodes network,

the link-path model achieved results taking only 1.9 to 14.1 percent of the time taken by the node-link

one, while for the Abilene Core network, the values observed ranged from 0.6 to 2.1 percent.

The superior time-wise performance of link-path formulations can be traced to the reduction of

complexity that comes with bounding the routing options to a set of paths calculated prior to the

problem’s execution. It must be noted, however, that due to this higher bound imposed on the

candidate paths between the nodes, the node-link approaches may prove more satisfying in

minimizing the number of wavelengths in cases where large networks with high mean nodal degrees

are considered and where the amount of requested traffic between the nodes is rather higher than the

one considered in the targeted test cases.

As the traffic demand increases and more lightpaths are required to be established, the number

of physical routes that must be allocated increases accordingly. As so, the resource consumption is

expected to reflect such trend and climb to higher values. As observed in the tables above referring to

the minimum number of wavelengths necessary to respond to traffic demand, the values vary in direct

proportionality to parameter M which stands associated to the volume of inputted traffic, thereby

confirming the assumption made.

3.3.2 Running times’ sensitivity to network’s dimensions

The intent of the current section is to determine whether a pattern exists linking the traffic load

and the network’s dimensions to the computational times required to attain solutions. With test cases

targeting three networks with distinct characteristics, a set of bidirectional traffic matrices, one for each

value of M in a range from one to twelve, was assigned to each. The results for the simulations

applying the link-path symmetrical routing model to those scenarios are showcased in the tables

below. As displayed in Tables 3.7 and 3.8, the simulations’ times oscillate as the traffic load

33

increases, making it impossible to discern a dependency or trend line. However, for all scenarios

tested and for the same value of M, the computational effort always increases proportionally to the

network’s dimension. This situation reflects the RWA Ilp problem’s NP-hard trait.

Table 3.6: Network Parameters

Network Abilene Cesnet Nsfnet

Number of Nodes 10 12 14

Number of bidirectional links 13 19 21

Mean Nodal Degree 2.60 3.17 3.00

Table 3.7: Computational time’s sensitivity to traffic load and network’s dimension

Computational times [s]

M Via Vbns Nsfnet

1 1.14 8.04 139.13

2 1.11 5.85 147.63

3 1.02 8.75 42.55

4 0.65 10.28 346.66

5 0.76 8.69 526.01

6 0.69 13.64 271.57

7 0.77 18.26 70.31

8 2.18 12.24 120.29

9 0.62 16.99 58.85

10 0.5 17.93 60.76

11 0.72 25.138 49.03

12 0.58 27.881 44.91

3.3.3 Symmetric and asymmetrical routing comparison

When dealing with symmetric traffic patterns, either symmetric or asymmetrical routing

approaches can be pursued. The reduction of the problem’s dimension by restricting the lightpaths to

establish to a single direction causes for the reduction of the number of variables and constraints and

provides for the symmetrical routing methodology’s lower computational times as supported by Tables

3.8 and 3.9. These correspond to the results of simulations applying Link path models to the Via and

Vbns networks.

Table 3.8: Via Network results applying symmetric and asymmetrical routing

M 𝜆𝑠𝑦𝑚𝑚𝑖𝑛 𝜆𝑎𝑠𝑦𝑚

𝑚𝑖𝑛 𝜆𝑎𝑠𝑦𝑚𝑚𝑖𝑛 − 𝜆𝑠𝑦𝑚

𝑚𝑖𝑛 𝑡𝑠𝑦𝑚 [𝑠] 𝑡𝑎𝑠𝑦𝑚 [𝑠] 𝑡𝑠𝑦𝑚 𝑡𝑎𝑠𝑦𝑚⁄ [%]

1 7 7 0 2.6 29.2 8.9

2 11 11 0 6.5 35.1 18.5

3 17 17 0 4.3 23.1 18.6

4 22 22 0 3.3 24.6 13.4

5 29 29 0 5.0 29.1 17.2

6 33 33 0 5.2 30.4 17.1

7 39 39 0 5.3 28.3 18.7

8 43 43 0 4.4 21.9 20.1

9 49 49 0 3.9 18.2 21.4

10 55 55 0 4.1 18.4 22.3

11 60 60 0 4.7 25.4 18.5

12 65 65 0 4.1 19.8 20.7

34

Table 3.9: Vbns Network results applying symmetric and asymmetrical routing

M 𝜆𝑠𝑦𝑚𝑚𝑖𝑛 𝜆𝑎𝑠𝑦𝑚

𝑚𝑖𝑛 𝜆𝑎𝑠𝑦𝑚𝑚𝑖𝑛 − 𝜆𝑠𝑦𝑚

𝑚𝑖𝑛 𝑡𝑠𝑦𝑚 [𝑠] 𝑡𝑎𝑠𝑦𝑚 [𝑠] 𝑡𝑠𝑦𝑚 𝑡𝑎𝑠𝑦𝑚⁄ [%]

1 10 10 0 15.2 128.2 11.8

2 19 19 0 29.9 471.1 6.3

3 27 27 0 90.3 251.0 36.0

4 35 35 0 27.4 246.1 11.1

5 46 46 0 24.9 266.1 9.4

6 57 57 0 31.5 275.3 11.4

7 63 63 0 39.0 224.1 17.4

8 73 73 0 40.9 288.2 14.2

9 83 83 0 36.9 236.8 15.6

10 91 91 0 30.3 240.4 12.6

11 101 101 0 19.6 199.2 9.8

12 109 109 0 21.2 170.5 12.4

There can be, however, a drawback to this approach as evidenced by Figure 3.2. Considering

the problem of satisfying the traffic matrix of Figure 3.1 for the equaly depicted 4 nodes network laid

out as a bidirectional ring, the solutions obtained employing the two methodologies diverged. In fact,

the results for asymmetrical routing proved to be more economic in terms of wavelength usage than

those of the symmetrical counterpart. The explanation behind this difference comes with the larger

space of possible RWA options that the asymmetric method allows for.

Figure 3.1: Physical topology and traffic matrix used for comparative example

Figure 3.2: Symmetrical routing (left) and asymmetrical routing (right) results

Despite this observation, the specific case mentioned is not always the rule: in regards to the

simulations accounted for in Tables 3.8 and 3.9, the minimum number of wavelengths obtained proved

to be the same for both routing scenarios. Upon such circumstances, one can conclude a tradeoff

between computational time and the possible compromise of the optimality of the solution must be

made when deciding which routing scheme to apply.

35

3.3.4 Results for networks with distinct mean nodal degrees

To evaluate how the network’s mean nodal degree conditions the minimum number of

wavelengths required to satisfy all requests, simulations were conducted considering distinct physical

topologies while keeping the number of network nodes constant. The same bidirectional traffic matrix

attained by setting parameter M equal to 5 was used throughout all tests performed. Ten different

networks were generated by changing the way in which 12 nodes were interconnected. For every

physical layout, it was chosen to make it so that all nodes had the same degree. Starting from a ring

layout and evolving to the mesh topology scenario in which all nodes are connected, RWA link-path

symmetrical routing formulations were used to solve the set of problems. Results obtained and

presented in Figure 3.3 show a decrease in the number of wavelengths as the Mean Nodal Degree

increases. The described behavior can be explained by the expansion of the number of possible paths

between each pair of nodes that allows for more routing options and for a better load distribution.

Two real life networks were also analyzed, both with 14 nodes but with distinct Mean Nodal

Degrees as showcased in Table 3.10. The networks were subjected to tests with the same set of input

matrixes, one for each value of M in a range from 1 to 12. As before, the link-path model was chosen

to conduct the simulations. The impact of the mean nodal degree was made apparent once again as

proven in Figure 3.4. Not only the network with higher connectivity conceded for a lower number of

wavelengths but also the gap between the results for the two networks increased as the traffic load

escalated.

Figure 3.3: Effect of the mean nodal degree on the required number of wavelengths

Table 3.10: Network Parameters

Network Vbns Cesnet Number of Nodes 12 12

Number of bidirectional links 17 19 Mean Nodal Degree 2.83 3.17

Figure 3.4: Comparison for networks with distinct mean nodal degrees

0

20

40

60

80

2 3 4 5 6 7 8 9 10 11

Nu

mb

er

of

Wav

ele

ng

ths

Mean Nodal Degree

Sensitivity to the mean nodal degree

0

50

100

150

1 2 3 4 5 6 7 8 9 10 11 12

Nu

mb

er

of

Wav

ele

ng

ths

M

Comparison for networks with distinct mean nodal degrees

CesnetNetwork

Vbns Network

36

3.4 Heuristic Methodology

The Ilp formulations presented in the first sections of this chapter guarantee an optimal solution

to the RWA problem by satisfying traffic demand in conformity with the imposed restrictions at the

expense of the lowest number of wavelengths. However, such problems are NP-Complete [20] and

the computational effort required to achieve exact solutions increases exponentially with the problems’

complexity. Such trend was partially analyzed in 3.3.2 where it was noted the running times of

simulations featuring networks with mismatched number of nodes and links were dependent on the

networks’ size, varying in direct proportionality. With the purpose to overcome the inherent complexity

of Ilp formulations, it is common to recur to heuristic methodologies. In order to provide for

formulations that could take in real-life networks of considerable reach, one such approach was taken

to tackle the RWA problem.

The main concept surrounding the developed heuristic was that of architecting an algorithm at

the expense of very little complexity, applying simple concepts based on network characteristics and

traffic demand. Notwithstanding the drive for compelling results, the task to develop an original RWA

heuristic was faced as a study, primarily. On the matters of selecting strategies for the RWA problem,

the option fell upon applying a routing algorithm and a wavelength assignment one inspired on the

listings of methodologies for the decoupled RWA sub-problems presented in [20]. The emphasis was

then laid upon a variety of original traffic selection schemes unattached from literary references to

manipulate the information provided by the problem. These were perceived as the motor for the

search of satisfying solutions. Backed up by the assumption that the routing and wavelength

assignment conducted for each attended demand would account for reduced running times, a choice

was made to solve the problem once for every scheme defined. In result, the range of iterations

concedes for a broader space of feasible solutions from which the one accounting for the lowest

number of wavelengths is to be selected as the output to the heuristic. The traffic selection schemes,

routing and wavelength assignment procedures and a step-by-step description on the present

heuristic are showcased in the remaining sections.

3.4.1 Traffic Selection Schemes

Crucial to the evolution of the algorithm towards a final solution, the traffic selection schemes

govern the ways in which demands are satisfied. Responsible for providing an ordering to the set of

requested optical channels, the selection process stems in a sequential fashion, a demand attended in

turn following the determination of the links spanned and wavelengths assigned at each segment of

that path. As opposed to an Ilp model in which a multitude of solutions is exhausted until the final

outcome is achieved, each combination of a unique traffic selection scheme with a common routing

and wavelength assignment algorithm confines the problem to the space of a single solution that may

or may not be feasible. The previously mentioned choice over RWA approaches of reduced

complexity came in intent to delegate the processing capacity to the exploration of a variety of traffic

selection schemes so as to expand the space of solutions. The traffic selection schemes were chosen

37

so that the algorithm could evolve based on information on the current state of resources. A localized

approach was pursued taking into account the number of available links with spare wavelengths at the

end-nodes of each request. It was chosen not to consider the availability of resources in the spanned

links of candidate path(s) uniting those end-points so as not to compromise the computational times.

The amount of demands yet left to satisfy for each request was also taken into consideration when

developing the traffic selection schemes.

Each traffic selection scheme is characterized by a cost 𝐶𝑡𝑠𝑠𝑟𝑒𝑞

assigned to each request. The

assigned costs weight on the current wavelength consumption at the fiber links delimited by the

source or destination node of the current request and on how many of its demands have yet to be

attended. The list is iterated as many times as the number of traffic demands until none are left to

attend and the list is empty. To explain how the costs are calculated the following notation must be

presented:

𝑳𝒊𝒊𝒏 Number of links with available wavelengths that have node 𝑖 as the terminating node;

𝑳𝒊𝒐𝒖𝒕 Number of links with available wavelengths that have node 𝑖 as the starting node;

𝑫𝒓𝒆𝒒 Number of connections yet to be satisfied for request 𝑟𝑒𝑞.

Parameter 𝐶𝑡𝑠𝑠𝑟𝑒𝑞

is calculated as follows:

Table 3.11: Traffic Selection Schemes and associated cost metrics

Traffic Selection Scheme Cost metric

Weighted Connectivity 𝐶𝑡𝑠𝑠𝑟𝑒𝑞

= 0,5 ∗ 𝐿𝑑(𝑟𝑒𝑞)𝑖𝑛 + 0,5 ∗ 𝐿𝑠(𝑟𝑒𝑞)

𝑜𝑢𝑡

Connectivity 𝐶𝑡𝑠𝑠𝑟𝑒𝑞

= max(𝐿𝑑(𝑟𝑒𝑞)𝑖𝑛 , 𝐿𝑠(𝑟𝑒𝑞)

𝑜𝑢𝑡 )

Demands Left 𝐶𝑡𝑠𝑠𝑟𝑒𝑞

= 𝐷𝑟𝑒𝑞

Resource Availability per Demand 𝐶𝑡𝑠𝑠𝑟𝑒𝑞

= max(𝐿𝑑(𝑘)

𝑖𝑛 , 𝐿𝑠(𝑘)𝑜𝑢𝑡 )

𝐷𝑘

Weighted Resource Availability per Demand 𝐶𝑡𝑠𝑠𝑟𝑒𝑞

= 0,5 ∗ 𝐿𝑑(𝑘)

𝑖𝑛 + 0,5 ∗ 𝐿𝑠(𝑘)𝑜𝑢𝑡

𝐷𝑘

Notice that at this point, no mention was made to the order, highest to lowest cost or

otherwise, applied to set of requests. With the goal set to perform a more extensive research and

conditioned by the perception that a given order is not always guaranteed to outperform the other, it

was chosen to run the problem twice for every defined cost metric, one where the requests of higher

cost are chosen first and another where the lowest cost one is preferred. In doing so, the count of

Traffic Selection Schemes was elevated to ten, as was the number of iterations and of achieved

outcomes. The set of Traffic Selection Schemes 𝑇𝑆𝑆 is given by {𝑡𝑠𝑠1 , 𝑡𝑠𝑠2, … , 𝑡𝑠𝑠10}, where each 𝑡𝑠𝑠𝑘

is characterized by an order 𝑂𝑡𝑠𝑠𝑘 ∈ {𝐿𝑜𝑤𝑒𝑠𝑡 − 𝑓𝑖𝑟𝑠𝑡, 𝐻𝑖𝑔ℎ𝑒𝑠𝑡 − 𝑓𝑖𝑟𝑠𝑡} and by a cost metric 𝐶𝑡𝑠𝑠𝑘 .

∀ 𝑘 ∈ [1,10], 𝑘 𝑚𝑜𝑑 2 ≠ 0 , 𝐶𝑡𝑠𝑠𝑘 = 𝐶𝑡𝑠𝑠𝑘+1 , 𝑂𝑡𝑠𝑠𝑘 = 𝐿𝑜𝑤𝑒𝑠𝑡 − 𝑓𝑖𝑟𝑠𝑡, 𝑂𝑡𝑠𝑠𝑘+1

= 𝐻𝑖𝑔ℎ𝑒𝑠𝑡 − 𝑓𝑖𝑟𝑠𝑡.

38

3.4.2 Routing and wavelength Assignment Algorithm

Whenever a traffic request is selected, an optical channel is required to be set up between its

end points by means of the determination of the set of fiber links traversed and wavelength assigned

at each composing segment of that route. The review on the methodologies presented in [20], inspired

an original algorithm based of the first-fit wavelength assignment and shortest path routing

methodologies. The aforementioned first fit (FF) wavelength assignment policy requires wavelengths

at each fiber link to be numbered. Considering the current context where it is assumed no wavelength

converters are available, a first fist approach determines the selected wavelength to be the lowest

numbered one available on all segments of a given path. In regards to the optical channels’ routing,

the shortest path algorithm bases its choice on the physical hop count of candidate paths, establishing

the selected route as the one spanning the least number of links.

In order to fit both methodologies into an integrated algorithm two approaches were considered:

either to determine the shortest path route and apply the FF policy for the determination of the

selected wavelength, or to give preferential treatment to the First Fit assignment component of the

algorithm. This last solution would comprise the determination of the subset of paths where a FF

policy would outcome the lowest numbered wavelength that could be assigned to a requested optical

channel. In the end, the selection would fall upon the shortest path among those candidate routes.

Eventually, after performing a set of simulations employing both approaches and the Traffic Selection

Schemes mentioned above, it was concluded that the second option would provide for more satisfying

results, hence being the one chosen.

3.4.3 Integrated and Iterative algorithm

Following the expositions of the Traffic Selection Schemes and RWA algorithm supporting the

developed heuristic, a set by set description is carried out in the figure bellow.

Step 1 Make 𝑘 = 0;

Step 2 Increment 𝑘 by one unit. If 𝑘 ≡ 11, move over to Step 12. Otherwise select Traffic

Selection Scheme 𝑡𝑡𝑠𝑘.

Step 3 Insert all the traffic requests into list 𝐿𝑟𝑒𝑞;

Step 4 Calculate, for every traffic request, the associated cost 𝐶𝑡𝑡𝑠𝑘

𝑟𝑒𝑞;

Step 5 Sort list 𝐿𝑟𝑒𝑞 according to the specified order 𝑂𝑡𝑡𝑠𝑘;

Step 6 Select the first traffic request from 𝐿𝑟𝑒𝑞;

Step 7 Route and assign a wavelength to one demand of the selected traffic request in

compliance with the First Fit Shortest Path algorithm developed;

Step 8 Decrease the number of demands of the selected traffic request (𝐷𝑟𝑒𝑞 = 𝑟𝑒𝑞 − 1).If

all the demands have been attended (𝐷𝑟𝑒𝑞 ≡ 0) remove the traffic request from list

𝐿𝑟𝑒𝑞;

39

Step 9 If no more traffic requests are left to satisfy 𝐿𝑟𝑒𝑞 = ∅ , store the end result

𝑤𝑡𝑡𝑠𝑘 regarding the number of wavelengths used to satisfy all the requests and return

to step 2. Otherwise, continue; Step 10 Update, if necessary, the values of 𝐿𝑑(𝑟𝑒𝑞)

𝑖𝑛 and 𝐿𝑠(𝑟𝑒𝑞)𝑜𝑢𝑡 , where 𝑟𝑒𝑞 is the attended

request. Update the cost 𝐶𝑡𝑡𝑠𝑘

𝑟𝑒𝑞 of all requests affected by changes, if relevant, to

variables 𝐿𝑑(𝑟𝑒𝑞)𝑖𝑛 , 𝐿𝑠(𝑟𝑒𝑞)

𝑜𝑢𝑡 and 𝐷𝑟𝑒𝑞 ;

Step 11 Return to step 5;

Step 12 Select the most satisfying result from the ones obtained by means of iterations

through the set of Traffic Selection Schemes, corresponding to min(𝑤𝑡𝑡𝑠𝑘) , ∀ 𝑘 ∈

[1,10].

Figure 3.5: Step by step description of the heuristic algorithm

3.5 Ilp and Heuristic methodologies comparison

In order to attest to the quality of the developed heuristic, a comparison with the classic Ilp

formulations was due. Considering five real life networks with disparate number of nodes and fiber

links, the number of wavelengths and the running times attained were taken as comparison criteria.

The networks were chosen so that an analysis could be performed on the influence of the networks’

dimensions. Also, for networks with the same number of nodes, the traffic matrixes were shared in

order to establish an influence of the mean nodal degree on the heuristic results. The network’s most

relevant aspects are resumed in Table 3.12. When employing Ilp formulations, link-path routing

methodologies were applied and the number k of pre-computed paths was fixed to 7. Both models

employed symmetrical routing. The results are presented in the tables below.

Table 3.12: Network Parameters

Network Vbns Cesnet Nsfnet Italy Arnes

Number of Nodes 12 12 14 14 15

Number of bidirectional links 17 19 21 29 20

Mean Nodal Degree 2.83 3.17 3.00 4.14 2.35

Table 3.13: Number of required wavelengths applying Ilp models

Number of wavelengths 𝜆𝐼𝐿𝑃𝑚𝑖𝑛

M Vbns Cesnet Nsfnet Italy Arnes

1 10 8 6 6 17

2 19 14 14 10 35

3 27 20 19 14 48

4 35 25 26 19 68

5 46 33 32 23 83

6 57 40 40 30 102

7 63 45 45 33 119

8 73 51 52 38 133

9 83 59 58 43 152

10 91 64 65 48 170

11 101 72 71 51 185

12 109 78 78 57 203

40

Table 3.14: Comparison on the required wavelengths applying Ilp and heuristic models

Number of wavelengths 𝜆ℎ𝑒𝑢𝑚𝑖𝑛 and comparison to 𝜆𝐼𝐿𝑃

𝑚𝑖𝑛

Vbns Cesnet Nsfnet Italy Arnes

M 𝜆𝐻𝑒𝑢𝑚𝑖𝑛

𝜆𝐻𝑒𝑢𝑚𝑖𝑛 − 𝜆𝐼𝐿𝑃

𝑚𝑖𝑛

𝜆𝐼𝐿𝑃𝑚𝑖𝑛

[%] 𝜆𝐻𝑒𝑢𝑚𝑖𝑛

𝜆𝐻𝑒𝑢𝑚𝑖𝑛 − 𝜆𝐼𝐿𝑃

𝑚𝑖𝑛

𝜆𝐼𝐿𝑃𝑚𝑖𝑛

[%] 𝜆𝐻𝑒𝑢𝑚𝑖𝑛

𝜆𝐻𝑒𝑢𝑚𝑖𝑛 − 𝜆𝐼𝐿𝑃

𝑚𝑖𝑛

𝜆𝐼𝐿𝑃𝑚𝑖𝑛

[%] 𝜆𝐻𝑒𝑢𝑚𝑖𝑛

𝜆𝐻𝑒𝑢𝑚𝑖𝑛 − 𝜆𝐼𝐿𝑃

𝑚𝑖𝑛

𝜆𝐼𝐿𝑃𝑚𝑖𝑛

[%] 𝜆𝐻𝑒𝑢𝑚𝑖𝑛

𝜆𝐻𝑒𝑢𝑚𝑖𝑛 − 𝜆𝐼𝐿𝑃

𝑚𝑖𝑛

𝜆𝐼𝐿𝑃𝑚𝑖𝑛

[%]

1 10 0.00 8 0.00 7 16.67 6 0.00 19 11.76

2 19 0.00 15 7.14 15 7.14 11 10.00 35 0.00

3 28 3.70 21 5.00 21 10.53 16 14.29 50 4.17

4 35 0.00 26 4.00 28 7.69 20 5.26 69 1.47

5 46 0.00 34 3.03 34 6.25 25 8.70 84 1.20

6 57 0.00 42 5.00 43 7.50 31 3.33 103 0.98

7 64 1.59 47 4.44 47 4.44 36 9.09 119 0.00

8 73 0.00 53 3.92 53 1.92 41 7.89 134 0.75

9 83 0.00 60 1.69 63 8.62 46 6.98 152 0.00

10 91 0.00 67 4.69 69 6.15 51 6.25 170 0.00

11 10

1

0.00 74 2.78 73 2.82 54 5.88 185 0.00

12 10

9

0.00 80 2.56 80 2.56 60 5.26 203 0.00

Table 3.15: Comparison on the number of used optical links applying Ilp and heuristic models

Comparison on the number of consumed optical links 𝑂𝑙ℎ𝑒𝑢 and 𝑂𝑙𝐼𝑙𝑝

Vbns Cesnet Nsfnet Italy Arnes

M 𝑂𝑙ℎ𝑒𝑢 − 𝑂𝑙𝐼𝑙𝑝

𝑂𝑙𝐼𝑙𝑝[%]

𝑂𝑙ℎ𝑒𝑢 − 𝑂𝑙𝐼𝑙𝑝

𝑂𝑙𝐼𝑙𝑝[%]

𝑂𝑙ℎ𝑒𝑢 − 𝑂𝑙𝐼𝑙𝑝

𝑂𝑙𝐼𝑙𝑝[%]

𝑂𝑙ℎ𝑒𝑢 − 𝑂𝑙𝐼𝑙𝑝

𝑂𝑙𝐼𝑙𝑝[%]

𝑂𝑙ℎ𝑒𝑢 − 𝑂𝑙𝐼𝑙𝑝

𝑂𝑙𝐼𝑙𝑝[%]

1 10.19 -9.09 -9.57 -15.57 -5.04

2 -15.64 -12.95 5.83 -7.46 -12.93

3 -18.51 -15.29 -0.86 -7.25 -12.29

4 -18.30 -15.20 4.89 -6.17 -13.54

5 -15.59 -15.53 0.68 -8.45 -12.94

6 -10.86 -15.29 0.69 -9.75 -10.18

7 -16.77 -15.97 1.22 -8.29 -13.31

8 -17.26 -11.08 -4.14 -9.66 -10.32

9 -20.31 -14.72 1.95 -8.59 -9.44

10 52.41 -13.04 3.08 -8.61 -9.14

11 40.44 -12.40 -0.61 -9.92 -5.24

12 -15.95 -12.95 -2.62 -10.42 -8.95

Table 3.16: Observed running times

Running Times Comparison

Vbns Cesnet Nsfnet Italy Arnes

𝑡𝐼𝑙𝑝[𝑠]

𝑡ℎ𝑒𝑢

𝑡𝐼𝑙𝑝

[%]

𝑡𝐼𝑙𝑝[𝑠]

𝑡ℎ𝑒𝑢

𝑡𝐼𝑙𝑝

[%]

𝑡𝐼𝑙𝑝[𝑠]

𝑡ℎ𝑒𝑢

𝑡𝐼𝑙𝑝

[%]

𝑡𝐼𝑙𝑝[𝑠]

𝑡ℎ𝑒𝑢

𝑡𝐼𝑙𝑝

[%]

𝑡𝐼𝑙𝑝[𝑠]

𝑡ℎ𝑒𝑢

𝑡𝐼𝑙𝑝

[%]

1 15.17 7.84 15.17 8.98 174.87 3.84 135.31 7.91 61.99 4.16

2 29.89 6.89 29.89 9.85 101.70 5.32 1658.55 1.08 573.20 1.11

3 90.3 2.43 90.3 11.00 609.88 0.92 1352.25 2.09 200.64 1.96

4 27.39 9.89 27.39 6.56 220.92 3.07 186.24 21.28 210.70 1.84

5 24.9 12.29 24.9 10.18 109.25 5.89 197.38 23.15 345.73 1.59

6 31.5 10.44 31.5 11.77 274.71 2.52 286.17 21.90 157.25 1.53

7 39.01 14.20 39.01 11.03 144.77 5.91 115.52 42.83 167.15 4.08

8 40.87 8.05 40.87 16.03 231.93 3.68 168.28 46.48 141.62 3.50

9 36.93 11.18 36.93 14.77 223.82 4.20 257.88 38.44 284.36 8.17

10 30.32 13.42 30.32 21.53 358.53 2.83 353.77 33.13 81419.10 0.03

11 19.55 23.43 19.55 20.78 158.57 11.66 134.29 44.82 12362.60 0.23

12 15.17 22.48 15.17 12.45 175.13 7.91 129.70 32.15 197351.10 0.02

41

The results for simulations featuring bidirectional routing attest to a somewhat satisfying

performance of the heuristic as most results lay bellow the ten percent window. In relation to the

networks’ dimensions, there doesn’t seem to be a trend on the performance of the heuristic as the

number of nodes increases. Likewise, there are no evident ties between the amount of traffic

controlled by parameter M and the displayed gaps between both methods.

On the mean nodal degree’s influence on the results, observations show that the networks for

which the gaps are the highest are those with higher mean nodal degrees. When comparing the two

12 nodes networks that were subjected to the same traffic conditions, Table 3.14 attests to a superior

performance of the heuristic algorithm when applied to the network with lower mean nodal degree.

The same cannot be stated however when discussing the 14 nodes networks sharing the same traffic

matrices where it is hard to discern which network is tied to the most compelling results.

In regards to Table 3.15’s comparison on the number of optical links used, most often the

heuristic is accountable for the lowest number of wavelengths assigned over all fiber links. Nothing

can be stated on whether the gaps to the Ilp solution are conditioned by the relation between the

optical link consumption of the heuristic and the mathematical model.

The heuristic proves satisfying in complying with the expectation of lower running times in

comparison with the complex linear programming models. In general, it can be stated that considering

the simplicity that characterizes the developed algorithm, the results obtained and the moderate times

the simulations took to conclude are satisfactory. Results discriminated by Traffic Selection Scheme

can be found bellow.

Vbns

Table 3.17: Comparing the Traffic Selection Schemes for the Vbns Network

𝑊𝐶 𝐶 𝐷𝐿 𝑅𝐴𝐷 𝑊𝑅𝐴𝐷

M 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 𝑂𝐿𝐹

1 10 10 10 10 11 11 10 10 10 10

2 22 20 22 21 20 21 21 19 21 19

3 30 28 31 30 28 29 29 29 28 28

4 38 36 39 38 36 38 37 36 38 35

5 51 48 52 49 46 49 50 47 48 46

6 63 59 63 60 58 59 60 57 59 57

7 71 66 70 69 64 67 66 64 67 64

8 80 76 82 78 73 77 77 74 78 73

9 89 87 96 89 83 88 87 83 89 83

10 98 97 106 98 91 97 97 93 95 91

11 108 107 117 108 101 107 108 101 106 101

12 118 116 127 117 110 116 115 109 115 109

Cesnet

42

Table 3.18: Comparing the Traffic Selection Schemes for the Cesnet Network

𝑊𝐶 𝐶 𝐷𝐿 𝑅𝐴𝐷 𝑊𝑅𝐴𝐷

M 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹

1 8 9 8 10 9 9 8 10 8 9 2 16 15 16 15 15 16 15 16 15 15 3 23 23 23 24 22 23 22 21 22 21 4 27 29 29 29 27 28 29 26 28 26 5 39 37 39 38 34 38 38 35 38 34 6 45 47 46 47 43 46 46 42 45 42 7 51 52 52 52 47 51 52 48 52 48 8 58 59 58 60 54 57 60 53 62 54 9 68 68 70 68 62 68 68 62 69 60

10 74 75 78 74 68 73 78 68 75 67 11 82 82 85 81 75 83 85 74 84 74 12 91 90 92 89 81 90 88 81 89 80

Nsfnet

Table 3.19: Comparing the Traffic Selection Schemes for the Nsfnet Network

𝑊𝐶 𝐶 𝐷𝐿 𝑅𝐴𝐷 𝑊𝑅𝐴𝐷

M 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 𝑂𝐿𝐹

1 8 7 8 7 8 8 8 7 8 7

2 16 16 15 16 15 16 16 15 16 16

3 24 22 24 24 21 23 23 21 22 21

4 34 32 33 32 29 30 30 28 31 28

5 45 39 39 39 35 39 37 35 38 34

6 54 47 48 47 43 46 48 43 46 43

7 60 53 56 56 47 55 53 49 55 49

8 69 60 65 63 53 63 63 55 62 54

9 79 68 72 70 63 71 71 63 70 63

10 86 75 80 79 69 78 77 69 77 69

11 95 83 88 86 73 84 86 75 87 76

12 113 93 99 97 80 95 96 81 94 82

Italy

Table 3.20: Comparing the Traffic Selection Schemes for the Vbns Network

𝑊𝐶 𝐶 𝐷𝐿 𝑅𝐴𝐷 𝑊𝑅𝐴𝐷

M 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 M 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 𝑂𝐿𝐹

1 6 6 7 6 7 7 7 6 6 6

2 13 11 12 11 11 12 12 11 12 11

3 18 16 19 17 16 17 16 16 17 16

4 23 23 25 23 20 22 24 21 24 21

5 32 28 31 28 25 29 30 26 28 26

6 38 35 38 35 32 35 37 32 38 31

7 43 39 43 40 37 40 42 36 42 36

8 50 45 51 46 41 46 46 42 48 41

9 59 50 57 51 46 50 54 47 54 46

10 65 54 63 58 51 58 61 51 61 52

11 71 61 69 62 54 61 64 56 68 55

12 81 67 76 70 60 72 73 63 72 61

43

Arnes

Table 3.21: Comparing the Traffic Selection Schemes for the Arnes Network

𝑊𝐶 𝐶 𝐷𝐿 𝑅𝐴𝐷 𝑊𝑅𝐴𝐷

M 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 𝑂𝐿𝐹 𝑂𝐻𝐹 𝑂𝐿𝐹

1 8 7 8 7 8 8 8 7 8 7

2 16 16 15 16 15 16 16 15 16 16

3 24 22 24 24 21 23 23 21 22 21

4 34 32 33 32 29 30 30 28 31 28

5 45 39 39 39 35 39 37 35 38 34

6 54 47 48 47 43 46 48 43 46 43

7 60 53 56 56 47 55 53 49 55 49

8 69 60 65 63 53 63 63 55 62 54

9 79 68 72 70 63 71 71 63 70 63

10 86 75 80 79 69 78 77 69 77 69

11 95 83 88 86 73 84 86 75 87 76

12 113 93 99 97 80 95 96 81 94 82

Regarding the tables above, though a clear trend cannot be found, it can be stated that the two

selection schemes that stand out negatively are the Weighted Connectivity and the Connectivity one

when iterated from the request with highest to lowest cost metric.. On the opposite side, the Demands

Left scheme iterated from highest cost metric to lowest and the Weighted Resource Availability per

Demand scheme iterated from lowest to highest cost seem to be the ones most often accountable for

the most satisfying outcomes. This behaviour leads to the assumption that a prioritized treatment

should be held for requests with the highest volume of optical connections to satisfy between their

end-nodes and in which such nodes are accountable for lower mean nodal degrees.

3.6 Applying the heuristic to networks of greater reach

As the previously attained results didn’t compromise the heuristic’s viability as a solution for

the RWA problem, a choice was made to conduct simulations for networks of greater dimensions

applying the developed algorithm. The considered networks’ characteristics are showcased in Table

3.22. The same set of traffic matrices was applied to the Optosunet and Arpanet networks considering

they both have the same number of nodes and distinct mean nodal degrees. All simulations were

carried applying bidirectional routing. The results are showcased in Table 3.23.

Table 3.22: Network Parameters

Network Optosunet Arpanet Ibn31 Metrona Cost37

Number of Nodes 20 20 31 33 37

Number of bidirectional links 24 32 51 41 57

Mean Nodal Degree 2.4 3.20 3.29 2.48 3.08

44

Table 3.23: Results applying the heuristic to networks of large dimensions

M Optosunet Arpanet Ibn31 metrona Cost37

1 21 18 33 82 47

2 46 33 65 148 90

3 66 49 89 215 139

4 96 67 127 309 186

5 120 88 162 373 216

6 136 94 184 410 268

7 152 110 220 518 316

8 170 138 248 547 373

9 211 147 282 641 406

10 221 165 309 484 440

11 231 181 356 729 491

12 252 190 365 818 550

The attained results support the premise that networks with higher mean nodal degrees are

able to better distribute the optical connections over their fiber links consuming a lower number of

wavelengths when in comparison to networks with lower nodal degrees in the same traffic conditions.

An interesting observation is also made regarding the fact that the network accountable for the higher

wavelength consumption is not the one with the larger dimensions from among the ones studied.

Comparing the three networks of greater reaches, the one with the lower mean nodal degree requires

a significant larger number of wavelengths in relation to the other two.

3.7 Conclusions

The present chapter aimed to present distinct methodologies with which to solve the Routing and

Wavelength Assignment problem. Integer linear programming formulations were developed

considering scenarios for bidirectional and unidirectional traffic routing. Initially, link-path and node-link

approaches were compared, in order to establish which would be more advantageous. Results

showed that the link-path models’ imposition of a higher bound to the number of pre-computed routing

paths provided the lowest running times and the same wavelength consumption. On the routing

schemes, an example showcased that the symmetrical approach’s simplification to a single direction

could come at the expense of a higher number of wavelengths. However, conducted simulations did

not exhibit the same behavior. The impact of the network’s mean nodal degree was also analyzed and

results for a set of test cases proved a trend of higher nodal degrees providing for fewer wavelengths

required to satisfy the optical connection demands.

The optimum solutions attained via Integer Linear Programming methodologies come at the cost

of high running times with implications in terms of their suitability for networks of practical dimension.

To work around this limitation, it is common practice to develop alternative models. On that note, an

original heuristic model was presented and its performance was compared against the mathematical

model with satisfying results.

45

4 OTN/WDM network planning: GRWA

methodologies

The current chapter is concerned with the traffic grooming problem. Dealing with traffic demands

of finer granularity, this problem extends that of the previous chapter by combining the establishment

of the virtual topology with the efficient grooming of sub-wavelength connection requests to the high

capacity lightpaths that compose such topology. At first, ILP formulations for the static traffic grooming

problem are pursued to maximize the network’s throughput in resource scarcity scenarios. The scope

is broadened to include transparent, opaque and translucent networks, all of which are targeted in a

series of simulations conducted for comparison purposes. In account of the problem’s NP-Hard

property, selected published heuristic methodologies are analyzed and their viability as optional

procedures is brought under consideration. In the end, the results of simulations applying the Ilp and

heuristic models are presented, compared and interpreted.

46

4.1 Introduction

Traffic grooming as explained in Chapter 2, is the technique of combining sub-wavelength

streams to share the available bandwidth of a bulkier optical pipe. In this chapter, the network topology

design is extended to include considerations on how the client signals are routed over the optical

transport network. In alignment with network optimization strategies, the static traffic grooming, routing

and wavelength assignment (GRWA) problem is applied to scenarios with resource scarcity in which a

portion of the requested client connections cannot be satisfied. In such conditions, signal aggregation

at source and intermediate nodes is pursued in order to increase wavelength channel occupation and

optimize resource utilization for maximum network’s throughput.

At translucent nodes equipped with ODU/WDM switching devices such as the one presented

in 2.3.2, optical connections arriving to the incoming WDM ports can be terminated or forwarded to the

appropriate outgoing WDM outgoing ports via ROAMDs in what is called optical bypassing. Regarding

those first terminated wavelength channels, all transported ODU encapsulated signals surpass the

ODU switching fabrics. While the streams destined for the nodes are locally dropped to the

appropriate client cards, the in-transit sub-wavelength streams are groomed so that new groupings are

constituted to pack outgoing wavelengths. Weighting in on both strategies, optical bypassing can

provide for savings on the number of transponders by having client signals surpassing in-transit nodes

entirely in the optical domain. As for intermediate traffic grooming, while the technique requires for

wavelengths to be terminated for traffic to be collected, the increased wavelength utilization when

efficiently performed lies as an enabler for the reduction of the number of optical channels,

transponders and eventually wavelength links. Under such considerations, the throughput

maximization problem in resource scarcity situations oughts to determine the optimized combination of

traffic grooming and optical bypassing such that the highest volume of traffic can be expedited.

In 2.3.2 three possible network configurations were introduced: transparent, translucent and

opaque. Sub-wavelength signal aggregation in all-optical networks is restricted to the multiplexing of

same-source destination pairs (source or end-to-end grooming). While lightpaths can hop from one

fiber link to the next thanks to ROADMs placed at intermediate nodes on route to destination, client

connections must be forwarded over a single direct lightpath among their end-points. Oppositely, in

opaque network schemes, lightpaths are restricted to a single fiber span and sub-wavelength streams

are permitted to hop from one lightpath to another by means of ODU switching fabrics at in-transit

nodes. Without restrictions, translucent networks flexibly allow for multi-hop physical routes for the

optical channels and for multi-hop virtual routes for the individual ODU connections.

The throughput maximization problem is initially addressed using mathematical programming

models following in on the work reported in [21]. Such work features single and multi-hop Ilp traffic

grooming formulations for mesh networks with static traffic patterns. The models presented in the

current chapter differ for those of the referenced publication in that link-path formulations were

pursued as opposed to node-link ones. Contrary to the same referenced formulations that consider the

routing of each end-to-end connection individually, the models developed in the scope of the current

work consider groups of end-to-end connections between the same end-points and of the same data-

47

rate that are carried over the same lightpath. Also, while the multi-hop traffic grooming formulations in

[21] consider all nodes to have electric switching capabilities, this chapter’s formulations take the

electric switching capabilities of each node as input to the problem allowing for only a subset of nodes

to be able to perform intermediate grooming. Besides the transparent and translucent configurations,

an additional Ilp formulation was also developed to target the specific case of opaque network

configurations. In the present chapter, a comparative analysis is drawn on the performance of opaque,

translucent and transparent configurations under resource scarcity constraints taking into account the

attained throughputs, consumed lightpaths, medium channel occupation and wavelength link

consumption.

In the previous chapter it was mentioned that the RWA problem is NP-Hard. If we were to

assume each connection required for the full capacity of a lightpath, then the traffic grooming problem

would just become the standard RWA problem. As an extension to that problem, the traffic grooming

problem is NP-Hard itsef. The increased complexity that comes with the exponential increase of the

number of variables and equations with the size of the network restricts the application of Ilp

formulations to small sized networks. To target networks of larger size heuristic methodologies were

pursued with its basis laid on [21] and [22]. The Maximum Single Hop Traffic and the Maximum

Resource Utilization heuristics are overviewed in the first place with the display of a series of

adaptations performed against the published models in achievement of increased performance. Later,

the Auxiliary Graph Model heuristic is attended. Considerations on the quality of the heuristic

approaches are left for the final sections where the results of simulations applying each individual

algorithm are presented and examined. Comparisons are established taking into account their

proximity to the Ilp models and the running times. Finally, the three examined heuristics are applied to

real life networks of larger dimensions and the throughputs attained are compared for the same

resource availability.

4.2 Mathematical Models in resource scarcity scenarios

This section presents Ilp models for the static traffic grooming problem in opaque, transparent

and translucent mesh networks. The developed work is based on [21]. The general traffic grooming

problem can be described as follows: given a graph 𝐺(𝑉, 𝐸) where 𝑉 corresponds to the network

nodes and 𝐸 to the fiber links connecting them, and a set of traffic matrixes 𝑇𝑈, each corresponding to

the demand in terms of ODU signals of the same rate 𝑢 ∈ 𝑈, a virtual topology and the routing of the

client signals are to be determined in achievement of maximum network’s throughput. The problem is

constrained by the optical channels’ capacity 𝐶 that limits the volume of carried connections and by

the number of wavelengths 𝑊 and transceivers 𝑇𝑟. OTN switches at selected nodes concede for low

speed streams to be processed in the electric domain at intermediate nodes and in turn, ROADMs

work on the optical layer to allow for optical bypassing of wavelength channels.

The assumptions, inputs, notation and variables common to all the presented traffic grooming

formulations are as follows:

Assumptions:

48

The network is laid out as an irregular mesh topology;

Bidirectional fibers are used to connect the network nodes. Fibers are deployed in pairs, one

fiber for each direction;

The network nodes have no wavelength conversion capabilities: lightpaths must be assigned

the same wavelength on all physical links spanned in accordance to the wavelength

continuity constraint;

The transceivers featured in the network nodes are tunable to any of the available

wavelengths on the fiber;

All nodes are equipped with the same number of transceivers;

Optical impairments are despised removing the need for regeneration of the optical signals

thus assumed to be able to travel any considered distance.

There are no limitations to the grooming capacity of the ODU switches;

A connection request cannot be broken down into lower rate connections and routed

separately from source to destination. The traffic on a connection request must at all times

follow the same route between its end-points.

Problem inputs:

A physical topology 𝐺 = (𝑉, 𝐸), consisting of a bidirectional graph, where 𝑉 is the set of

network nodes and 𝐸 the set of fiber links connecting the nodes;

Number of wavelength channels per fiber 𝑊;

Number of transceivers per node 𝑇𝑟;

Optical channels’ rate or capacity 𝑅;

Set of considered ODU signals’ rates 𝑈;

Traffic matrices set 𝑇𝑈 corresponding to the ODU connection requests.∀ 𝑠, 𝑑 ∈ 𝑉, 𝑢 ∈ 𝑈, 𝑡𝑠𝑑𝑢

denotes the number of ODU requests of rate 𝑢 to establish among source-destination

pair (𝑠, 𝑑). The notation is as follows: every individual connection is referred to as a traffic

demand and a group of traffic demands of the same rate between the same end-points is

conceived as a traffic request;

Binary variable 𝛼𝑖 that indicates the presence or not of an ODU switching fabric at node

𝑖. 𝛼𝑖 = 1 if electric switching (intermediate grooming) is possible and 𝛼𝑖 = 0 otherwise.

Notation:

𝐴 stands for the set of network arcs. Each network arc 𝑎 ∈ 𝐴 is an unidirectional

representation of a physical connection among two nodes (𝑠(𝑎), 𝑑(𝑎)) such that there is at

least one fiber link among those nodes. A given arc is characterized by 𝑙𝑎 , the number of

optical fibers uniting 𝑠(𝑎) and 𝑑(𝑎). Given that fibers are deployed in pairs, if we consider arc

𝑎 from 𝑠(𝑎) to 𝑑(𝑎) and arc 𝑎′ such that 𝑠(𝑎′) = 𝑑(𝑎) and 𝑑(𝑎′) = 𝑠(𝑎), then 𝑙𝑎 = 𝑙𝑎′ ;

𝑖 and 𝑗 denote the origin and destination of an optical channel, respectively. A given lightpath

may traverse one or multiple network arcs;

𝑠 and 𝑑 stand for the origin and destination, respectively, of an end-to-end traffic request.

The end-to-end traffic can be carried over one or more optical channels. The figure bellow

displays how a connection request may be carried.

49

Figure 4.1: Example of the transport of an end-to-end connection request

Variables:

𝑃𝑖𝑗 : Set of possible paths between node i and node j. These paths must be calculated offline

prior to the problem’s execution;

𝑃𝑖𝑗𝑎 : Set of possible paths between node i and node j that traverse arc 𝑎 ∈ A.

𝐿𝑖𝑗: Number of lightpaths between 𝑖 and 𝑗. 𝐿𝑖𝑗 ∈ 𝛮0 ;

𝐿𝑖𝑗

𝑝𝑖𝑗,𝑤: Number of lightpaths between 𝑖 and 𝑗 routed on path 𝑝𝑖𝑗 over wavelength 𝑤.

𝐿𝑖𝑗

𝑝𝑖𝑗,𝑤 ∈ 𝛮0;

𝑍𝑠𝑑𝑢 : Number of successfully routed ODU connections of rate 𝑢 between 𝑠 and 𝑑.

𝑍𝑠𝑑𝑢 ∈ [0, 𝑡𝑠𝑑

𝑢 ];

𝐺𝑖𝑗,𝑠𝑑𝑢 : Number of ODU connections of rate 𝑢 between 𝑠 and 𝑑 carried over a lightpath with

end-points (𝑖, 𝑗). 𝐺𝑖𝑗,𝑠𝑑𝑢 ∈ 𝛮0

4.2.1 Ilp model for translucent networks

The current section concerns the traffic groming problem applied to translucent networks. In result

of the presence of ROADMs at each network node, lightpaths may span multiple arcs on route to

destination. In turn, intermediate traffic grooming may be performed at selected nodes with ODU

switching capabilities. The formulation is as follows:

Formulation:

Objective function:

(4.1) 𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒 ∑ ∑ ∑ 𝑍𝑠𝑑𝑢 ∗ 𝑟

𝑢 ∈ 𝑈𝑑 ∈ 𝑉𝑠 ∈ 𝑉

Constraints:

(4.2) ∑ 𝐿𝑖𝑗 ≤ 𝑇𝑟

𝑗 ∈𝑉

∀ i ∈ V

(4.3) ∑ 𝐿𝑖𝑗 ≤ 𝑇𝑟

𝑗 ∈𝑉

∀ j ∈ V

(4.4) ∑ ∑ 𝐿𝑖𝑗

𝑝𝑖𝑗,𝑤= 𝐿𝑖𝑗

𝑤 ∈ 𝑊𝑝𝑖𝑗 ∈ 𝑃𝑖𝑗

∀ 𝑖, 𝑗 ∈ 𝑉

50

(4.5) ∑ ∑ ∑ 𝐿𝑖𝑗

𝑝𝑖𝑗,𝑤

𝑝𝑖𝑗 ∈ 𝑃𝑖𝑗𝐴

≤

𝑗 ∈𝑉𝑖 ∈𝑉

𝑙𝑎 ∀ 𝑎 ∈ 𝐴; 𝑤 ∈ 𝑊

(4.6) ∑ 𝐺𝑠𝑛,𝑠𝑑𝑢

𝑛 ∈ 𝑉

= 𝑍𝑠𝑑𝑢 ∀ 𝑠, 𝑑 ∈ 𝑉; 𝑢 ∈ 𝑈

(4.7) ∑ 𝐺𝑚𝑠,𝑠𝑑𝑢

𝑚 ∈ 𝑉

= 0 ∀ 𝑠, 𝑑 ∈ 𝑉; 𝑢 ∈ 𝑈

(4.8) ∑ 𝐺𝑚𝑑,𝑠𝑑𝑢

𝑚 ∈ 𝑉

= 𝑍𝑠𝑑𝑢 ∀ 𝑠, 𝑑 ∈ 𝑉; 𝑢 ∈ 𝑈

(4.9) ∑ 𝐺𝑑𝑛,𝑠𝑑𝑢

𝑛 ∈ 𝑉

= 0 ∀ 𝑠, 𝑑 ∈ 𝑉; 𝑢 ∈ 𝑈

(4.10) ∑ 𝐺𝑚𝑘,𝑠𝑑 𝑢

𝑚 ∈ 𝑉

= 𝛼𝑖 ∗ ∑ 𝐺𝑘𝑛,𝑠𝑑𝑢

𝑛 ∈ 𝑉

∀ 𝑘 ∈ 𝑉, 𝑘 ≠ 𝑠, 𝑑; 𝑢 ∈ 𝑈

(4.11) 𝑧𝑠𝑑𝑢 ≤ 𝑡𝑠𝑑

𝑢 ∀ 𝑠, 𝑑 ∈ 𝑉 , ∀ 𝑢 ∈ 𝑈

(4.12) ∑ ∑ ∑ 𝐺𝑖𝑗,𝑠𝑑𝑢 ∗ 𝑢

𝑢 ∈ 𝑈𝑑 ∈ 𝑉

≤ 𝐿𝑖𝑗 ∗ 𝑅

𝑠 ∈𝑉

∀ 𝑖, 𝑗 ∈ 𝑉

The presented equations can be explained as follows:

Equation (4.1) shows the optimization objective function;

Equation (4.2) ensures that the number of lightpaths originated at a node is less than or equal to

the number of transponders at that node and (4.3) that the number of lightpaths terminated at a

given node is less than or equal to the number of transponders at that node;

Equation (4.4) assures that each lightpath is assigned a physical route from among those

calculated offline and also a wavelength from among those available at the network fibers. By

defining variable 𝐿𝑖𝑗

𝑝𝑖𝑗,𝑤 the wavelength continuity constraint is implicitly accounted for as each

path is associated with a single wavelength;

Equation (4.5) concerns the wavelength clash constraint. It ensures that the number of lightpaths

assigned a specific wavelength at a given network arc is at most equal to the number of fiber links

among the arc’s endpoints;

Equations (4.6) to (4.9) respect to the routing of the end-to-end connection requests over the

optical channels.

Equation (4.10) is tied to intermediate traffic grooming. It states that all connections of the same

rate and between the same node-pair carried in a lightpath terminated at an intermediate node

must be forwarded to outgoing lightpaths. 𝛼𝑖 controls the ability to perform or not intermediate

grooming;

Equation (4.11) bounds the number of successfully carried connections of a given rate and

between the same end-points to at most the number of requested connections in such conditions;

Equation (4.12) respects to the lightpath’s bandwidth constraint and assures that the volume of

end-to-end sub-wavelength connections carried over a lightpath does not surpass its capacity.

The equation is straight forward because the OTU signal rates considered are a multiple of the

ODU signal rates taken into account.

The presented general formulation for the traffic grooming problem in translucent networks poses

appropriate when dealing with either bidirectional or unidirectional traffic requests. For the particular

51

case of traffic symmetry, simplifications can be performed by considering only the traffic requests in

the direct direction (the ones where the destination node’s index is lower than the source node’s one).

By doing so, a virtual topology is attained composed of bidirectional lightpaths carrying traffic between

the same end-nodes in reverse directions. The formulation for this specific case as derived from the

one presented above requires for the following changes:

Make 𝑠 > 𝑑 whenever 𝐺𝑖𝑗,𝑠𝑑𝑢 is concerned so that only the requests in the direct direction are

considered;

Replace 4.2 and 4.3 with constraint 4.13. The deployment of bidirectional optical channels

requires that for every lightpath originated or terminated at a node and carrying direct traffic, a

transponder card is consumed (the implicit reverse lightpath occupies the other available port).

(4.13) ∑ 𝐿𝑖𝑘+ ∑ 𝐿𝑘𝑖

𝑘 ∈𝑉

≤ 𝑇𝑟

𝑘 ∈𝑉

∀ 𝑖 ∈ 𝑉

Replace 4.5 with 4.14. Again, the reservation of resources (in this particular case wavelength

links) for the implicit lightpath carrying the connections in the reverse direction is assured.

(4.14) ∑ ∑ ∑ 𝐿

𝑖𝑗

𝑝𝑖𝑗,𝑤

𝑝𝑖𝑗 ∈ {𝑃𝑖𝑗𝑎 ∪ 𝑃𝑖𝑗

𝑎′}

≤

𝑗 ∈𝑉𝑖 ∈𝑉

𝑙𝑎 ∀ 𝑎, 𝑎′ ∈ 𝐴; 𝑤 ∈ 𝑊

𝑎′ => 𝑠(𝑎) = 𝑑(𝑎′) , 𝑑(𝑎) = 𝑠(𝑎′)

4.2.2 Ilp model for transparent networks

In all-optical or transparent networks the absence of ODU switches imposes that only end-to-end

traffic grooming is allowed. Consequently, ODU demands are required to be transported over a single

direct lightpath between its end-points. The single-hop traffic grooming formulation for transparent

networks is very much similar to the one presented above except for the routing of connection

requests on the virtual topology. Only the differences are presented as follows:

Replace equations (4.6) – (4.10) with:

4.2.3 Ilp model for opaque networks

From among all the aforementioned configurations, the opaque is the one where most opto-

electric conversion takes place. All incoming lightpaths at a node are terminated, whether the client

signals carried are in transit or otherwise. Given that no optical bypass is allowed and all signals are

electronically processed, optical channels can only be established between physically adjacent nodes.

To reflect this situation, no direct changes have to be applied to the first formulation presented.

Instead, the required adaptations are only reflected on the offline computation of the candidate routes

among the nodes:

𝑃𝑖𝑗 = {∅ , 𝑖𝑓 ∄ 𝑎 ∈ 𝐴 ∶ 𝑠(𝑎) = 𝑖 , 𝑑(𝑎) = 𝑗

{𝑝𝑖𝑗 ,0 }, 𝑝𝑖𝑗 ,0 = {𝑖, 𝑗}, 𝑖𝑓 ∃ 𝑎 ∈ 𝐴 ∶ 𝑠(𝑎) = 𝑖 , 𝑑(𝑎) = 𝑗

(4.25) 𝐺𝑠𝑑,𝑠𝑑𝑟 = 𝑍𝑠𝑑

𝑟 ∀ 𝑠, 𝑑 ∈ 𝑉; 𝑟 ∈ 𝑅

52

4.3 Applying the Ilp methodologies

The further sections exploit the models presented above by performing simulations and

drawing conclusions on the results attained. In a translucent network scenario where all nodes have

integrated OTN switching fabrics that allow to undertake intermediate grooming, experiences are

conducted for the Via Network to observe how varying the number of available transceivers and

wavelengths influences the volume of connections that can be successfully routed. Additionally,

considerations are made on the wavelength channels’ occupation, on the number of deployed

lightpaths, consumed wavelength links and amount of electric switching performed.

Posteriorly, the same network is analysed in a scenario where intermediate traffic grooming is

restricted to the sub-set of nodes with a nodal degree higher than two. Under the same traffic and

resource availability conditions, the intention of the conducted experiment is to conclude whether the

node selection performed can be advantageous by limiting the number of necessary ODU switches

that must be deployed while still attaining results close to the solution where all nodes are translucent.

Finally, translucent, transparent and opaque network scenarios are brought under the scope

by comparing the results obtained applying each model under the same conditions (number of

transceivers, wavelengths and traffic load) in a network. The goal is to support the benefits that

allowing for the coexistence of wavelength and sub-wavelength switching can bring over the other

configurations.

For all conducted simulations the following considerations were made:

The set of offline computed paths was determined applying the k-shortest path algorithm

described in B.1 and 𝑘 was fixed to 7;

Available line cards are 1 x 40G OUT-3;

Accepted ODU requests are ODU-0, ODU-1 and ODU-2. Consequently, 𝑈 = {1.25, 2.5, 10};

For every accepted ODU signal a bidirectional traffic matrix was generated according to a

discrete uniform distribution between 0 and 𝑀𝑢, 𝑢 ∈ 𝑈 . 𝑀𝑢 establishes an upper bound on the

number of ODU requests of rate 𝑢 between every node-pair. For every traffic matrix only the

upper triangle was filled and then the values were mirrored in respect to the main diagonal to the

lower triangle so that 𝑡𝑠𝑑𝑢 = 𝑡𝑑𝑠

𝑢 ∀ 𝑠, 𝑑 ∈ 𝑉, 𝑢 ∈ 𝑈. That being, the bidirectional traffic routing Ilp

model was applied at all times and bidirectional optical channels or lightpaths were deployed.

4.3.1 Sensitivity to resources’ variation in translucent scenarios

The number of available wavelengths and transponders conditions the way in which lightpaths

can be established and, as a consequence, the way in which client signals can be attended. The

wavelength constraint removes degrees of freedom from the physical routing of optical channels and

can prevent lightpaths from being set up over unavailability of a path composed of fiber links with

common wavelengths. In turn, the transponder constraint places limitations on the maximum number

of lightpaths that can be deployed. To study these effects, simulations were run for the Via network

varying the availability of both resources. The conditions under which simulations were carried are

53

described in Table 4.1. It is assumed that all nodes have OTN switching capabilities, 𝛼𝑖 = 1 , ∀ 𝑖 ∈ 𝑉.

The bidirectional traffic matrixes were generated so that for every node pair (𝑖, 𝑗), 𝑗 > 𝑖 the number of

ODU-0, ODU-1 and ODU-2 demands was a random number uniformly distributed between 0 and 32, 0

and 16 and 0 and 2 respectively. Bellow, the results attained for the network’s throughput under

different wavelength and transponder availabilities are displayed. Additionaly, the number of

established lightpaths, medium lightpath length, medium lightpath occupation and total volume of

connections routed in multi-hop routes are presented as well.

Table 4.1: Simulation Parameters

Network Via (9 nodes, 12 bidirectional links)

Traffic volume [Gbps]: ∑ ∑ ∑ 𝑡𝑠𝑑𝑟 ∗

𝑑 ∈𝑉𝑠 ∈𝑉𝑟 ∈𝑅

𝑟 = 4265

Contribution to the

total traffic [%]

1.25 ∑ ∑ tsd

1.25 ∗ 𝑑 ∈ 𝑉𝑠 ∈ 𝑉 1.25

∑ ∑ ∑ tsdr ∗ 𝑑 ∈𝑉𝑠 ∈ 𝑉𝑟 ∈ 𝑅 𝑟

= 40.68

2.5

∑ ∑ tsd2.5 ∗ 𝑑 ∈ 𝑉𝑠 ∈ 𝑉 2.5

∑ ∑ ∑ tsdr ∗ 𝑑 ∈𝑉𝑠 ∈ 𝑉𝑟 ∈ 𝑅 𝑟

= 41.50

10 ∑ ∑ tsd

10 ∗ 𝑑 ∈ 𝑉𝑠 ∈ 𝑉 10

∑ ∑ ∑ tsdr ∗ 𝑑 ∈𝑉𝑠 ∈ 𝑉𝑟 ∈ 𝑅 𝑟

= 17.82

Figure 4.2: Throughput attained against wavelength and transponder availability variations

Table 4.2: Medium Lightpath Length

Medium lightpath length [fiber hops]

W T 8 9 10 11 12 13 14

8 2.22 2.17 1.95 1.82 1.70 - -

9 1.97 2.35 2.09 2.02 1.98 - -

10 - 2.20 2.22 2.12 2.02 - -

11 - - 2.27 2.22 2.07 2.07 -

12 - - - 2.31 2.19 2.24 -

13 - - - - 2.26 2.29 2.16

14 - - - - - 2.31 2.30

65

70

75

80

85

90

95

100

8 9 10 11 12 13 14

Thro

ugh

pu

t [%

]

T

W=8

W=9

W=10

W=11

W=12

W=13

W=14

54

Table 4.3: Number of established lightpaths

Number of established lightpaths

W T 8 9 10 11 12 13 14

8 72 80 88 98 - - -

9 72 80 90 98 104 - -

10 - 80 90 98 106 - -

11 - - 90 98 108 108 -

12 - - - 98 108 116 -

13 - - - - 108 116 124

14 - - - - - 116 126

Table 4.4: Volume of sattisfied connections in multi-hop virtual routes

Volume of satisfied connections in multi-hop virtual routes [%]

W T 8 9 10 11 12 13 14

8 0.00 14.29 13.52 20.68 27.45 - -

9 0.00 2.89 10.15 16.76 20.92 - -

10 - 1.92 7.58 15.75 17.36 - -

11 - - 6.10 9.47 18.09 - -

12 - - - 8.64 15.66 21.89 -

13 - - - - 14.54 21.34 23.55

14 - - - - - 16.81 18.99

Table 4.5: Medium Lightpath Occupation

Medium Lightpath Occupation [%]

W T 8 9 10 11 12 13 14

8 98.61 98.75 98.72 95.28 90.16 - -

9 100.00 98.59 97.92 97.32 95.31 - -

10 - 98.44 98.89 99.62 95.99 - -

11 - - 98.47 98.72 97.69 97.69 -

12 - - - 98.72 98.84 97.20 -

13 - - - - 98.84 97.46 95.56

14 - - - - - 97.31 92.86

Figure 4.2 presents the variation of the network’s throughput as the number of wavelengths

and transponders increases. To satisfy all demanded end-to-end connections 14 wavelengths and 14

transponders are necessary. For a number of available wavelengths in a range from 8 to 12 it can be

seen that increasing the number of transponders allows to increase throughput until a point comes

where the effects of a larger transponder availability no longer are felt and the network’s throughput

stabilizes. This is because there are not enough wavelengths to establish further lightpaths to carry

the remaining connections.

Given that multi-hop traffic grooming is considered, when the number of transponders is not a

limitation in regards to the number of wavelengths, a larger number of short length lighpaths can be

established to carry the connections through multiple lightpaths. This behaviour is perceived by

looking through Tables 4.2, 4.3 and 4.4 and considering a fixed number of wavelengths and an

increasing number of transponders: in general the medium lightpath length decreases and the number

of established lightpaths increases as does the amount of sub-wavelength switching performed. On

the other hand, when the number of wavelengths increases and the number of transponders poses as

a limitation, the larger space of physical routing options may permit for a more careful selection of the

55

lightpaths to establish so that a higher volume of connections is attended. This can be noted when

observing the scenario where the number of transponders is fixed to 11. While the number of

established lightpaths is constant for the whole range of considered wavelengths, Figure 4.2 presents

an increase in the attained throughput when the number of wavelengths varies from 8 to 11. From

then on however, additional wavelengths per fiber are no longer useful and the network’s throughput

mantains constant.

Regarding Table 4.5 concerning the medium lightpath utilization, it can be stated that the

lightpaths are well packed as all presented values lay above 95 percent of the available capacity.

4.3.2 Translucent scenarios with selected hub nodes

The previously conducted simulations assume all network nodes are equipped with ODU

switching fabrics. In such conditions, the space of routing solutions for the client signals is the largest.

In cases where only a subset of network nodes is equipped with electric switching devices the capital

expenditures can be lowered. However, the cost benefits provided may come at the cost of decreased

network performance as the number of successfully routed connections may drop.

Ideally, the case of having the number of nodes with ODU switching facilities limitied to a given

inputted value should be addressed with a formulation that determined the subset of nodes to which

delegate the intermediate grooming functionality so that throughput could be maximized. For

simplification purposes, in the scope of this thesis, this issue is regarded under a different approach

where a node’s ability to perform ODU switching is taken as an input to the problem and given by the

boolean variable 𝛼𝑖 , 𝑖 ∈ 𝑁.

To study the advantages and drawbacks of placing limitations on the number of deployed OTN

switches, a comparison was made against the fully translucent network scenario (𝛼𝑖 = 1, ∀ 𝑖 ∈ 𝑉)

addressed in the previous section. The choice of the subset of nodes with ODU switching capabilities

fell upon those with a nodal degree higher than two. The nodes are displayed in Figure 4.3 with a

dashed blue line surrounding them. The same traffic conditions were applied. The results are

showcased in Table 4.6.

Figure 4.3: Selected nodes with integrated OTN switches

56

Table 4.6: Comparison of the throughput obtained for both scenarios

𝑇ℎ𝑟ℎ𝑢𝑏 𝑛𝑜𝑑𝑒𝑠 − 𝑇ℎ𝑟 𝑓𝑢𝑙𝑙𝑦−𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

𝑇ℎ𝑟 𝑓𝑢𝑙𝑙𝑦−𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

[%]

W T 8 9 10 11 12 13 14

8 -12.68 -7.64 -6.30 -1.92 -0.73 -0.00 -0.00

9 -13.89 -7.40 -7.61 -1.14 -0.70 -0.00 -0.00

10 -13.89 -7.69 -9.04 -1.66 -1.34 -0.00 -0.00

11 - -7.69 -9.30 -2.03 -1.81 -0.90 -0.00

12 - - -9.30 -1.89 -2.40 -2.34 -0.86

13 - - - -1.89 -2.38 -2.20 -2.37

14 - - - - -2.38 -1.92 -2.11

Table 4.7: Comparing the required resources to satisfy all demand in scenarios with hub nodes and where all nodes are translucent

Resources required to satisfy all demand

Lightpaths 132 (+4.76%)

Transceivers 15 (+7.14%)

Wavelengths 15 (+7.14%)

The purpose of the conducted simulations was to assess how the imposed switching limitations

could compromise some of the optimality of the solution, in respect to the case where those

restrictions were lifted. In the scenario above, the option of relegating to the nodes with a nodal degree

higher then two the task to conduct OTN switching produced satisfying outcomes. In the end, the

option of installing ODU switches in only a third of the network nodes proved to require solely for an

extra wavelength per fiber and an extra transponder per node to route the entire traffic volume when in

comparison to the fully translucent solution. While the gaps observed for a number of transponders

fixed to 8 lay above the ten per cent mark, that stands as an exception that cannot be reproduced for

all other considered scenarios of resource availability. As so, the configuration depicted in Figure 4.3

can be considering attractive, allowing for six network nodes to be released from costly OTN switching

tasks. Despite this observation, no conclusions can be drawn for the general case of limited and

previously selected OTN switching nodes. In fact, the dependency with a number of scenario specific

parameters such as the node selection, the inputted traffic matrixes or the network’s physical topology

requires for the benefits and drawbacks to be analyzed case to case.

4.3.3 Translucent, transparent and opaque networks comparison

Section 4.2 featured a collection of translucent, transparent and opaque formulations for the

GRWA problem in resource scarcity scenarios. The divergent capabilities of the nodes in each

network configuration cause for different constraints to be placed on the matters of the establishment

of optical channels and routing of sub-wavelength signals over the virtual topology.

Multiplexing of finer grained signals in transparent networks is restricted to client connections

whose end-points are the same. The optimality of the throughput maximization problem in such

scenarios is achieved by determining the set of lightpaths that can be deployed with the available

resources such that the sum of the traffic carried by each is the highest. While this so called source

grooming technique allows for the bandwidth of direct lightpaths to be shared, the wavelength

57

channels’ utilization is dependent on how the volume of requested traffic among the node pairs

compares to the capacity of those optical pipes.

On the opposite side of the spectrum, opaque configurations trade optical for electrical switching,

providing for the wavelength channels’ capacity to be shared among a group of signals whose end-

points may be mismatched. However, the restriction of a single fiber span for every lightpath may

prove demanding on the number of required transponders. In fact, the number of virtual hops a

connection must sustain on its way from source to destination is lower bounded by the physical hop

count of the shortest path between those nodes which may prove to be a disadvantage when dealing

with networks with low mean nodal degrees.

In intent to draw comparisons and evaluate the performance of each network configuration,

transparent and opaque formulations were applied to the scenario presented in 4.3.1. The previously

attained results applying the translucent model served as baseline for the analysis performed and only

the distance to those solutions was considered. For further comparison data, the Bren Network was

less extensively examined for each configuration and those results are presented in Appendix C. The

following Tables and Figures are the result of the application of opaque and translucent models to the

scenario presented in 4.3.1.

Table 4.8: Performance of the transparent solution in regards to throughput

𝑇ℎ𝑟𝑡𝑟𝑎𝑛𝑠𝑝𝑎𝑟𝑒𝑛𝑡 − 𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

[%]

W T 8 9 10 11 12 13 14

8 0.00 -1.79 -3.07 -4.43 -3.94 -2.92 -1.90

9 0.00 -0.96 -2.54 -3.84 -3.77 -2.79 -1.81

10 - -0.48 -2.92 -4.14 -4.27 -2.67 -1.74

11 - 0.00 -2.18 -4.33 -5.43 -3.46 -1.92

12 - 0.00 -2.18 -4.18 -6.19 -5.54 -3.32

13 - - - -3.78 -5.89 -6.19 -5.68

14 - - - -3.78 -5.89 -6.00 -5.51

Table 4.9: Performance of the opaque solution in regards to throughput

𝑇ℎ𝑟𝑜𝑝𝑎𝑞𝑢𝑒 − 𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

[%]

W T 8 9 10 11 12 13 14

8 -38.20 -39.02 -37.79 -37.08 -34.01 -30.80 -26.72

9 -39.06 -39.71 -39.55 -39.49 -36.96 -33.89 -29.99

10 -39.06 -39.90 -40.96 -41.16 -39.65 -36.72 -32.98

11 - -39.90 -41.13 -42.35 -41.60 -39.31 -35.72

12 - - -41.13 -42.51 -42.93 -41.70 -38.25

13 - - - -42.51 -43.36 -42.70 -40.59

14 - - - - -43.36 -43.10 -41.15

Table 4.10: Resources required in opaque and transparent networks against translucent ones

Resources required to satisfy all demand

Transparent Opaque

Lightpaths 144 (+4.76%) 258 (+104.76%)

Transceivers 16 (+16.29%)

14,29

%)

49 (+250.00%)

14,29

%)

Wavelengths 18 (+28,57%) 14 (0.00%)

58

Table 4.11: Comparing the lightpaths' occupation in transparent and translucent scenarios

𝑀𝑒𝑑𝑖𝑢𝑚 𝐿𝑖𝑔ℎ𝑡𝑝𝑎𝑡ℎ 𝑂𝑐𝑐𝑢𝑝.𝑡𝑟𝑎𝑛𝑠𝑝𝑎𝑟𝑒𝑛𝑡− 𝑀𝑒𝑑𝑖𝑢𝑚 𝐿𝑖𝑔ℎ𝑡𝑝𝑎𝑡ℎ 𝑂𝑐𝑐𝑢𝑝.𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

𝑀𝑒𝑑𝑖𝑢𝑚 𝐿𝑖𝑔ℎ𝑡𝑝𝑎𝑡ℎ 𝑂𝑐𝑐𝑢𝑝.𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

[%]

W T 8 9 10 11 12 13 14

8 0.00 -4.43 -9.21 -7.74 -4.97 -7.21 -11.85

9 0.00 -2.38 -7.38 -9.42 -9.51 -13.44 -10.64

10 0.00 -1.43 -6.46 -11.14 -10.22 -9.97 -2.49

11 - 0.00 -5.08 -8.66 -11.63 -16.24 -10.06

12 - 0.00 -5.48 -8.15 -11.36 -13.36 -17.11

13 - - - -7.88 -12.27 -14.20 -14.55

14 - - - -7.88 -12.27 -13.29 -12.50

Table 4.12: Comparing the lightpaths' occupation in opaque and translucent scenarios

Table 4.8 shows that intermediate traffic grooming leads to higher network throughputs than end-

to-end traffic grooming. These observations are in agreement with those made in [21]. The allowance

for connections with mismatched end-points to share a common lightpath’s bandwidth makes for

better packed wavelength channels as displayed in Table 4.11. Where transparent configurations

require for a lightpath to be set up between every node pair with traffic requests, the intermediate

grooming approach permits for requests between two end-nodes to be transported consuming only

the spare capacity of lightpaths carrying single-hop connections between other node pairs. As a

consequence, not only translucent configurations permit for a larger volume of connections to be

satisfied under the same resource availability but they also allow to fulfill the entire traffic demand at

the expense of a lower number of optical channels, transponders and wavelengths as described in

Table 4.10.

The all-optical configuration clearly outperforms the opaque solution with all of its results

concerning throughput falling within a seven percent window to the translucent solutions against the

forty something percent window accounted on the application of the opaque model. In this latter case,

the imposition that a lightpath can only span a single fiber link proves to be extremely demanding on

the number of required transponders. Given the discrete uniform distribution applied to generate the

traffic matrixes, some volume of traffic is likely to be requested among every node pair. If all nodes

were adjacent to each other this wouldn’t present as much as a drawback. However, for the

considered Via Network, most of the nodes have a nodal degree of two. As a consequence, the

greatest portion of the shortest paths between the network node-pairs are composed of more than one

physical link requiring for more optical channels to be deployed even though intermediate grooming is

𝑀𝑒𝑑𝑖𝑢𝑚 𝐿𝑖𝑔ℎ𝑡𝑝𝑎𝑡ℎ 𝑂𝑐𝑐𝑢𝑝.𝑜𝑝𝑎𝑞𝑢𝑒− 𝑀𝑒𝑑𝑖𝑢𝑚 𝐿𝑖𝑔ℎ𝑡𝑝𝑎𝑡ℎ 𝑂𝑐𝑐𝑢𝑝.𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

𝑀𝑒𝑑𝑖𝑢𝑚 𝐿𝑖𝑔ℎ𝑡𝑝𝑎𝑡ℎ 𝑂𝑐𝑐𝑢𝑝.𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

W T 8 9 10 11 12 13 14

8 -3.54 -3.34 -2.20 -2.75 2.32 5.96 5.99

9 -5.65 -4.91 -2.19 -2.89 2.53 3.45 4.02

10 -4.84 -15.12 -4.53 -9.26 -6.72 0.89 11.22

11 - -8.97 -2.50 -3.42 -1.27 -0.98 6.09

12 - - -12.12 -12.87 -3.61 -1.17 -1.19

13 - - - -4.06 -15.27 -1.80 -10.77

14 - - - - -3.13 -10.68 4.59

59

permitted.The impact of the transponder limitation is clearly perceived in the Figure 4.4 bellow where it

can be seen that throughput’s growth curve with the number of available transponders is considerably

slower in comparison to the translucent case. In the end, though the entire traffic demand can be

satisfied with the same number of wavelengths as in the translucent case, the number of transponders

and lightpaths required is far superior.

Figure 4.4: Variation of the network's throughput in opaque and translucent schemes

4.4 Heuristic Approach

The traffic grooming, routing and wavelength assignment problem can be partitioned into the

following four sub-problems:

Determination, for each node pair, of the number of lightpaths to establish between those

endpoints;

Routing the lightpaths over the physical topology;

Assigning wavelengths for every lightpath so that the clash constraint is respected;

Routing each client signal over the determined virtual topology, respecting each optical channel’s

capacity.

One solution that comes from sequentially attaining the optimal result for each of the sub-

problems does not necessarily grant an optimum output for the whole of the problem. This comes as

consequence of the potential dependencies among each of the subjects, the results obtained at one

stage serving as an input and conditioning the degrees of freedom in the posterior phase.

Derived from the routing and wavelength assignment problem, the GRWA ILP methodology

inherits its NP-Hard trait. As proven in the previous chapter, this condition restricts the application of

these mathematical models to small sized networks. To overcome the issue, the approach is often to

resort to heuristic methodologies. These are the topic of the current section.

In [21], the authors propose two very much alike heuristic methodologies following a sequential

approach where the virtual topology is established in the first stage and posteriorly the connection

requests are routed over the lightpaths composing that topology. The basis for both of the algorithms

lays on the assumption that throughput can be maximized by carrying the highest volume of traffic in

unique direct lightpaths between the node-pairs. A more complex and elaborated methodology to the

40

50

60

70

80

90

100

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48

Thro

ugh

pu

t [%

]

T

W = 8W = 10W = 12

W = 14TranslucentTransparent

60

traffic grooming problem of throughput maximization is presented in [22]. Making use of an auxiliary

graph that considers the network’s physical topology, each node’s grooming capabilities and the

available transponders and wavelengths, connection requests are routed over the graph in a

methodology that integrates the four sub-problems. In the process of satisfying traffic demands,

lightpaths are established making use of the available wavelength links and transponder cards and

their capacities are filled. The following sections describe the aforementioned algorithms and the

adaptations perfomermed in the scope of this work.

4.4.1 MST and MRU heuristics

The Maximum Single Hop Traffic (MST) and the Maximum Resource Utilization (MRU) are

presented in [21] as alternatives to the computationally demanding mathematical formulation. Both

heuristics share the same concept based on the premise that carrying the higher amount of

connections in single hop routes is an enabler for maximum throughput. That being, the underlying

question becomes how to select the lightpaths to establish so that the number of attended requests is

as high as can be. On that note, the MST heuristic values the total volume of traffic between nodes the

most while in turn, the MRU methodology opts to reward the efficiency with which connections are

satisfied. The algorithms first order the node pairs according to a metric (in the MST case the

aggregated volume of traffic and in the MRU case the aggregated volume of traffic divided by the hop

count of the shortest path between the nodes). From highest to lowest, attempts are made to establish

lightpaths among the node pairs applying shortest path routing and first fit wavelength assignment.

Once the virtual topology is finished all traffic demands that can be routed in single hop routes are

attended subjected to the constrains in terms of the channels’ capacity. In the end, the remaining

connections, if any, are routed over multi-hop routes using the spare capacity available. The order in

which they are attended is once again accoding to the requested traffic volume in the MST case and

to the resource utilization value in the MRU scenario.

The original formulations reported in [21] were adapted in this work. Not only was it felt that the

algorithms’ description was not completely explicit on how to perform certain steps but it also felt

appropriate to trade some degree of simplicity in search of increased performance. The changes

performed are as described:

Regarding the lightpath establishment, addition of three mechanisms to determine the selection

order when two or more node pairs share the same volume of aggregated requested traffic

(MST) or the same resource utilization value (MRU) and the establishment of one lightpath

between one of those node-pairs prevents the others from being set up. The considered

mechanisms are as follows:

“blocked node-pairs”: for every node pair in concurrency conditions and featuring at the

same position in the ordered list, the one chosen is that whose establishment causes less

damage. That is, the one that causes for the least number of potential lightpaths to

become unfeasible over unavailability of consumed wavelengths and/or transponders.

“exposed capacity”: the selected node-pair is that whose establishment causes for the

greatest increase in spare capacity in the network;

61

“potentially exposed capacity”: similar to be above only that it also takes into consideration

potential capacity that can be made available if lightpaths are set up among the following

end-nodes on the ordered list;

For the MST heuristic, addition of another routing and wavelength assignment algorithm.

Besides the one presented on the original formulation that required for a lightpath to be

established on the shortest path route and assigned the lowest numbered wavelength, the

methodology applied in the RWA heuristic presented in 3.4.2 was also considered. As a

consequence, the heuristic is performed more than once in iterative fashion over the available

RWA possibilities. The first option was designated as “shortest-path first” and the second as

“first-fit wavelength assignment first”. This was not applied to the MRU heuristic given that the

node-pairs are selected based on their resource utilization value that is dependent on the

number of hops on the shortest path route.

Addition of two strategies to route the remaining connections that cannot be transported in

single-hop routes. The first Greedy scheme states that for a given set of remaining connections

of the same rate and between the same node-pairs, all available virtual paths are consumed

until all connections are satisfied or are deemed unable to route. The paths are selected in

order such that the first one attempted is the one whose spare capacity permits for more

connections to be successfully carried. This requires for a more exhaustive computation as all

available paths must be calculated in advance. The second Sharing Scheme attempts to share

the remaining capacity in the virtual topology over the connections that are yet to be satisfied.

Ordering the paths in the same manner as the alternative scheme, in this case only the first

virtual path is consumed. If there are still connections left to attend for a given request they must

wait their turn while others are taken care of first.

For the remaining requests, the MST and MRU metrics used to determined which is chosen first

take only into account the volume of traffic that can actually be routed under the network’s

current conditions and not all demanded traffic left to satisfy.

In order to explore the set of options to untie situations in which node pairs have the same MST or

MRU metrics, the two possible RWA approaches for the MST case and the two schemes to route the

remaing connection requests, the algorithm must be performed multiple times combining each

possible strategy. The solutions resulting from each iteration ought to be kept and in the end the

selected one is that accountable for the highest volume of successfully routed traffic. In the end, some

simplicity is compromised and some extra complexity added in exchange of a larger space of

solutions.

4.4.2 Graph Heuristic

In [22] another methodology is used to target the traffic grooming problem in regards to

throughput maximization. The presented auxiliary graph heuristic tackles the problem over a different

angle, one where connections are routed while the virtual topology is being created, each sub-problem

feeding information to the other and evolving together towards the final solution. The algorithm is

62

supported in an auxiliary graph that expresses the network’s both physical and virtual topologies, as

well as each node’s capabilities and overall state of resources. Requests are attended individually and

sequentially and routed over the graph on the minimum weighted path. The order in which requests

are chosen is controlled by a set of traffic selection schemes and the edge’s weights are defined

according to a traffic grooming policy, set to achieve a specific goal such as the minimization of virtual

hops, of lightpaths or of wavelength links. The structure of the graph is dynamically updated as

demands are attended and resources consumed. The model is extremely flexible and its range of

applicability extremely wide, as the establishment of edges among selected graph nodes can convey a

large number of network configuration scenarios (physical nodes with and without wavelength

conversion capabilities, with or without grooming capabilities and so on). The model was only briefly

adapted such that instead of having a wavelength edge for each available wavelength per fiber, a

single edge was considered and an additional algorithm created to save the current state of

wavelength link availability over the network’s fibers. Also, for simulation purposes, all traffic selection

schemes and traffic grooming policies were integrated into a single iterative algorithm over all possible

combinations. As before, the intent was to increase the space of possible solutions. More details on

this approach and a demonstrative example can be found in Appendix D.

4.5 Ilp and heuristic comparison

In the sections bellow, a comparative analysis between the presented heuristics and the linear

programming methodology is presented via simulations performed targeting a real life network. The

aim of the analysis is to determine how each model performs in terms of quality of the solution and

computational time necessary to achieve results. The development of a heuristic model must always

be ruled by the intent to achieve results as close to the optimum as possible and at the cost of low

computational times. In such terms, the quality of the presented heuristic algorithms is measured in

how their solutions compare to the ILP model (how short the gap is between the throughputs attained)

and how much faster they can produce results. On that line, the Ilp results attained applying the

translucent Ilp model to the Via network in 4.3.1 are put against the MST, MRU and Graph heuristics

and the results are dissected in the following lines.

Table 4.13: Throughput attained by the MRU heuristic compared to the Ilp model

𝑇ℎ𝑟𝑀𝑟𝑢 − 𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

[%]

W T 8 9 10 11 12 13 14

8 -1.24 -1.47 -5.07 -3.55 -1.90 -0.44 -0.44

9 -2.62 -2.74 -2.99 -5.54 -1.54 -0.70 -0.70

10 -2.62 -2.73 -0.73 -3.73 -1.47 -0.67 -0.67

11 - -2.73 -1.02 -3.92 -1.81 -1.79 -0.26

12 - - -1.02 -2.29 -2.02 -1.97 -0.25

13 - - - -2.29 -2.76 -1.96 -1.19

14 - - - - -2.76 -2.40 -1.41

63

Table 4.14: Throughput attained by the MST heuristic compared to the Ilp model

𝑇ℎ𝑟𝑀𝑠𝑡 − 𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

[%]

W T 8 9 10 11 12 13 14

8 -0.53 -0.65 -1.08 -2.95 -4.09 -4.09 -4.09

9 -0.01 -0.96 -1.20 -2.70 -2.93 -2.09 -2.09

10 0.00 -0.48 -3.36 -2.64 -2.80 -1.87 -0.27

11 - 0.00 -0.87 -4.33 -3.49 -1.92 -0.26

12 - 0.00 -0.87 -2.30 -5.18 -3.69 -1.97

13 - - - -2.30 -4.01 -2.93 -2.01

14 - - - - -4.14 -4.44 -2.58

Table 4.15: Throughput attained by the Graph heuristic compared to the Ilp model

𝑇ℎ𝑟𝐺𝑟𝑎𝑝ℎ − 𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

[%]

W T 8 9 10 11 12 13 14

8 -3.87 -6.02 -3.53 -3.25 -3.21 -1.02 0.00

9 -5.21 -4.18 -4.33 -4.26 -2.93 -0.98 0.00

10 -5.21 -2.88 -4.52 -2.49 -3.34 -1.34 0.00

11 - -2.88 -2.18 -3.52 -4.13 -3.07 -1.02

12 - - -2.18 -2.70 -2.90 -3.57 -1.97

13 - - - -3.37 -3.01 -3.29 -2.37

14 - - - -3.37 -3.01 -2.88 -1.41

Table 4.16: Resources required to satisfy demand for the three heuristics

Resources required to satisfy all demand

Mru Mst Graph

Lightpaths 140 (+11.11%) 136 (+7.94%) 130 (+3.17%)

Transceivers 16 (+14.29%)

14,29

%)

16 (+14.29%)

14,29

%)

16 (+14.29%)

Wavelengths 17 (+21.43%) 16 (+14.29%)

14 (0.00%)

Table 4.17: Running Times observed applying the Ilp model

𝑇𝑖𝑚𝑒𝐼𝑙𝑝 [𝑠]

W T 8 9 10 11 12 13 14

8 44.27 51.79 163.67 113.76 88.87 40.73 80.11

9 51.17 54.84 114.38 487.65 154.00 134.66 56.08

10 61.04 64.29 310.02 112.70 144.57 541.00 93.32

11 70.97 68.12 214.20 510.66 2577.21 660.40 54.13

12 81.05 127.33 112.51 311.96 234.87 152.19 146.72

13 91.08 234.21 214.61 117.90 98.51 2085.94 145.79

14 41.11 128.50 213.15 97.75 96.01 1594.26 81.80

Table 4.18: Comparing the running times for the Ilp and the MRU heuristic

𝑇𝑖𝑚𝑒𝑀𝑟𝑢

𝑇𝑖𝑚𝑒 𝐼𝑙𝑝

[%]

W T 8 9 10 11 12 13 14

8 0.22 0.25 0.07 0.08 0.70 0.11 0.34

9 0.62 0.78 0.04 0.10 0.11 0.12 0.63

10 0.23 0.99 0.50 0.08 0.06 0.12 0.18

11 0.25 0.80 0.50 0.79 0.00 0.53 0.02

12 0.24 0.74 0.65 0.59 0.26 0.19 0.05

13 0.97 0.43 0.64 0.49 0.23 0.01 0.05

14 0.32 0.66 0.36 0.47 0.14 0.02 0.07

64

Table 4.19: Comparing the running times for the Ilp and the MST heuristic

𝑇𝑖𝑚𝑒𝑀𝑠𝑡

𝑇𝑖𝑚𝑒 𝐼𝑙𝑝

[%]

W T 8 9 10 11 12 13 14

8 0.93 0.38 0.80 0.45 0.74 0.25 0.04

9 0.38 0.78 0.13 0.08 0.11 0.31 0.92

10 0.40 0.19 0.67 0.07 0.04 0.25 0.23

11 0.26 0.52 0.99 0.94 0.00 0.13 0.45

12 0.77 0.05 0.19 0.93 0.23 0.06 0.05

13 0.64 0.14 0.74 0.20 0.23 0.00 0.04

14 0.58 0.21 0.09 0.17 0.24 0.00 0.07

Table 4.20: Comparing the running times for the Ilp and the Graph heuristic

𝑇𝑖𝑚𝑒𝐺𝑟𝑎𝑝ℎ

𝑇𝑖𝑚𝑒 𝐼𝑙𝑝

[%]

W T 8 9 10 11 12 13 14

8 9.67 8.87 8.75 5.42 6.13 5.62 5.51

9 9.19 8.63 4.91 6.97 7.01 6.39 5.68

10 8.63 8.12 5.17 5.51 6.59 6.86 5.69

11 9.14 7.71 4.68 5.68 5.27 7.62 5.49

12 7.78 6.02 4.36 6.49 7.90 4.69 9.10

13 9.58 5.99 9.75 5.18 7.91 0.34 5.17

14 7.31 6.41 4.22 5.52 8.27 0.45 5.25

The tables bellow attest to a very satisfying performance of all the algorithms as most results fall

within a five per cent gap to the mathematical models. It is hard to say which of the algorithms

performs better in such conditions. However, by looking through Table 4.16 respecting the required

resources to route all traffic, it can be noted that the graph model is the less demanding in all cases

considered. In regards to the computational times to solve the GRWA problem, all presented

heuristics accomplish the goal of requiring substantially less effort than the Ilp approach. The same

methodology used for the tests conducted above was applied towards a network of greater

dimensions. The attained results are displayed in Appendix C.

4.6 Applying the heuristics to networks of larger dimensions

In this section the heuristics serve their purpose as they are applied to networks of large

dimension for which the Ilp models are unfit. Simulations were run for the Germany and for the

Arpanet Network in order to perform a comparative analysis between the studied models. Again,

bidirectional traffic matrixes were considered and symmetric traffic routing was performed. The

aggregated volume of traffic considered for the Germany Network, that is, the sum of the number of

connections between each node pair multiplied by their data-rate, was a little over seven Terabits per

second (7017.5 Gbps). In turn, for the Arpanet, the total demanded traffic rose above the value of ten

Terabits per second (10337.5 Gbps). The results are displayed bellow:

Germany Network

65

Figure 4.5: Comparing the heuristics' performance for the Germany Network

Table 4.21: Resources required to satisfy demand for the three heuristics

Resources required to satisfy all demand

MRU MST Graph

Lightpaths 242 248 244

Transceivers 16

14,

%)

16

14,

%)

15

Wavelengths 18 19 17

Arpanet

Figure 4.6: Comparing the heuristics' performance for the Arpanet

Table 4.22: Resources required to satisfy demand for the three heuristics

Resources required to satisfy all demand

MRU MST Graph

Lightpaths 242 248 352

Transceivers 20

1

%)

19

14

%)

18

Wavelengths 25 29 26

Overall, the graph model seems to be the one from among all the considered heuristics that is

able to expedite more traffic with the least number of resources. It also seems to be the one to exhibit

the highest growth curve with the number of transponders. In a comparative analysis of the MRU and

MST models, the first one shows more sensitivity to the transponders’ availability. In the figures

displayed above, for a constant number of wavelengths, the variation of the network’s throughput with

the transmission devices is more accentuated. Also, the MRU heuristic achieves maximum throughput

80

85

90

95

100

12 13 14 15

Thro

ugh

pu

t [%

]

T

MRUMSTGraphW = 11W = 13W = 15

85,00

87,00

89,00

91,00

93,00

95,00

97,00

99,00

101,00

15 16 17 18 19 20

Thro

ugh

pu

t [%

]

T

MRUMSTGraphW = 19W = 21W = 25

66

with fewer wavelengths than the MST one. That can be explained by the fact that the algorithm

attempts to utilize wavelengths efficiently, prioritizing the pairs of nodes with higher volumes of

aggregated traffic that can be routed over the shortest paths in the physical topology.

4.7 Conclusions

This chapter featured a range of integer linear programming methodologies applied to the

grooming, routing and wavelength assignment problem in situations with scarce resources.

Translucent, opaque and transparent network configurations were embraced by the formulations to

exploit how the process of aggregating lower rate streams developed in all-optical networks, in

networks were the WDM layer offers point-to-point connectivity to the OTN nodes and in networks

where some or all of its nodes have both electric and optical switching fabrics. On the topic of

translucent networks, each node’s ability to perform switching at the OTN domain was taken as an

input to tackle cases in which only a subset of the network nodes can perform intermediate grooming.

Tests performed for the Via Network in a configuration where only a limited set of nodes had OTN

switching capabilities were compared against those attained for the full-OTN switching configuration. A

compelling tradeoff was attained restricting intermediate grooming to three out of the nine nodes, the

choice falling upon those that had a nodal degree higher than two. Results showed that the gaps to

the solutions in which all nodes were equipped with OTN fabrics were short and only an extra

wavelength per fiber and transponder per node were required to route all demand in comparison to the

fully translucent solution.

The grooming, routing and wavelength assignment problem is an extension of the RWA problem

to include the aggregation and routing of client signals over optical channels. As so, just like the topic

addressed in chapter three, the GRWA problem is NP-Hard and its application to networks of practical

size is compromised by the elevated and in cases untrackable computational times. To work around

this situation, the course of action usually falls over developing heuristic mechanisms to achieve

quality results in lower running times. In 4.4, the adaptations performed on three published heuristics

were presented. Simulations were conducted to compare their performance against the Ilp models in

terms of throughput achieved and required computational effort. Results were satisfying on both

accounts. Finally, the three heuristic methodologies were compared in more depth. Applying those

models to two real life networks of large dimensions, the observed results were quite close in that no

heuristic proved a noticeable improved performance in regards to the other two. That being, the graph

model was at all times the one to be accounted for the lowest lightpath, wavelength and transponder

consumption in satisfaction of the entire traffic demand.

67

5 Cost Minimization Methodologies

When addressing the planning stages of a transport network, the challenge of cost

minimization always lies as an underlining concern. The current chapter considers the design of

optical networks employing OTN/WDM switches with mixed rate transponders in achievement of the

optimal combination of optical bypassing and traffic grooming for the lowest overall expenditures. The

work developed relates solemnly to the line card costs. The mixed line rate translucent configuration is

compared against transparent and opaque mixed rate solutions and with single rate translucent

schemes in scenarios with symmetric traffic matrixes. In that scope, Ilp formulations are presented and

applied to a series of test cases. Likewise, an original heuristic applying the previously introduced

graph model is described and put to comparison against the mathematical approach. In the end, that

algorithm is applied to networks of large dimensions.

Derived from the conclusions drawn in [27], the viability of employing asymmetrical optical

connections is considered for scenarios with asymmetrical traffic requests. A set of distinct line card

configurations is analysed to conclude on which is more suitable for driving down the costs of

networks that deal with traffic asymmetry. The comparative analysis is made by means of Integer

linear formulations developed for the purpose.

68

5.1 Introduction

In Chapter 2 it was mentioned how the Optical Transport Network protocol came to replace the

previously dominant SONET/SDH technologies as the standard for transport networks. Whenever

such a migration takes place, a great deal of planning must be laid on cost optimization strategies.

The expenditures accouted on the installation of new eqquipments should be met with a return in

investment over the years to come and for that purpose it is of extreme importance to minimize the

cost per transported bit and the maintenance and operational expenditures to increase the profit

margins. On that note, the choice for OTN technologies lies as an enabler for cost effectiveness on

itself by permitting for a plethora of services with distinct signal characteristics and quality

requirements to share a common transport platform with unified management.

Over the years the WDM network has evolved to tame the capacity strand problematic by

increasing the wavelength channels’ capacity. As described in Chapter 2, the mismatched service

rates and the optical transmission line rates posed challenges to operators that had to come up with

solutions to efficiently fill the bulky optical pipes. In the last chapter the advantages of deploying

translucent networks where some or all nodes are eqquiped with ODU/WDM switching fabrics were

outlined. The higher throughputs attained in resource scarcity scenarios and the requirement for fewer

wavelengths and transponders for the satisfaction of the entire traffic demand made a realy compeling

case for the allowance of both wavelength and sub-wavelength switching as a core strategy to reduce

equipment related costs.

In [24], further comparisons on all-optical and translucent networks are developed in regards to

the network optimization subject of cost minimization. Considering optical impairment aware networks

and accounting expenditures on the use of line, client, regenerator, transponder and grooming cards,

the authors intend to access on the best placement of cards for minimizing capital expenditures. The

strategies considered were a transparent configuration employing client, transponder and regenerator

cards and two translucent configurations employing client, line and grooming cards being that one

allowed for the placement of regenerator cards as well. Results conducted applying the developed

heuristic model for each individual scenario proved the grooming and regenerator card approach to be

the enabler for the lower costs with the grooming card only solution coming closely behind. Despising

the degradation of the light pulses transmitted over the optical fibers and consequently crossing out

the need for regenerator cards, this chapter intends to corroborate that the translucent approach is

more cost effective than the all-optical one. On that note, Integer Linear Programming models are

developed for both network configurations and also extended to include opaque scenarios. The cost of

grooming and client cards is despised on the reasoning that those expenditures are negligible against

those associated with line cards. The considered line cards are those presented in 2.2.3 comprising a

transponder and an OTN mux/demux.

In [26] mixed line rate networks are addressed and their performance is compared against

single-rate ones. Supported on the assumption that establishing lightpaths of different bandwidths is a

more fitting approach for networks with traffic heterogeneity where the demands have very different

capacity requirements, the authors propose a heuristic and make use of the auxiliary graph model

69

briefly discussed in the previous chapter to assess on the cost effectiveness of translucent networks

with availability of transponders of disparate rates. As opposed to the former referenced publication,

the authors consider that every node is optically reachable at any line rate.The application of the

algorithm to test cases for single-rate networks with either 10 or 100 Gbps line cards and for mixed

rate networks where both line cards were allowed to coexist proved that the mixed line rate solution

conceded for the lowest expenditures. In this chapter, the developed formulations take this matter into

account and it is assumed that a set of line cards with transponders capable of transmitting in different

rates are available. It is intended to corroborate the heuristic results of [26] with results attained with

the application of mathematical models.

The studies conducted for the two researched subjects culminated in the development of Ilp

models and of a heuristic algorithm. This last one puts the graph model of [22] to use in order to

achieve an initial virtual topology and possible solution for the routing of the sub-rate streams. Those

results are then reconstructed and the connections re-routed so that a number of established optical

channels can be taken down in reduction of the number of line cards. Both the developed heuristic

and the Ilp formulation assume traffic requests to be bidirectional and seize that trait to perform

symmetrical routing of the traffic demands.In such conditions, the outcomes produced by the

developed models comprise a virtual topology composed of bidirectional lightpaths carrying traffic

between the same end-points in different directions. In [27] the authors focus on traffic asymmetry and

conclude that asymmetrical lightpaths are more fitting in those conditions. The proposition that in such

cases bidirectional line cards could be replaced by asymmetrical line cards or by unidirectional line

cards composed of a standalone transmitter or receiver is developed later on this chapter.

Formulations are developed for the asymmetric traffic scenario considering the establishment of

symmetrical and asymmetrical lightpaths. Unidirectional and asymmetrical line card approaches are

analysed as well. The studies comprise the enunciation of Ilp models and posterior application to a

test case in intent to assess on the most suiting line card configuration and lightpath selection to

achieve minimum cost.

5.2 Ilp Model for symmetrical traffic

This section presents Ilp models for the traffic grooming problem of cost minimization. The

general problem statement can be described as follows: given a graph 𝐺(𝑉, 𝐸) where 𝑉 corresponds to

the network nodes and 𝐸 to the fiber links connecting them, a set of traffic matrixes 𝑇𝑈, each

corresponding to the demand in terms of ODU signals of the same rate 𝑢 ∈ 𝑈, a set of available line

rates 𝑟 ∈ 𝑅, and the associated costs of the line cards transmitting/receiving on those rates,a virtual

topology and the routing of the client signals are to be determined in achievement of the lowest

network expenditures. The problem is constrained by the optical channels’ capacity 𝐶 that limits the

volume of carried connections and by the number of wavelengths 𝑊. OTN switches at all nodes

concede for low speed streams to be processed in the electric domain at intermediate nodes and in

turn, ROADMs work on the optical layer to allow for optical bypassing of wavelength channels. On the

assumption that traffic demand is symmetric the sub-rate signals are routed over bidirectional virtual

70

paths. Bellow, formulations for translucent, transparent and opaque networks are presented. The

assumptions are the same made in 4.2. The notation, inputs and variables are as follows:

Problem inputs:

A physical topology 𝐺 = (𝑉, 𝐸), consisting of a bidirectional graph, where 𝑉 is the set of

network nodes and 𝐸 the set of fiber links connecting the nodes;

Number of wavelength channels per fiber 𝑊;

Number of transceivers per node 𝑇𝑟;

Available line rates 𝑟 ∈ 𝑅;

Set of considered ODU signals’ rates 𝑈;

Traffic matrices set 𝑇𝑈 corresponding to the ODU connection requests.∀ 𝑠, 𝑑 ∈ 𝑉, 𝑢 ∈ 𝑈, 𝑡𝑠𝑑𝑢

denotes the number of ODU requests of rate 𝑢 to establish among source-destination

pair (𝑠, 𝑑). The notation is as follows: every individual connection is referred to as a traffic

demand and a group of traffic demands of the same rate between the same end-points is

conceived as a traffic request;

Normalized costs of the line cards 𝐶𝑟𝑅 associated to a given rate 𝑟 ∈ 𝑅. The costs are

normalized to the lowest rate 𝑟 ∈ 𝑅 that is , 𝐶𝑟𝑟 =𝑐𝑜𝑠𝑡min (𝑟 ∈𝑅)

𝑐𝑜𝑠𝑡 𝑟 .

Notation:

𝐴 stands for the set of network arcs. Each network arc 𝑎 ∈ 𝐴 is an unidirectional

representation of a physical connection among two nodes (𝑠(𝑎), 𝑑(𝑎)) such that there is at

least one fiber link among those nodes. A given arc is characterized by 𝑙𝑎 , the number of

optical fibers uniting 𝑠(𝑎) and 𝑑(𝑎). Given that fibers are deployed in pairs, if we consider arc

𝑎 from 𝑠(𝑎) to 𝑑(𝑎) and arc 𝑎′ such that 𝑠(𝑎′) = 𝑑(𝑎) and 𝑑(𝑎′) = 𝑠(𝑎), then 𝑙𝑎 = 𝑙𝑎′ ;

𝑖 and 𝑗 denote the origin and destination of an optical channel, respectively. A given lightpath

may traverse one or multiple network arcs;

𝑠 and 𝑑 stand for the origin and destination, respectively, of an end-to-end traffic request.

The end-to-end traffic can be carried over one or more optical channels.

Variables:

𝑃𝑖𝑗 : Set of possible paths between node i and node j. These paths must be calculated offline

prior to the problem’s execution;

𝑃𝑖𝑗𝑎 : Set of possible paths between node i and node j that traverse arc 𝑎 ∈ A.

𝐿𝑖𝑗𝑟 : Number of lightpaths of rate 𝑟 ∈ 𝑅 between 𝑖 and 𝑗. 𝐿𝑖𝑗

𝑟 ∈ 𝛮0 ;

𝐿𝑖𝑗

𝑝𝑖𝑗,𝑤: Number of lightpaths between 𝑖 and 𝑗 routed on path 𝑝𝑖𝑗 over wavelength 𝑤.

𝐿𝑖𝑗

𝑝𝑖𝑗,𝑤 ∈ 𝛮0;

𝐺𝑖𝑗,𝑠𝑑𝑢 : Number of ODU connections of rate 𝑢 between 𝑠 and 𝑑 carried over a lightpath with

end-points (𝑖, 𝑗). 𝐺𝑖𝑗,𝑠𝑑𝑢 ∈ 𝛮0

5.2.1 Translucent Networks

Objective Function:

71

(5.1) 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 ∑ ∑ ∑ 𝐿𝑖𝑗𝑟 ∗ 𝐶𝑟𝑟

𝑟 ∈ 𝑅

∗ 2

𝑗 ∈ 𝑉𝑖 ∈ 𝑉

Constraints:

(5.2) ∑ ∑ 𝐿𝑖𝑗

𝑝𝑖𝑗,𝑤= ∑ 𝐿𝑖𝑗

𝑟

𝑟 ∈ 𝑅𝑤 ∈ 𝑊𝑝𝑖𝑗 ∈ 𝑃𝑖𝑗

∀ 𝑖, 𝑗 ∈ 𝑉

(5.3) ∑ ∑ ∑ 𝐿

𝑖𝑗

𝑝𝑖𝑗,𝑤

𝑝𝑖𝑗 ∈ {𝑃𝑖𝑗𝑎 ∪ 𝑃𝑖𝑗

𝑎′}

≤

𝑗 ∈𝑉𝑖 ∈𝑉

𝑙𝑎 ∀ 𝑎, 𝑎′ ∈ 𝐴; 𝑤 ∈ 𝑊

𝑎′ => 𝑠(𝑎) = 𝑑(𝑎′) , 𝑑(𝑎) = 𝑠(𝑎′)

(5.4) ∑ 𝐺𝑚𝑠,𝑠𝑑𝑢

𝑚 ∈ 𝑁

= 0 ∀ 𝑠, 𝑑 ∈ 𝑉, 𝑢 ∈ 𝑈

(5.5) ∑ 𝐺𝑚𝑑,𝑠𝑑𝑢

𝑚 ∈ 𝑁

= 𝑡𝑠𝑑𝑢 ∀ 𝑠 ∈ 𝑉, 𝑑 > 𝑠, 𝑑 ∈ 𝑉, 𝑢 ∈ 𝑈

(5.6) ∑ 𝐺𝑠𝑛,𝑠𝑑𝑢

𝑛 ∈ 𝑁

= 𝑡𝑠𝑑𝑢 ∀ 𝑠 ∈ 𝑉, 𝑑 > 𝑠, 𝑑 ∈ 𝑉, 𝑢 ∈ 𝑈

(5.7) ∑ 𝐺𝑑𝑛,𝑠𝑑𝑢

𝑛 ∈ 𝑁

= 0 ∀ 𝑠 ∈ 𝑉, 𝑑 > 𝑠, 𝑑 ∈ 𝑉, 𝑢 ∈ 𝑈

(5.8) ∑ 𝐺𝑚𝑘,𝑠𝑑 𝑢

𝑚 ∈ 𝑁

= ∑ 𝐺𝑘𝑛,𝑠𝑑𝑢

𝑛 ∈ 𝑁

∀ 𝑘 ∈ 𝑉, 𝑘 ≠ 𝑠, 𝑘 ≠ 𝑑, 𝑠 ∈ 𝑉,

𝑑 > 𝑠, 𝑑 ∈ 𝑉, 𝑢 ∈ 𝑈

(5.9) ∑ ∑ ∑ 𝐺𝑖𝑗,𝑠𝑑𝑢 ∗ 𝑢

𝑢 ∈ 𝑈𝑑 ∈𝑁

≤ ∑ 𝐿𝑖𝑗𝑟

𝑟 ∈ 𝑅

∗ 𝑟

𝑠 ∈𝑁

∀ 𝑖, 𝑗 ∈ 𝑉

The factor of 2 in the objective function is associated with the fact that only the lightpaths

carrying connections in the direct direction are considered. As so, for every lightpath established a line

card must be accounted on the source and on the destination node of the optical channel. (5.1)

establishes the objective to minimize the total cost of deploying line cards. (5.2) and (5.3) concern the

physical routing of the lightpaths assuring that for each established optical channel, the same

wavelength channel is reserved in all spanned links. Also, (5.3) assures the wavelength clash

constraint by establishing that a wavelength can be assigned to at most one lightpath per fiber link.

Equations (5.4) to (5.8) regard the virtual routing of each individual traffic flow, ensuring the

assignment of client signals onto a set of one or more lightpaths. Inequation (5.9) guarantees that

connections are assigned to lightpaths as long as the available bandwidth is not exceeded.

5.2.2 Opaque Networks

The required changes concern the offline computed paths of the link path model and are as follows:

𝑃𝑖𝑗 = {∅ , 𝑖𝑓 ∄ 𝑎 ∈ 𝐴 ∶ 𝑠(𝑎) = 𝑖 , 𝑑(𝑎) = 𝑗

{𝑝𝑖𝑗 ,0 }, 𝑝𝑖𝑗 ,0 = {𝑖, 𝑗}, 𝑖𝑓 ∃ 𝑎 ∈ 𝐴 ∶ 𝑠(𝑎) = 𝑖 , 𝑑(𝑎) = 𝑗

5.2.3 Transparent Networks

For the all-optical model it is necessary to replace 5.4 to 5.8 with:

(5.10) 𝐺𝑠𝑑,𝑠𝑑𝑢 = 𝑡𝑠𝑑

𝑢 ∀ 𝑠 ∈ 𝑉, 𝑑 > 𝑠, 𝑑 ∈ 𝑉, 𝑢 ∈ 𝑈

72

(5.11) ∑ ∑ ∑ ∑ ∑ 𝐺𝑠𝑑,𝑖𝑗𝑢

𝑢 ∈𝑈𝑗 ∈ 𝑉, (𝑖,𝑗)≠(𝑠,𝑑)

𝑖 ∈ 𝑉𝑑>𝑠, 𝑑 ∈ 𝑉

𝑠 ∈ 𝑉

= 0

5.1 Applying symmetrical traffic Ilp models

The current section comprises the results obtained for a number of simulations regarding two

test networks with six and seven nodes whose topology will be presented further on. The distinct

network configuration schemes are put to comparison and conclusions are drawn. Regarding

translucent scenarios, simulations are conducted assuming the availability of 40 Gbps and/or 100

Gbps lightpaths in single and mixed line rate conditions. A range of cost ratios is considered and an

analysis conducted regarding the dependency of the number of established lightpaths of each rate on

the cost ratio defined. As previously stated, the defined cost metric results in that the problem of

minimizing capital expenditures becomes a lightpath minimization problem when dealing with single

rate networks. The same cannot be affirmed for the cases of mixed rate networks where the

lightpath’s rate assignment is another factor that impacts the total cost. The number of lightpaths used

in single and mixed-rate configurations in the same testing conditions are compared. The choice over

test networks with six and seven nodes was a result of the struggle to conduct the Ilp simulations.

When trying to move to networks with eight nodes and even further to the Via Network with nine

nodes, either the majority of the simulations would take several days to perform or constant “Out of

Memory” exceptions would be thrown by cplex [15] no matter how much tunning was performed to

relax the problems. A range of cost ratios was considered to assess on how the cost relations

between line cards of different rates impacted the solutions. In all displayed graphics the total traffic

volume TTV is accounted correspondending to the aggregated sum of requested traffic.

5.1.1 Comparing Translucent, Opaque and Transparent Networks

The following conditions were made common to all simulations performed:

Table 5.1: Conditions common to all simulations

Cost ratios 𝐶𝑟 = {1.5, 2, 2.5}

Available line rates [Gbps] 𝑅 = {40,100 }

Accepted client signal rates [Gbps] 𝑈 = {1.25, 2.5, 10}

Six Nodes Network

The physical topology of the tested six nodes network is displayed in the figure bellow:

Figure 5.1: Six nodes network's physical topology

73

Figure 5.2: Cost obtained for transparent, translucent and opaque models

Table 5.2: Number of established lightpaths in translucent mixed rate configurations

Total traffic Volume TTV [G]

Cr Lightpaths 900 1200 1500 1800 2100 2400 2700 3000 3300 3600 3900

1.5 40 2 4 2 2 6 4 4 10 4 6 4

100 14 16 20 22 22 28 30 30 36 38 42

total 16 20 22 24 28 32 34 40 40 44 46

2 40 16 10 14 6 6 8 16 10 10 12 16

100 6 12 14 20 22 24 24 30 32 34 36

total 22 22 28 26 28 32 40 40 42 46 52

2.5 40 28 32 34 36 38 40 52 34 62 48 42

100 0 2 4 6 8 10 8 18 10 18 24

total 28 34 38 42 46 50 60 52 72 66 66

Seven Nodes Network

The physical topology of the simulated seven nodes network is displayed in the figure bellow:

Figure 5.3: Seven nodes network's physical topology

Figure 5.4: Cost obtained for transparent, translucent and opaque models

20

40

60

80

100

120

140

160

900 1200 1500 1800 2100 2400 2700 3000 3300 3600 3900

Co

st

TTV [G]

20

40

60

80

100

120

140

160

900 1200 1500 1800 2100 2400 2700 3000 3300 3600 3900

Co

st

TTV [G]

74

5.1.2 Comparing Single and Mixed-Line Rate Transparent Networks

Six Nodes Network

Figure 5.5: Cost obtained for single and mixed line rate networks

Seven Nodes Network

Figure 5.6: Cost obtained for single and mixed line rate networks

As in the preceding chapter, a comparison was performed featuring the translucent, transparent

and opaque scenarios. For the all optical network design, the problem becomes that of routing and

wavelength assignment as it is possible to calculate, by simple observation of the traffic matrixes, the

least costly lightpath configuration between any two nodes with demand. For every node pair, the

occupation of the lightpaths is solemnly dependent on the aggregated volume of traffic flowing

between those nodes. On the topic of opaque approaches, the restriction that lightpaths can only be

established among physically adjacent nodes, results in the impossibility to perform optical bypassing.

As a result, in general, a higher number of lightpaths must be deployed when in comparison to the

translucent case. This last configuration featuring the allowance of both lambda and sub-lambda

switching is deemed the most fit to achieve higher lightpath filling ratios. The higher flexibility over

opaque solutions on the establishment of optical channels and over transparent solutions on the

routing of client signals concedes for the lowest expenditures as perceived in Figures 5.2 and 5.4

accounting for the results attained for simulations in mixed line rate scenarios with the availability of

both 40 and 100 Gbps line cards. For every traffic volume considered, the translucent scheme is

always the one that is most compliant with the established goal. In turn, the opaque approach’s

obligation that all lightpaths can only span a single fiber link results in the higher costs from among all

possible configurations. The superior performance of translucent solutions over transparent ones goes

in line with the results displayed in [24].

20

40

60

80

100

120

1 2 3 4 5 6 7 8 9 10 11

Co

st

TTV [G]

20

40

60

80

100

120

140

1200 1600 2000 2400 2800 3200 3600 4000 4400 4800

Co

st

TTV [G]

75

Figures 5.5 and 5.6 suggest that the mixed line rate design is the one that allows for the lowest

capital expenditures when deploying a WDM/OTN network. These results assert what was concluded

applying heuristics to mixed and single rate scenarios in [26]. When the cost ratios vary from 1.5 to 2,

the single rate solution employing 100 Gbps line cards provides for lower costs in comparison with the

40 Gbps solution. That is because the cost charged per bit transported is lower. That cost is only

made equal for both line cards when the cost ratio is made equal to 2.5 (100/40=2.5). For that value

the 40 Gbps single rate solution provides for lower costs in comparison to the other approach and its

results come closer to the mixed rate solution. By observing Table 5.2 it can be seen that for cost

ratios of 1.5 and 2 the mixed rate scheme prefers establishing 100 Gbps lightpaths. The behaviours

changes for a cost ratio equal to 2.5 where the dominant lightpaths are those of 40 Gbps. This comes

in agreement with the associated costs per transported bit associated with each card.

5.1 Heuristic for symmetrical traffic

To workaround the NP-complete property of the Ilp formulations, a heuristic approach was

developed targeting application to networks of greater reaches for which the mathematical

programming approach is unsuitable and often times impracticable. The designed algorithm makes

use of the graph model presented in the previous chapter to provide an initial input to be manipulated

in achievement of lower costs. Given a set of traffic matrixes, the graph methodology is put to use to

satisfy the client demands in their entirety. As a result, a virtual topology and each established

lightpath’s routing and wavelength assignment is attained as is the virtual routing of each individual

traffic flow over such topology. Using the obtained configuration as a starting point, the purpose of the

algorithm is to re-route traffic, rearranging the assignment of connections onto optical channels to

eliminate the need for some of the lightpaths in the initial set-up. A lightpath is selected in turn and

considered for elimination by exploring alternative virtual routing options to the connections it carries. If

a portion or all of its traffic is averted, it may be possible to replace the associate line-cards for others

of lower cost (replacing a 100 Gbps lightpath with a 40 Gbps one) or to completely discharge the

optical channel. Among each node pair connected by means of one or more optical channels, one and

only one lightpath is selected and subjected to this process. If the configuration attained after

considering all the candidate lightpaths for elimination is of lower cost than before the rearrangement

performed, the process is repeated. Otherwise, the algorithm terminates.

The assumption and inputs to the heuristic algorithm are the same as the ones used for the Ilp

model. To attain the graph input, the following variables are necessary:

𝑅 Set of requests to attend 𝑅 = {𝑟0, 𝑟1, … , 𝑟|𝑅|−1}. Each request 𝑟𝑚 = (𝑠𝑟 , 𝑑𝑟 , 𝑢𝑟 , 𝑥𝑟), 𝑚 ∈ [0, |𝑅| −

1] stands for 𝑥𝑟 demands of rate 𝑢𝑟 to attend between nodes 𝑠𝑟 and 𝑑𝑟;

𝑇𝑟𝑆𝑐ℎ Set of traffic selection schemes as presented in 4.7.2.

𝑇𝑟𝑆𝑐ℎ = {𝑇𝑟𝑆𝑐ℎ0, 𝑇𝑟𝑆𝑐ℎ1, 𝑇𝑟𝑆𝑐ℎ2} where 𝑇𝑟𝑆𝑐ℎ0 = 𝑀𝐴𝐹, 𝑇𝑟𝑆𝑐ℎ1 = 𝑀𝑈𝐹 and 𝑇𝑟𝑆𝑐ℎ2 = 𝐿𝐶𝐹.

𝑀𝐴𝐹 refers to the Maximum Amount First scheme, 𝑀𝑈𝐹 to Maximum Utilization First and

𝐿𝐶𝐹 to Least Cost First;

𝐺𝑟𝑃𝑜𝑙 Set of Grooming Policies as presented in 4.7.2.

𝐺𝑟𝑃𝑜𝑙 = {𝐺𝑟𝑃𝑜𝑙0, 𝐺𝑟𝑃𝑜𝑙1 , 𝐺𝑟𝑃𝑜𝑙2} where 𝐺𝑟𝑃𝑜𝑙0 = 𝑀𝑖𝑛𝑊𝑙 , 𝐺𝑟𝑃𝑜𝑙1 = 𝑀𝑖𝑛𝑇𝐻 and 𝐺𝑟𝑃𝑜𝑙2 =

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𝑀𝑖𝑛𝐿𝑝. 𝑀𝑖𝑛𝑊𝑙 refers to the Minimum Wavelength Link policy, 𝑀𝑖𝑛𝑇𝐻 to Minimum Traffic

Hops and 𝑀𝑖𝑛𝐿𝑝 to Minimum Lightpaths;

𝐺𝑟𝑆𝑟𝑐 Binary variable that controls the initial graph state 𝐺𝑟𝑆𝑟𝑐 = {0,1}.

If 𝐺𝑟𝑆𝑟𝑐 = 1, source grooming is performed initially to reduce the complexity of the algorithm.

For node pairs that met certain conditions, lightpaths are established beforehand and filled

with single hop routed connections. To reflect this situation, a subset of the edges present in

the initial graph configuration are lightpath ones. The source grooming process is performed

as follows:

Select the rate 𝑟 of the lightpaths to establish beforehand as:

𝐿𝑟 = 100 𝑖𝑓

100

40> 𝐶100

40 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

Select the threshold as :

𝑇ℎ𝑟 =

80 𝑖𝑓 𝐿𝑟 = 100

40 𝑖𝑓 𝐿𝑟 = 40

Determine 𝑥 = ⌊∑ 𝑡𝑠𝑑

𝑢 ∗𝑢𝑢

𝑟⌋ and 𝑦 = ∑ 𝑡𝑠𝑑

𝑢 ∗ 𝑢𝑢 − ⌊∑ 𝑡𝑠𝑑

𝑢 ∗𝑢𝑢

𝑟⌋ ∗ 𝑟 ;

If 𝑦 ≥ 𝑇ℎ𝑟 establish 𝑥 + 1 lightpaths between 𝑠 and 𝑑. Otherwise establish 𝑥 lightpaths

between 𝑠 and 𝑑;

Route as many direct demands between the lightpaths’ end-points as long as the capacity

deployed is not exceeded. Demands of higher data-rate are prioritized, being the ones

attended in first place.

Insert the lightpath edges on the graph with the updated remaining capacities.

𝐿𝑝𝑆𝑒𝑙 Set of possible lightpath selection options 𝐿𝑝𝑆𝑒𝑙 = {𝐿𝑝𝑆𝑒𝑙0 , 𝐿𝑝𝑆𝑒𝑙1 , 𝐿𝑝𝑆𝑒𝑙2} where 𝐿𝑝𝑆𝑒𝑙0 =

𝑚𝑖𝑛, 𝐿𝑝𝑆𝑒𝑙1 = 𝑚𝑎𝑥 and 𝐿𝑝𝑆𝑒𝑙1 = 𝑚𝑖𝑥𝑒𝑑. Whenever a connection is routed over the graph

that demands the creation of one or more lightpaths, the rate of the lightpaths to establish is

calculated according to the lightpath selection defined.

For the case of 𝐿𝑝𝑆𝑒𝑙 = 𝑚𝑖𝑥𝑒𝑑, it is necessary in the first place to determine the configuration

with the least associated cost 𝐶 between the node-pairs such that the volume of traffic 𝑇 can

be attended. 𝑇 respects to the total volume of unattended traffic between the lightpath’s end-

points if the selected grooming policy concerns minimization of the traffic hops or to the

maximum among the volume of traffic that must be satisfied between the source of the

lightpath and all other nodes, or between the all other nodes and the destination.

Consider

𝑥 Number of 100 Gbps lightpaths

𝑦 Number of 40 Gbps Lightpaths

The selected configuration is the one meeting the conditions:

𝑥 ∗ 100 + 𝑦 ∗ 40 ≥ 𝑇; 𝑥, 𝑦 minimize (𝑥 ∗ 𝐶𝑟100 + 𝑦 ∗ 𝐶𝑟40)

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The selected rate 𝑟 assigned to the newly established lightpath is given by:

𝐿𝑟 = 40 𝑖𝑓 𝐿𝑝𝑆𝑒𝑙 = min 𝑜𝑟 (𝐿𝑝𝑆𝑒𝑙 = mixed 𝑎𝑛𝑑 𝑥 = 0 )

100 𝑖𝑓 𝐿𝑝𝑆𝑒𝑙 = max 𝑜𝑟 (𝐿𝑝𝑆𝑒𝑙 = mixed 𝑎𝑛𝑑 𝑥 > 0)

𝑆𝑜𝑙 Set of solutions obtained by running the graph algorithm for every combination of values of

(𝑇𝑟𝑆𝑐ℎ, 𝐺𝑟𝑃𝑜𝑙, 𝐺𝑟𝑆𝑟𝑐, 𝐿𝑝𝑆𝑒𝑙). These structures store the final graph state after all connections

are routed.

The necessary steps to perform to achieve the graph inputs are:

(Step 1) Make 𝑇𝑟𝑆𝑐ℎ = 𝑇𝑟𝑆𝑐ℎ0.

(Step 2) Make 𝐺𝑟𝑃𝑜𝑙 = 𝐺𝑟𝑃𝑜𝑙0

(Step 3) Make 𝐺𝑟𝑆𝑟𝑐 = 0

(Step 4) Make 𝐿𝑝𝑆𝑒𝑙 = 𝐿𝑝𝑆𝑒𝑙0

(Step 5) If 𝐺𝑟𝑆𝑟𝑐 = 1, perform initial source grooming as described when defining the binary

variable and reflect the actions taken onto the graph by establishing the required

lightpath edges with their updated capacity. Update the set of requests 𝑅, by removing

those attended in this process;

(Step 6) Sort 𝑅 according to the Traffic Selection Scheme 𝑇𝑟𝑆𝑐ℎ;

(Step 7) Select the first request 𝑟0 and route as many demands as possible over the path with the

least weight on the graph. This measure is calculated by summing the weights of all the

edges comprised in said path. Each edge’s weight is given by the defined Grooming

Policy 𝐺𝑟𝑃𝑜𝑙;

(Step 8) If the selected path requires for the establishment of one or more lightpaths, insert the

associated lightpath edges on the graph. The lightpaths’ rate or capacity is determined

according to 𝐿𝑝𝑆𝑒𝑙.

(Step 9) Decrease 𝑥0 to reflect the attended demands. If 𝑥0 = 0, remove the request from 𝑅;

(Step 10) If 𝑅 is empty, meaning all requests were attended, save the final graph state in 𝑆𝑜𝑙 .

Otherwise return to (Step 6)

(Step 11) Select the next 𝐿𝑝𝑆𝑒𝑙 from the set of possible lightpath selection options. If no more are

available continue. Otherwise return to (Step 5).

(Step 12) Select the next 𝐺𝑟𝑆𝑟𝑐 from the set of possible values for the variable. If no more are

available continue. Otherwise return to (Step 4).

(Step 13) Select the next 𝐺𝑟𝑃𝑜𝑙 from the set of available Grooming Policies. If no more are

available continue. Otherwise return to (Step 3).

(Step 14) Select the next 𝑇𝑟𝑆𝑐ℎ from the set of available Traffic Selection Schemes. If no more

are available the graph algorithm ends. Otherwise return to (Step 3).

Figure 5.7: Algorithm to obtain the graph inputs

A set of initial inputs to the cost minimization algorithm is attained by running the graph

scenario in every possible combination of values (𝑇𝑟𝑆𝑐ℎ, 𝐺𝑟𝑃𝑜𝑙, 𝐺𝑟𝑆𝑟𝑐, 𝐿𝑝𝑆𝑒𝑙). For each, the final

graph state representing the lightpaths established, their physical routing, wavelength assignment and

demands carried is kept. These values are saved in a structure that serves as the object to be

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manipulated to achieve minimum expenditure. The input variables given by the graph solution to the

cost minimization method are:

𝐿𝑝𝑖𝑗 Set of lightpaths established between 𝑖 and 𝑗. 𝐿𝑝𝑖𝑗 = {𝑙𝑝𝑖𝑗 0, . . . , 𝑙𝑝𝑖𝑗 |𝐿𝑝𝑖𝑗|−1

}. Every lightpath is

characterized by its rate 𝑟 (𝑙𝑝𝑖𝑗𝑘)and by the total volume of demands it carries 𝑑 (𝑙𝑝𝑖𝑗 𝑘

) ;

𝑊𝑖𝑗 Set of wavelengths assigned to lightpaths between 𝑖 and 𝑗.𝑊𝑖𝑗 = {𝑤𝑖𝑗,0, … , 𝑤𝑖𝑗,|𝑊𝑖𝑗|−1};

𝑃𝑖𝑗 Set of physical routes used by lightpaths established between 𝑖 and 𝑗.

𝑃𝑖𝑗 = {𝑝𝑖𝑗,0, … , 𝑝𝑖𝑗,|𝑃𝑖𝑗|−1}

𝑍𝑖𝑗,𝑠𝑑,𝑢 Set of demands carried in lightpaths between 𝑖 and 𝑗. 𝑧𝑖𝑗,𝑠𝑑,𝑢

represents the number of demands of rate 𝑢 between 𝑠 and 𝑑.

𝐴𝑖𝑗 Total amount of traffic carried in lightpaths between 𝑖 and 𝑗;

𝐴𝑖𝑗 = ∑ ∑ ∑ 𝑍𝑖𝑗,𝑠𝑑,𝑢𝑢 ∈𝑈𝑑 ∈𝑉𝑠 ∈𝑉 ∗ 𝑢.

Besides these variables, the algorithm also makes use of the additional following ones:

𝐿𝑟𝑒𝑚 List of lightpaths from which traffic is to be averted onto other lightpaths. The lightpaths

featured in this list are potential candidates to be fully relieved from traffic and eliminated;

𝑇𝑖𝑜𝑢𝑡 Total amount of traffic carried in lightpaths in list 𝐿𝑟𝑒𝑚 with node 𝑖 as their source;

𝑇𝑖𝑖𝑛 Total amount of traffic carried in lightpaths in list 𝐿𝑟𝑒𝑚 with node 𝑖 as their destination;

𝐶𝑖𝑜𝑢𝑡 Spare capacity of the lightpaths in list 𝐿𝑟𝑒𝑚 with node 𝑖 as their source;

𝐶𝑖𝑖𝑛 Spare capacity of the lightpaths in list 𝐿𝑟𝑒𝑚 with node 𝑖 as their destination;

𝑉𝑃𝑠𝑑,𝑢 Set of virtual paths that allow to carry at least one demand of rate 𝑢 between 𝑠 and 𝑑.

𝑃𝑠𝑑,𝑢 = {𝑝𝑠𝑑,𝑢0, … , 𝑝𝑠𝑑,𝑢|𝑃𝑠𝑑,𝑢|

}.Every path 𝑝𝑠𝑑,𝑢𝑘 is comprised of a set of one or more

lightpaths creating a route from 𝑠 and 𝑑. The hop count of the virtual path 𝐻(𝑝𝑠𝑑,𝑢𝑘) is given

by the number of lightpaths spanned minus one. The capacity of the virtual path 𝐶(𝑝𝑠𝑑,𝑢𝑘) is

given by the spare capacity of the most occupied lightpath traversed;

𝐶𝑘 Cost attained running iteration 𝑘.

Once the graph algorithm terminates, the virtual topology obtained is deconstructed. For every

node pair with established lightpaths, the lightpaths are rearranged to attain the configuration with the

least cost. Post that, one of the lightpaths in the rearranged configuration is chosen as a potential

candidate for elimination from the virtual topology. To determine such configuration as well as the

selected lightpath, the following steps must be performed for every pair (𝑖, 𝑗), 𝑖, 𝑗 ∈ 𝑁:

(Step 1) Consider

𝑥𝑖𝑗 Number of 100 Gbps lightpaths between 𝑖 and 𝑗

𝑦𝑖𝑗 Number of 40 Gbps Lightpaths between 𝑖 and 𝑗

Determine the least costly configuration such that:

𝑥 ∗ 100 + 𝑦 ∗ 40 ≥ 𝐴𝑖𝑗 , 𝑥, 𝑦 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 (𝑥 ∗ 𝐶𝑟100 + 𝑦 ∗ 𝐶𝑟40)

(Step 2) If (𝑥 + 𝑦 > |𝑝𝑖𝑗|), 𝑥 + 𝑦-|𝑝𝑖𝑗| lightpaths must be established. If the spare unassigned

wavelength channels in the network’s fiber links allow it to, establish the required

lightpaths. Otherwise, maintain the configuration reflected in the final graph state and

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update the values of 𝑥𝑖𝑗 and 𝑦𝑖𝑗;

(Step 3) Update 𝑝𝑖𝑗 such that 𝐿𝑝𝑖𝑗 = {𝑙𝑝𝑖𝑗 0, … , 𝑙𝑝𝑖𝑗 𝑥+𝑦−1

}.

(Step 4) Given that all optical channels are filled to the most of their capacity but potentially one,

perform the following actions:

If 𝑥 > 0:

If 𝑦 > 0: make 𝑑𝐿𝑝𝑖𝑗𝑘= 40, ∀ 𝐾 ∈ [0, 𝑥 − 1]

make 𝑑𝐿𝑝𝑖𝑗𝑘= 100, ∀ 𝐾 ∈ [𝑥, 𝑥 + 𝑦 − 2]

make 𝑑𝐿𝑝𝑖𝑗𝑘= 𝐴𝑖𝑗 − 40 ∗ 𝑥 − 100 ∗ (𝑦 − 1), 𝑘 = 𝑥 + 𝑦 − 1

Else: make 𝑑𝐿𝑝𝑖𝑗𝑘= 100, ∀ 𝐾 ∈ [0, 𝑦 − 2]

make 𝑑𝐿𝑝𝑖𝑗𝑘= 𝐴𝑖𝑗 − 100 ∗ (𝑦 − 1), 𝑘 = 𝑦 − 1

Else:

make 𝑑𝐿𝑝𝑖𝑗𝑘= 40, ∀ 𝐾 ∈ [0, 𝑥 − 2]

make 𝑑𝐿𝑝𝑖𝑗𝑘= 𝐴𝑖𝑗 − 40 ∗ (𝑥 − 1), 𝑘 = 𝑥 − 1

This process determines which of the lightpaths from among those in set 𝐿𝑝𝑖𝑗 is the one

with spare capacity if any.

(Step 5) Insert 𝑙𝑝𝑖𝑗 𝑥+𝑦−1 in list 𝐿𝑟𝑒𝑚.

Figure 5.8: Algorithm to select the candidate lightpaths for elimination

To select the order in which the lightpaths in list 𝐿𝑟𝑒𝑚 are attended, a weight is assigned to

each according to a given Lightpath Selection Scheme. The list is sorted so that optical channels with

the lowest associated weight are prioritized over the ones with highest weights. The set of Lightpath

Selection Schemes and the formulas to calculate the related weights are as described below:

Table 5.3 - Lightpath Selection Schemes and associate weight calculations

Lightpath Selection Scheme Weight Calculation:

Least Traffic 𝑤𝐿𝑝𝑖𝑗𝑘= 𝑑𝐿𝑝𝑖𝑗𝑘

, 𝑖 ∈ 𝑁, 𝑗 ∈ 𝑁 , 𝑘 = |𝐿𝑝𝑖𝑗| − 1

Node utilization 𝑤𝐿𝑝𝑖𝑗𝑘=

𝑇𝑖𝑜𝑢𝑡

𝐶𝑖𝑜𝑢𝑡 ∗ 0.5 +

𝑇𝑗𝑖𝑛

𝐶𝑗𝑖𝑛

∗ 0.5 , 𝑖 ∈ 𝑁, 𝑗 ∈ 𝑁 , 𝑘 = |𝐿𝑝𝑖𝑗| − 1

Lightpath utilization 𝑤𝐿𝑝𝑖𝑗𝑘=

𝑑𝐿𝑝𝑖𝑗𝑘

𝐶𝑖𝑜𝑢𝑡 ∗ 0.5 +

𝑑𝐿𝑝𝑖𝑗𝑘

𝐶𝑗𝑖𝑛

∗ 0.5 , 𝑖 ∈ 𝑁, 𝑗 ∈ 𝑁 , 𝑘 = |𝐿𝑝𝑖𝑗| − 1

Whenever the algorithm tries to eliminate the need for a given lightpath by averting all of its

traffic to other already deployed lightpaths, the selection of the virtual routing must be performed for

each of the demands carried. The alternative virtual paths must comprise a new set of optical

channels that connect the end-points of the demands, averting the lightpath candidate for elimination.

Whenever a set of possible virtual routes is available, an order must be imposed to selected which

one is selected first. Three lines of options were made available:

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Table 5.4 - Virtual Path Selection Schemes

Virtual Path Selection Scheme Description

Least Capacity

The path chosen is the one with the least spare capacity

corresponding to the lightpath in the route with highest

occupation.

Highest Capacity As opposed to the scheme above, this approach settles for

prioritizing the virtual routes with the most spare capacity;

Least Number of Hops The selected path is the one from the set that spans the least

number of lightpaths.

The steps to the algorithm are as follows:

(Step 1) Select the first solution from set

𝑆𝑜𝑙, attained by running the graph algorithm in distinct combinations; If all solutions

have been attended, move to step 17;

(Step 2) Select the first Lightpath Selection Scheme;

(Step 3) Select the first Virtual Path Selection Scheme;

(Step 4) Starting from the virtual topology obtained with the graph model, rearrange, for every

pair of nodes with connecting optical channels, the lightpath configuration. If the

available wavelength resources do not allow it, maintain the current configuration;

(Step 5) Determine the initial cost𝐶0 of deploying the defined virtual topology;

(Step 6) For every node pair with connecting optical channels, insert the lightpath with spare

capacity if there is one, or one of the established lightpaths of higher rate otherwise, in

list 𝐿𝑟𝑒𝑚;

(Step 7) Sort list 𝐿𝑟𝑒𝑚 according to the defined Lightpath Selection Scheme;

(Step 8) Select the first lightpath 𝐿𝑝0 from list 𝐿𝑟𝑒𝑚 and try to deviate as many carried

connections as possible to other lightpaths with spare capacity;

(Step 9) Update 𝐴𝑠(𝐿𝑝0)𝑑(𝐿𝑝0) to reflect an eventual decrease in occupation.

(Step 10) If any number of connections were re-routed and removed from 𝐿𝑝0, recalculate the

least costly lightpath configuration among node-pair (𝑠(𝐿𝑝0), 𝑑(𝐿𝑝0)). If the attained

configuration is advantageous in regards to cost to the current one, update to such. If

the number of lightpaths diminishes, free up the no longer used wavelength resources.

Recalculate 𝑇𝑠(𝐿𝑝0)𝑜𝑢𝑡 , 𝑇𝑑(𝐿𝑝0)

𝑖𝑛 , 𝐶𝑠(𝐿𝑝0)𝑜𝑢𝑡 , 𝐶𝑑(𝐿𝑝0)

𝑖𝑛 ;

(Step 11) Remove the first lightpath from the list. If 𝐿𝑟𝑒𝑚 is empty, continue. Otherwise return to

step 8;

(Step 12) Calculate the cost 𝐶𝑖𝑡𝑒𝑟 of maintaining the current virtual topology. If 𝐶𝑖𝑡𝑒𝑟 < 𝐶𝑖𝑡𝑒𝑟−1,

return to step 6. Otherwise, continue;

(Step 13) Save the final cost in set 𝐶𝑠𝑜𝑙.

(Step 14) Select the next Virtual Path Selection Scheme. If all have been iterated, continue.

Otherwise, move to step 4;

(Step 15) Select the next Lightpath Selection Scheme. If all have been iterated, continue

.Otherwise, return to step 3;

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(Step 16) Select the next solution from set 𝑆𝑜𝑙. If all solutions have been attended, continue. On

the contrary, return to step 2.

(Step 17) Select the minimum value in set 𝐶𝑠𝑜𝑙 as the final solution.

Figure 5.9: Description of the overall heuristic

5.2 Comparing the Heuristic to the Ilp Methodologies

In order to assess the performance of the developed heuristic, the test cases for the six and

seven nodes networks presented in 5.1 and analyzed in the context of the integer linear programming

methodologies were reused applying the heuristic model. The focus was laid upon the quality of the

solutions attained and the running times required in comparison to the mathematical model. With such

purpose, the next sections present, for every scenario considered, the distances to the Ilp model

attained by applying the heuristic methodology.

Results for the six nodes test network in the conditions of 5.4.1 and 5.4.2

Figure 5.10: Distance on the cost of the heuristic to the Ilp (mixed translucent)

Figure 5.11: Distance on the cost of the heuristic to the Ilp (mixed opaque)

Figure 5.12: Distance on the cost of the heuristic to the Ilp (single rate)

0

2

4

6

8

900 1200 1500 1800 2100 2400 2700 3000 3300 3600 3900

Gap

to

th

e Il

p s

olu

tio

n

[%]

TTV [Gbps]

Network cost comparison in translucent, mixed-line rate scenarios

Cr=1.5

Cr=2

Cr=2.5

0

1

2

3

4

5

6

900 1200 1500 1800 2100 2400 2700 3000 3300 3600 3900

Gap

to

th

e Il

p

solu

tio

n [

%]

TTV [Gbps]

Network cost comparison in opaque, mixed-line rate scenarios

Cr=1.5

Cr=2

Cr=2.5

0

2

4

6

8

10

900 1200 1500 1800 2100 2400 2700 3000 3300 3600 3900

Gap

to

th

e Il

p s

olu

tio

n

[%]

TTV [Gbps]

Network cost comparison in translucent, single-rate scenariosSingle Rate 100G Cr=1.5Single Rate 100G Cr=2Single Rate 100G Cr=2.5Single Rate 40 G

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Figure 5.13: Distance on the times of the heuristic to the Ilp (mixed translucent)

Results for the seven nodes test network in the conditions of 5.4.1 and 5.4.2

Figure 5.14: Distance on the cost of the heuristic to the Ilp (mixed translucent)

Figure 5.15: Distance on the cost of the heuristic to the Ilp (mixed opaque)

Figure 5.16: Distance on the cost of the heuristic to the Ilp (single rate)

0

20

40

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Single Rate 100 GCr = 1.5Single Rate 100 GCr = 2Single Rate 100 GCr = 2.5Single Rate 40 G

83

Figure 5.17: Distance on the times of the heuristic to the Ilp (mixed translucent)

The presented figures suggest a compelling performance of the heuristic methodology by always

providing results within a ten percent window to those of the mathematical programming approach.

Furthermore, the computational effort demanded for the achievement of solutions to the cost

minimization problem in the analyzed scenario is in all cases only a small slice of that required by the

Ilp model.

5.3 Applying the heuristic to networks of larger dimensions

When analyzing the running times attained by the Ilp methodology for the six and seven nodes

networks it was perceived a considerable increase in computational effort, most of the those referring

to the network of higher dimensions climbing over the thousands of seconds. This observation

attesting to the NP-complete trait that characterizes Ilp solutions settles as a limitation to the

mathematical models, their space of feasibility contracting as the problem’s dimensions expand. As

so, it was chosen to run simulations applying the cost minimization problem to real life networks of

considerable reaches. As was the case when performing Ilp simulations, mixed and single line rate

scenarios were encompassed as were translucent, transparent and opaque configurations. The

results are as displayed below.

GBN

Figure 5.18: Cost obtained for transparent, translucent and opaque models

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Figure 5.19: Cost obtained for single and mixed line rate networks

Eon

Figure 5.20: Cost obtained for transparent, translucent and opaque models

Figure 5.21: Cost obtained for single and mixed line rate networks

The results applying the heuristics to the networks of large dimensions are in accordance with

those attained before when using the mathematical models. Again, the translucent mixed rate

configuration proves to be the solution that provides for the lowest costs. In regards to the opaque and

transparent schemes, the all-optical solution outperforms the opaque solution. As perceived in this

chapter and in the chapter before, the network’s architecture that has the WDM network’s functionality

limited to point-to-point transmission is the most demanding in terms of the number of required

lightpaths to satisfy demand. As a result, the costs escalate in comparison to the alternative solutions.

On the topic of single-rate networks, the results displayed in the figures above show once again that

the single rate solution with 100 Gbps line cards concedes for lower costs when the relative cost of

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85

those devices in comparison to 40 Gbps transponders are made equal to 1.5 and to 2. When that

values is increased to 2.5, the larger cost disproportion leads to the lowest costs associated with the

establishment of 40 Gbps lightpaths in favour of 100 Gbps.

5.4 Ilp Models for asymmetrical traffic

In this section an analysis is performed on the best configuration of lightpaths and line cards to

tame scenarios with asymmetric traffic. Following in on the suggestions made in [27], we study how

establishing asymmetrical optical connections may provide for lower costs in respect to symmetrical

connections. For this last case, the performance of bidirectional line cards where the transmission and

reception rate are the same is compared against the performance of asymmetrical line cards.

Unidirectional cards that feature either a standalone transmitter or receiver are also studied. Initially it

is considered only unidirectional cards are made available and afterwards, both unidirectional and

bidirectional line cards are made available.

As an example of an application where the asymmetrical line card configuration provides for

lower costs consider the figure below where a given asymmetric demand is required to be expedited

at the minimum expenses. In such case, both solutions provide for the same number of line cards.

However, the asymmetric approach allows to establish a 40 Gbps line card and two other

asymmetrical cards. If the costs associated with these are lower or equal to those of the 100 Gbps

line card then saving can be attained.

Figure 5.22: Comparing asymmetrical (top) and symmetrical (bottom) line cards

Another example is displayed in the figure below where we compare the establishment of

asymmetric lightpaths against the restriction of lightpath bidirectionality. As proven in the example, a

lower number of lightpaths is required in the second scenario displayed accounting for the deployment

of asymmetric lightpaths.

86

Figure 5.23: Using bidirectional optical channels to satisfy demand

Figure 5.24: Using asymmetrical optical channels to satisfy demand

To finalize an example is shown of the application of a combination of bidirectional and

unidirectional line cards against using only the bidirectional approach. It is assumed asymmetrical

lightpaths are allowed. If we assume like in [27] that an unidirectional line card has an associated cost

of 0.6 percent the cost of a bidirectional card of the same rate then savings can be provided with that

combination.

Figure 5.25: Advantages of combining unidirectional and bidirectional line cards

The formulations for the cases mentioned above are described below, discriminated by

scenario. The inputs, notation and variables are the same as the ones considered in 5.2 except stated

otherwise. Translucent configurations are considered.

87

5.4.1 Model for bidirectional line cards using symmetrical optical connections

In this case we consider that the lightpaths are established in pairs between the nodes, one in

each direction. The line cards are assumed bidirectional and it is considered that the transmission rate

is the same as the receiving rate. Since we are dealing with asymmetric traffic it is no longer possible

to consider only the traffic demands in a single direction. The formulation can be derived from that of

5.2.1 with the following changes:

Remove the factor of 2 in 5.1;

Remove the restriction 𝑑 > 𝑠 whenever present. This is justified because of the traffic

asymmetry;

Add constraint 5.12 to guarantee the establishment of bidirectional optical channels:

(5.12) 𝐿𝑖𝑗𝑟 = 𝐿𝑗𝑖

𝑟 ∀ 𝑖, 𝑗 ∈ 𝑉, 𝑟 ∈ 𝑅

5.4.2 Model for bidirectional line cards using asymmetrical optical connections

When considering the establishment of asymmetrical lightpaths, a line card may end up being

only partially filled. The number of incoming lightapths and outgoing lightpaths for every rate

considered must then be examined at each node: the maximum from among those values is the

number of required line cards at the node. The formulation can be derived from that of 5.2.1 with the

following changes:

Remove the restriction 𝑑 > 𝑠 whenever present;

Consider the following objective function:

Objective Function:

(5.13) 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 ∑ ∑ max (∑ 𝐿𝑖𝑘𝑟 ,

𝑘∈𝑉

∑ 𝐿𝑘𝑖𝑟

𝑘∈𝑉

)

𝑟∈𝑅𝑖 ∈𝑉

∗ 𝐶𝑟𝑟

5.4.3 Model for unidirectional line cards using asymmetrical optical

connections

In this case we consider a line card to only comprise either a transmitter or a receiver. A new

variable 𝐶𝑟𝑟𝑢𝑛𝑖 must be introduced to represents the cost of an unidirectional line card. Asymmetrical

optical connections are considered. The formulation can be derived from that of 5.2.1 with the

following changes:

Remove the restriction 𝑑 > 𝑠 whenever present;

Consider the following objective function:

Objective Function:

(5.14) 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 ∑ ∑ ∑ 𝐿𝑖𝑗𝑟 ∗ 𝐶𝑟𝑟

𝑢𝑛𝑖 ∗ 2

𝑟 ∈ 𝑅𝑗 ∈ 𝑉𝑖 ∈ 𝑉

Since every establish lightpath requires for two line cards to be deployed (a transmitter card at

the source and a receiver one at the destination node), a factor of two is added to the objective

function.

88

5.4.4 Formulation using unidirectional and bidirectional line cards using

asymmetrical optical connections

In this scenario we allow for both unidirectional as well as bidirectional line cards. Where a

bidirectional line card could only be partially filled if only those types of cards were allowed, in this

case, the unidirectional card may be applied to avoid unused ports on the cards. The formulation can

be derived from that of 5.2.1 with the following changes:

Remove the restriction 𝑑 > 𝑠 whenever present;

Introduce the following variables:

𝐿𝑐(𝑡𝑥)𝑖𝑟: Unidirectional line card at node 𝑖 composed of a single transmitter;

𝐿𝑐(𝑟𝑥)𝑖𝑟: Unidirectional line card at node 𝑖 composed of a single receiver;

𝐿𝑐(𝑡𝑟𝑥)𝑖𝑟: Bidirectional line card.

Consider 𝐶𝑟𝑟𝑢𝑛𝑖 the cost of a unidirectional card and 𝐶𝑟𝑟 the cost of a bidirectional card;

Rewrite the objective function as:

Objective Function:

(5.15) 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 ∑ ∑(𝐿𝑐(𝑡𝑥)𝑖𝑟 + 𝐿𝑐(𝑟𝑥)𝑖

𝑟) ∗ 𝐶𝑟𝑟𝑢𝑛𝑖 + 𝐿𝑐(𝑡𝑟𝑥)𝑖

𝑟 ∗ 𝐶𝑟𝑟

𝑟∈𝑅 𝑖 ∈ 𝑉

Introduce the following constraints:

(5.16) 𝐿𝑐(𝑡𝑥)𝑖𝑟 + 𝐿𝑐(𝑡𝑟𝑥)𝑖

𝑟 = ∑ 𝐿𝑖𝑘𝑟

𝑘∈𝑉

∀ 𝑖 ∈ 𝑉, 𝑟 ∈ 𝑅

(5.17) 𝐿𝑐(𝑟𝑥)𝑖𝑟 + 𝐿𝑐(𝑡𝑟𝑥)𝑖

𝑟 = ∑ 𝐿𝑘𝑖𝑟

𝑘∈𝑉

∀ 𝑖 ∈ 𝑉, 𝑟 ∈ 𝑅

5.4.5 Asymmetrical and symmetrical bidirectional line cards using

asymmetrical optical connections

In this case we allow the coexistence of symmetrical and asymmetrical line cards. In such a way

we provide for increase flexibility when deploying the optical channels and wasted capacity can be

tamed. The formulation can be derived from that of 5.2.1 with the following changes:

Remove the restriction 𝑑 > 𝑠 whenever present;

Consider 𝐶𝑟𝑟,𝑟′ the cost of an asymmetrical card that transmits at rate 𝑟 and receives at race

𝑟′ and 𝐶𝑟𝑟 the cost of a bidirectional card;

Introduce the following variables:

𝐿𝑐𝑖𝑟,𝑟′

: Line card at node 𝑖 transmitting a signal of rate 𝑟 and receiving a signal of rate 𝑟′;

𝐿𝑐𝑖𝑟: Bidirectional line card at node 𝑖 transmitting and receiving at rate 𝑟;

Rewrite the objective function as:

Objective Function:

(5.18) 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 ∑ ∑( ∑ 𝐿𝑐𝑖

𝑟,𝑟′

𝑟′≠𝑟, 𝑟′∈𝑅

∗ 𝐶𝑟𝑟,𝑟′

𝑟∈𝑅 𝑖 ∈ 𝑉

+ 𝐿𝑐𝑖𝑟 ∗ 𝐶𝑟𝑟)

Introduce the following constraints:

89

(5.19) ∑ 𝐿𝑖𝑘𝑟 =

𝑘∈𝑉

∑ 𝐿𝑐𝑟,𝑝 + 𝐿𝑐𝑖𝑟

𝑝 ≠𝑟, 𝑝∈𝑅

∀ 𝑖 ∈ 𝑉, 𝑟 ∈ 𝑅

(5.20) ∑ 𝐿𝑘𝑖𝑟 =

𝑘∈𝑉

∑ 𝐿𝑐𝑝,𝑟

𝑝≠𝑟,𝑝∈𝑅

+ 𝐿𝑐𝑖𝑟 ∀ 𝑖 ∈ 𝑉, 𝑟 ∈ 𝑅

5.5 Applying asymmetrical traffic Ilp models

The results of simulations applying the models presented above are presented in this section.

Traffic matrixes were attained applying a uniform discrete distribution. Translucent scenarios with

mixed line rates (40 and 100 Gbps) were considered at all times. The rates for the client signals used

in the previous formulations stand. When asymmetrical cards are considered, two costs measures

were applied: one where the expenditures of an asymmetrical card were made equal to 0.8 times the

expenditures associated with 100 Gbps line cards and another where they were made equal. The cost

of unidirectional line cards was made equal to 0.6 times the cost of a bidirectional card of the same

rate.

Figure 5.26: Comparing symmetrical and asymmetrical cards using bidirectional connections

As proven by Figure 5.23 above, in the conditions where the cost of an asymmetrical line card

lies equal or below to that of a 100 Gbps card, savings can be achieved by exploiting both

symmetrical and asymmetrical cards. In Figure 5.19 an example was displayed where cost savings

were achieved by replacing bidirectional 100 Gbps line card with 40 Gbps ones when moving from

symmetrical to a combination of symmetrical and asymmetrical cards. That lies as a plausible

reasoning as to why the gap between the costs associated with the considered startegies increase as

the cost ratio, the relative cost of a 100 Gbps card to a 40 Gbps card increases.

Figure 5.27: Comparing the establishment of bidirectional and unidirectional optical channles using

bidirectional line cards

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When the two directions are not dependent, a greater flexibility is conceded to the problem of

routing and grooming the low-rate connections as well as to the RWA problem. In consequence, and

in line with the examples in Figure 5.20 and 5.21, the lowest cost expenditures are achieved when

allowing for the establishment of asymmetrical lightpaths.

Figure 5.28: Comparing either bidirectional or solely unidirectional line cards using asymmetrical

lightpaths

As opposed to the conclusions obtained in [27], the use of unidirectional line cards did not

provide for lower costs in regards to the application of bidirectional cards. That could be a result of the

dissimilar processes used to attain the traffic matrixes and also of the fact that the authors considered

single rate networks whereas the current work considered mixed rate ones.

Figure 5.29: Comparing asymmetrical lightpath schemes: bidirectional and symmetrical line cards vs

symmetrical + asymmetrical line cards vs bidirectional + unidirectional line cards

As perceived in the figure above the configuration combining asymmetrical and symmetrical

cards when the asymmetrical card cost is made equal to 0.8 times that of a 100 Gbps line card and

the configuration combing unidirectional and bidirectional cards were the ones accountable for the

lowest expenditures. These observation lead to the conclusion that novel approaches should be

considered when dealing with asymmetric traffic. Not only the establishment of asymmetrical

lightpaths should be analysed as an alternative but new line card models should be examined.

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5.6 Conclusions

The present chapter featured the presentation of an integer linear programming model as well as

of a heuristic algorithm for the cost minimization problem. The intention lied on making use of traffic

grooming to minimize the number of necessary line cards to be deployed in satisfaction of the total

traffic demand. Translucent configurations were considered allowing for both traffic grooming and

optical bypassing to be performed at intermediate nodes. The transparent configuration with the

solemn allowance of source grooming and possibility of optical bypassing was also featured to

simulate an all-optical network. The last remaining case tackled was of the opaque network design

where a lightpath can only span a single optical fiber, optical bypassing an impossibility regardless of

whether the traffic flowing in the optical channels is in passing or not. Putting the three network

schemes to test in mixed line rate scenarios where the wavelength channels transmitted over a fiber

link can assume one among a set of allowed line rates, the translucent configuration proved the most

fit in accomplishing lower capital expenditures. In turn, the opaque design proved to be the one

attesting for the highest costs derived from its need to establish a higher number of lightpaths to

accommodate all traffic flows. On the subject of mixed line rate networks, these were brought to

comparison against single line rate networks assuming 40 and 100 Gbps lightpaths were made

available. Simulations conducted in translucent scenarios showed that the mixed configuration was

always the enabler for the lowest expenditures to be achieved. According to the cost ratios

considered, the single rate scenario that came closer to the mixed rate scenario varied. For the cases

where the cost traced to the higher rate line cards was 1.5 and 2 times that of the lowest rate cards,

the single rate scenario where all lightpaths run on 100 Gbps rates performed better. The opposite

was observed for the case where the cost ratio considered was of 2.5.

The presented heuristic model was subjected to tests in all mentioned scenarios of available line

rates and network configurations. The resulting solutions were compared to the ones attained via

application of the integer linear programming model for effects of comparison over the quality of the

solutions and computation times required. The observed behavior was considered satisfying as the

gaps between both methodologies for all cases considered was always shorted than ten percent.

Furthermore, the computational effort tarced to the heuristic algorithm always proved to be only a

fraction of that of the mathematical model.

Lastly, studies were performed on cost minimization strategies for networks dealing with

asymmetrical traffic. The establishment of asymmetrical lightpaths was brough under the scope and

unidirectional and asymmetrical line card configurations were examined. The results of simulations

applying the developed Ilm models to a small test case network made a point in favour of the

deployment of asymmetrical optical connections. In regards to the line card configuration, a

combination of unidirectional and bidirectional cards or a combination of symmetrical and

asymmetrical bidirectional cards proved to be more enticing to the objective of cost minimization.

92

6 Conclusions and Future Work

6.1 Conclusions

Over the course of the current work, OTN and WDM networks were explored and the target of

network planning methodologies. The conduct followed was that of studying the characterizing traits of

each to apply the acquired knowledge into the elaboration of models regarding the minimization of the

total cost of ownership of an OTN/WDM network.

Initially, wavelength division multiplexed networks with lambda switching functionality provided by

ROADMs and optical cross connects were taken upon consideration with the development of integer

linear programming models targeting the minimization of the number of wavelengths necessary to

accommodate an inputted set of lightpaths with no blockage. The defined models were compliant with

the wavelength clash constraint and with the wavelength continuity constraint imposed by the

unavailability of wavelength converters. Both link-path and node-link formulations for the routing and

wavelength assignment problem were presented. Simulations conducted applying both models in the

exact same conditions permitted to draw conclusions on the superior time-wise performance of the

link-path approach, the a priori calculation of a limited set of physical routing paths uniting any two

nodes providing for a tightening of the space of feasible solutions that assured for lower running times.

The showcased Ilp models also featured asymmetric and symmetrical routing approaches, the last

one more restrictive in that its suitability is limited to scenarios of bidirectional traffic. Though a case

was exposed where the application of the asymmetric methodology to a network coping with a

symmetric traffic pattern granted for a lower number of wavelengths necessary to establish the whole

lightpath demand, posterior simulations conducted returned matching results for both routing

approaches. It was also perceived how the reduction in complexity resulting from limiting the problem

to a single direction allowed for the computational times associated to the symmetrical routing solution

to be smaller. The NP-hard trait of the Ilp RWA model was certified by running simulations for three

networks with despair number of nodes and fiber links and noticing the proportional increase of the

computational effort with the dimension. Lastly, the effect of a network’s mean nodal degree were

brought under observation by conducting simulations for networks sharing the same number of nodes

but presenting distinct physical topologies. Starting from a ring topology to one where all nodes are

neighbors, the results attained considering the same traffic conditions showcased a decrease in the

number of required wavelengths with the increase in the mean nodal degree, derived from a higher

number of routing options. In the end, a heuristic model was developed featuring first fit wavelength

assignment and shortest path routing. Test cases were performed applying the Ilp model and the

heuristic algorithm in the same conditions to a number of networks. The observed results were

93

inconclusive in defining a space of suitability for the heuristic approach, especially regarding its

behavior with the variation of the mean nodal degree.

In chapter 2, the principles of the Optical Transport Network standards were covered and its

current appeal to network operators justified. The OTN/WDM synergy was the focus of Chapter 4 and

5. In Chapter 4 models were developed for the traffic grooming, routing and wavelength assignment

problem in situations with scarce resources. Translucent, transparent and opaque scenarios were

encompassed. In the first situation, nodes combining a ROADM with an OTN switch permitted for both

optical bypass and electrical switching and grooming to take place. The transparent design referred to

the all optical network were all switching functionality was relegated to the optical layer. On the

opposite side of the spectrum, the opaque configuration delegated such task to the electric domain,

the WDM network a solemn provider for point to point connectivity among OTN nodes with switching

functionality. Comparisons drawn by applying the three configurations under the same traffic demands

showcased a superior performance of the translucent scheme, the larger space of routing options for

the client signals enabling for higher throughputs to be achieved. The ability to perform single and

multi-stage multiplexing was also accounted for with the presentation of formulations targeting each

solution. The preference over the most complex multi-stage multiplexing scheme was justified with the

presentation of simulations where the ability to mix traffic of distinct data-rates into the same optical

channel allowed for the satisfaction of a higher volume of traffic. As was the case when approaching

the RWA problem, heuristic methodologies were pursued. The works carried in [21] and [22] were the

subject of analyses and three heuristics featured in such publications were transported from the

SONET/SDH world to the domain of OTN. The Maximum Single Hop Traffic and Maximum Resource

Utilization algorithms opted to follow a sequential approach of determining the virtual topology at first,

selecting the lightpaths to establish and performing routing and wavelength assignment and only post

to that routing the individual client traffic flows. The graph model in turn followed an integrated

approach building the virtual topology as client connections were satisfied. Comparisons made by

means of simulations revealed that the graph model was the one capable of achieving results of

higher quality, the gaps to the solutions attained by the mathematical model the lowest. In regards to

the computational effort required, all three heuristic succeeded in demanding only a small fraction of

the time taken by the Ilp models to attain results.

The analyses described in the above paragraphs were the input to the development of models

for the cost minimization problem. Assuming that all costs were related solemnly to the deployment of

line cards, an integer linear programming formulation and a heuristic model were presented featuring

traffic grooming as a solution to achieve the lowest expenditures. Mixed line rate network designs

were addressed assuming that optical channels of distinct rate could coexist over the same fiber. With

an availability of 40 and/or 100 Gbps line cards, the mixed rate scenario was opposed to the single

rate one and the attained results attested its ability to provide for lower expenditures. The transparent,

translucent and opaque configurations were once again brought to analysis and once more the

benefits of the lambda and sub-lambda switching approach were exalted by the lowest capital

expenditures obtained. As was the norm in the preceding chapters , a heuristic solution was

presented. Using the graph model analyzed when researching the GRWA problem in blocking

94

scenarios to produce a virtual topology capable of satisfying the entire traffic demand, the developed

algorithm intents to rearrange the lightpath configuration in achievement of a cost reduction.

Sequentially, established optical channels are selected and made candidates for elimination by

alleviating as much of their load as possible onto alternative virtual routes. Results attained applying

the heuristic methodology to mixed and single rate scenarios and to transparent, opaque and

translucent network schemes attest to a satisfying performance, the observed gaps to the Ilp solution

always falling below ten percent. In the end, cost minimization models specifically targeting networks

with asymmetric traffic were analysed. Distinct line card configurations were addressed and the

viability of asymmetrical optical connections was examined.

6.2 Future Work

The considerations on future work target the issues developed in Chapter 5. On that note, it can

be stated that the applied cost metrics can be made more accurate with the development of more

complex and adequate cost models. Also, a closer to the reality situation could be accounted for with

the regard of the optical impairments that impose limitations on the reach of the optical channels. The

dependency of these effects with the lightpaths’ data rates should not be overlooked for a more

detailed approach. The possibility to use OTN switching as an alternative to regenerator placement at

times comes as an issue of interest that could be explored if such approach were to be followed. It is

also worth mentioning the proposal to design, with the developed integer linear programming

formulations as basis, linear programming relaxations to expand the limits of feasibility to networks of

higher dimensions. Such models could then be used as another comparison tool to the heuristic

methodology developed. On the topic of cost minimization models in networks with traffic asymmetry,

an asymmetrical traffic model should be developed to conduct simulations in scenarios closer to the

reality. Also, the proposition to develop heuristics to target the scenarios in 5.4 would be of great

appeal in its ability to draw further conclusions. Given that only one network of small dimensions was

analysed, the application of a heuristic algorithm to scenarios with networks of greater dimensions

would be of great help to shed some more light on the topic mainly in terms of understanding which of

the considered approaches in terms of lightpaths’ establishment and type of line cards used is more

advantageous.

95

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98

Appendix A

Transport Networks considered in the simulations performed

Simulations conducted throughout the development of the current work focused on real life

transport networks. Its physical topologies and relevant parameters under the scope of this Thesis are

presented below.

A 1. Via Network

Figure A. 1: Via Network’s physical topology

Table A. 1: Via Network's relevant parameters

Number of Nodes 9

Number of bidirectional links 12

Mean Nodal Degree 2.67

A 2. Abilene Core Network

Figure A. 2: Abilene Core Network’s physical topology

99

Table A. 2: Abilene Core Network's relevant parameters

A 3. Czech Education and Scientific Network (CESNET)

Figure A. 3: Cesnet Network’s physical topology

Table A. 3: Cesnet Network's relevant parameters

A 4. National Foundation Science Network (NFSNET)

Figure A. 4: Nfsnet Network’s physical topology

Table A. 4: Nfsnet Network's relevant parameters

Seattle

Palo Alto

San Diego

Salt Lake City

Boulder

LincolnChampaign

Am Arbor

Pittsburgh

Ithaca

Princeton

College Pk

Atalanta

Houston

Number of Nodes 10

Number of bidirectional links 13

Mean Nodal Degree 2.60

Number of Nodes 10

Number of bidirectional links 13

Mean Nodal Degree 2.60

Number of Nodes 14

Number of bidirectional links 21

Mean Nodal Degree 3.00

100

A 5. Very-High Performance Backbone Network Service (Vbns)

Figure A. 5: Vbns Network’s physical topology

Table A. 5: Vbns Network's relevant parameters

A 6. Italy Network (ITALY)

Figure A. 6: Italy Network’s physical topology

Table A. 6: Italy Network's relevant parameters

Cagliari

Genova

Turin

Milan

Florence

Trento Venice

Bologne

Roma

Pescara

Bari

Naples

Calabria

Palermo

Number of Nodes 12

Number of bidirectional links 17

Mean Nodal Degree 2.83

Number of Nodes 12

Number of bidirectional links 17

Mean Nodal Degree 2.83

101

A 7. Slovenia Academic and Research Network (Arnes)

Figure A. 7: Arnes Network’s physical topology

Table A. 7: Arnes Network's relevant parameters

A 8. Optosunet (Sweden)

Figure A. 8: Optosunet’s physical topology

Number of Nodes 17

Number of bidirectional links 20

Mean Nodal Degree 2.35

102

Table A. 8: Optosunet’s relevant parameters

A 9. Arpanet

Figure A. 9: Arpanet’s physical topology

Table A. 9: Arpanet's relevant parameters

A 10. Cost37

Figure A. 10: Cost37 Network’s physical topology

Table A. 10: Cost37 Network's relevant parameters

Number of Nodes 20

Number of bidirectional links 24

Mean Nodal Degree 2.4

Number of Nodes 20

Number of bidirectional links 32

Mean Nodal Degree 3.20

Number of Nodes 37

Number of bidirectional links 57

Mean Nodal Degree 3.08

103

A 11. Germany Network (Gbn)

Figure A. 11: Gbn Network’s physical topology

Table A. 11: Gbn Network's relevant parameters

A 12. Italian Backbone Network (IBN)

Figure A. 12: IBN's physical topology

Table A. 12: IBN’s relevant parameters

Dusseldorf

Essen

Dortmund

Koln

Frankfurt

Mamheim

KarlruheStuttgart

UlmMunich

Numberg

Leipzig

Berlin

Hannover

Hamburg

BremenNorden

Number of Nodes 17

Number of bidirectional links 26

Mean Nodal Degree 3.06

Number of Nodes 33

Number of bidirectional links 51

Mean Nodal Degree 3.29

104

A 13. Metrona Network

Figure A. 13: Metrona Network's physical topology

Table A. 13: Metrona Network’s relevant parameters

A 14. Bulgarian Research and Education Network (BREN)

Figure A. 14: Bren's physical topology

Table A. 14: Bren's relevant parameters

Number of Nodes 33

Number of bidirectional links 41

Mean Nodal Degree 2.48

Number of Nodes 10

Number of bidirectional links 11

Mean Nodal Degree 2.20

105

A 15. European Optical Network (EON)

Figure A. 15: EON’s physical topology

Table A. 15: EON’s relevant parameters

Number of Nodes 19

Number of bidirectional links 37

Mean Nodal Degree 3.89

106

Appendix B

Auxiliary functions used to conduct RWA simulations

B 1. K-shortest paths algorithm

When applying RWA link-path formulations, it becomes necessary to determine the set of

possible paths among any two nodes in the network among which there are traffic requests. It is

common to consider only a subset of such paths, limiting the number of possible routing solutions

between nodes to an integer value k. The algorithm used to calculate the k-shortest paths is presented

below. It determines each path incrementally and by means of iterations, inserting a single untraveled

link at each step, until the destination node is reached.

Notation:

𝑁: Number of network nodes;

𝐾: Set of node pairs such that there is at least one traffic request from 𝑠(𝑘) to 𝑑(𝑘);

𝑃𝑘: Set of possible paths between node pair 𝑘;

𝑖: Current iteration;

𝑃𝑖𝑀: Set of paths obtained in iteration 𝑖. 𝑝𝑖

𝑚 refers to the 𝑚𝑡ℎ path built in iteration 𝑖 of the

algorithm;

𝑃𝑖𝑛,𝑗

: The 𝑗𝑡ℎ node of path 𝑝𝑖𝑚; 𝑝𝑖

𝑚 = {𝑝𝑖𝑚,0, 𝑝𝑖

𝑚,1, … 𝑝𝑖

𝑚,|𝑝𝑖𝑛 |−1

}

𝐴: Adjacency matrix describing the network’s physical topology. 𝑎𝑖𝑗 = 1 if 𝑖 and 𝑗 are adjacent

and 𝑎𝑖𝑗 = 0 otherwise;

𝐾: Number of paths to establish between any two nodes if there are that many possibilities.

Steps:

Step 0 Make 𝑝00 = {𝑠(𝑘)} ;

Step 1 For all paths 𝑝𝑖−1𝑁 obtained in the previous iteration, find all the nodes adjacent to the last

node inserted that have not yet been traversed. For every node in such condition, create a

new path by inserting it in the previously obtained path.

∀𝑗 ∈ 𝑁 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑎𝑝𝑖−1

𝑚,|𝑝𝑖−1𝑚 |−1

,𝑗 = 1 𝑎𝑛𝑑 𝑗 𝑛𝑜𝑡 𝑖𝑛 𝑝𝑖𝑚

{𝑝𝑖𝑛,0, 𝑝𝑖

𝑛,1, … 𝑝𝑖

𝑛,|𝑝𝑖𝑛 |−1

, 𝑗} ∈ 𝑃𝑖𝑀 ∀𝑚

Step 2 If 𝑗 = 𝑑(𝑘) insert 𝑝𝑖𝑚 = {𝑝𝑖

𝑛,0, 𝑝𝑖𝑛,1, … 𝑝

𝑖

𝑛,|𝑝𝑖𝑛 |−1

, 𝑑(𝑘)} in set 𝑃𝑘;

Step 3 If |𝑃𝑘| = K, the algorithm is over. Otherwise mode to next step.

Step 4 Increase the value of 𝑖 moving on to the next iteration and go back to Step 1.

Figure B. 1: Description of the k-shortest paths algorithm

107

An example of the behavior of the described algorithm is showcased below. Figure B.2

represents the network’s physical topology and figure B.3 the final results obtained by applying the

method to find the set of 7-shortest paths between node 1 and 7.

Figure B. 2: Network's physical topology

Figure B. 3: Results obtained applying the k-shortest path algorithm to node-pair (1,7)

𝑷𝑲 = {{𝟏, 𝟎, 𝟓, 𝟕} , {𝟏, 𝟐, 𝟓, 𝟕}, {𝟏, 𝟐, 𝟓, 𝟔, 𝟕}, {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟕}, {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔, 𝟕}}

B.2 Algorithm for generating traffic matrixes

Symmetrical and asymmetrical traffic matrixes were randomly generated according to a

uniform discrete distribution with interval [0, 𝑀]. For every scenario under analysis, a set of matrixes

was created by increasingly enhancing the load requested among nodes. The algorithm start by

108

creating an initial matrix populated with real numbers between 0 and 1 from which each matrix

corresponding to a given value of M is derived.

The inputs to the algorithm are described below:

𝑀𝑚𝑖𝑛 𝑎𝑛𝑑 𝑀𝑚𝑎𝑥 Minimum and maximum value considered for M. Parameter 𝑀 takes

values in such range, with incremental steps of 1.

M = {𝑀𝑚𝑖𝑛 , 𝑀𝑚𝑖𝑛 + 1, … , 𝑀𝑚𝑎𝑥 };

N Number of nodes in the network;

The algorithm is described in detail in the figure below, where RandomReal() represents a function

responsible for producing a pseudorandom real number in the range 0 to 1 and Round(x) one that

rounds real number x to the nearest integer.

Figure B. 4: Description of the Algorithm for generating traffic matrixes

109

Appendix C

Further Ilp and Heuristic comparisons

C 1. Comparing the network’s throughput applying translucent, transparent

and opaque models

In the conditions displayed in Table D.1, simulations were conducted for the Bren Network

varying the availability of both wavelengths per fiber and transponders per node. The bidirectional

traffic matrixes were generated so that for every node pair (𝑖, 𝑗), 𝑗 > 𝑖 the number of ODU-0, ODU-1

and ODU-2 demands was a random number uniformly distributed between 0 and 16, 0 and 8 and 0

and 2 respectively. The attained throughputs applying the Ilp model considering all nodes to be

translucent are presented in Table D.2. The following tables respect to observed network throughputs

resulting from the application of the transparent and opaque formulations in the same conditions. In

the end, the required resources to satisfy all demand are presented for the three configurations.

Table C. 1: Simulation Parameters

Network Bren (10 nodes,11 bidirectional links)

Traffic volume [Gbps]: ∑ ∑ ∑ 𝑡𝑠𝑑𝑟 ∗

𝑑 ∈𝑉𝑠 ∈𝑉𝑟 ∈𝑅

𝑟 = 2045

Contribution to the

total traffic [%]

1.25 32.27

2.5 .67

10 42.05

Table C. 2: Throughput attained applying the translucent model

𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡 [%]

W T 3 4 5 6 7 8

2 39.61 46.09 46.09 - - -

3 48.66 57.95 61.00 61.00 - -

4 51.59 65.89 69.93 72.37 72.37 -

5 51.96 68.46 77.38 80.20 80.20 -

6 - 68.46 80.81 88.02 88.02 -

7 - - 81.42 92.67 95.84 95.84

8 - - 81.42 97.86 99.02 100.00

Table C. 3: Performance of the transparent solution in regards to throughput

𝑇ℎ𝑟𝑡𝑟𝑎𝑛𝑠𝑝𝑎𝑟𝑒𝑛𝑡 − 𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

[%]

W T 3 4 5 6 7 8

2 -7.10 -15.38 -15.38 -15.38 -15.38 -15.38

3 -8.29 -9.07 -12.42 -12.42 -12.42 -12.42

4 -6.63 -12.06 -12.06 -14.19 -14.19 -14.19

5 -5.88 -10.89 -13.11 -11.43 -11.43 -11.43

6 -5.88 -10.36 -12.71 -13.19 -10.69 -10.69

7 - - -12.16 -15.30 -13.39 -12.37

8 - - -11.71 -17.68 -13.58 -11.61

110

Table C. 4: Performance of the opaque solution in regards to throughput

𝑇ℎ𝑟𝑜𝑝𝑎𝑞𝑢𝑒 − 𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

[%]

W T 3 4 5 6 7 8

2 -22.22 -15.38 -5.57 0.00 0.00 0.00

3 -36.68 -32.70 -26.65 -17.03 -10.82 -4.01

4 -40.28 -40.82 -36.01 -30.07 -23.14 -16.55

5 -40.71 -43.04 -42.18 -36.89 -30.64 -24.70

6 -40.71 -43.04 -44.63 -42.50 -36.81 -31.39

7 -40.71 -43.04 -45.05 -45.38 -41.96 -36.99

8 -40.71 -43.04 -45.05 -48.28 -43.83 -39.61

Table C. 5: Comparing the resources required by transparent and translucent solutions

Resources required to satisfy all demand

Intermediate Transparent Opaque

Lightpaths 78 92 (+17.95%) 154 (+97.44%)

Transceivers 8

14,29

%)

10 (+25.00%)

14,29

%)

19 (+137.50%)

14,29

%)

Wavelengths 8 13 (62.50%) 8 (0.00%)

As before, the intermediate grooming solution proves to provide for the highest throughputs.

The distances between the opaque and transparent solutions shortened in respect to the first set of

simulations and for a small number of available wavelengths and a large value of transponders per

node, the opaque solution even perfomes better than the all-optical one. Again, for the satisfaction of

the total demand, the transparent scheme is accounted for the highest number of wavelengths and the

opaque scehme for the highest number of transponders and lightpaths.

C 2. Applying the heuristics to the Bren Network considered in 4.3.3

Table C. 6: Performance of the MRU heuristic in regards to throughput

𝑇ℎ𝑟𝑀𝑟𝑢 − 𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

[%]

W T 3 4 5 6 7 8

2 -7.10 -11.94 -11.94 - - -

3 -2.26 -9.92 -6.81 -6.81 - -

4 -7.82 -12.99 -2.62 -5.91 -5.91 -

5 -8.47 -10.18 -9.48 -4.73 -4.73 -

6 -8.47 -10.18 -13.31 -8.75 -5.00 -5.00

7 - - -13.96 -7.92 -5.74 -5.74

8 - - -13.96 -12.80 -5.19 -6.11

Table C. 7: Performance of the MST heuristic in regards to throughput

𝑇ℎ𝑟𝑀𝑠𝑡 − 𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

[%]

W T 3 4 5 6 7 8

2 -11.11 -18.83 -18.83 - - -

3 -12.06 -12.03 -14.03 -14.03 - -

4 -17.30 -14.29 -12.94 -15.88 -15.88 -

5 -7.29 -9.82 -8.53 -4.88 -4.88 -

6 -7.29 -7.68 -8.32 -8.19 -6.25 -3.61

7 - - -6.76 -8.18 -5.99 -3.70

8 - - -9.61 -12.93 -7.28 -5.50

111

Table C. 8: Performance of the Graph heuristic in regards to throughput

𝑇ℎ𝑟𝐺𝑟𝑎𝑝ℎ − 𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

𝑇ℎ𝑟 𝑡𝑟𝑎𝑛𝑠𝑙𝑢𝑐𝑒𝑛𝑡

[%]

W T 3 4 5 6 7 8

2 -12.35 -5.04 -5.04 -3.98 -3.98 -

3 -18.34 -11.39 -10.22 -8.42 -6.01 -6.01

4 -14.93 -16.14 -11.36 -7.60 -7.09 -5.24

5 -11.76 -16.79 -8.37 -8.69 -5.64 -2.29

6 -11.76 -13.04 -10.14 -8.47 -5.28 -4.72

7 - -10.89 -10.81 -11.74 -9.95 -6.51

8 - -10.89 -10.81 -13.55 -8.64 -3.91

Table C. 9: Resources required to sattisfy demands for the three heuristics

Resources required to satisfy all demand

Mru Mst Graph

Lightpaths 88 (+12.82%) 86 (+7.94%) 86 (+7.94%)

Transceivers 10 (+25.00%)

14,

%)

10 (+25.00%)

14,

%)

10 (+25.00%)

Wavelengths 12 (+50.00%) 12 (+50.00%) 9 (12.50%)

Table C. 10: Computational time for the Ilp formulation

𝑇𝑖𝑚𝑒 𝐼𝑙𝑝 [𝑠]

W T 3 4 5 6 7 8

2 119.67 97.14 139.38 127.15 114.20 123.47

3 241.39 137.03 289.86 394.42 124.26 253.90

4 28.98 511.56 217.62 236.46 238.50 138.46

5 111.92 3457.37 289.86 726.98 2118.86 434.29

6 19.09 326.53 153.96 2327.82 289.52 324.48

7 410.99 448.93 301.96 3226.90 542.27 227.00

8 113.11 555.67 441.68 4356.32 3456.23 92.38

Table C. 11: Comparing the running times for the Ilp and the MRU heuristic

𝑇𝑖𝑚𝑒𝑀𝑟𝑢

𝑇𝑖𝑚𝑒 𝐼𝑙𝑝

[%]

W T 3 4 5 6 7 8

2 0.52 0.55 0.27 0.14 0.42 0.10

3 0.12 0.07 0.01 0.07 0.03 0.05

4 0.40 0.35 0.02 0.98 0.51 0.09

5 0.32 0.39 0.01 0.01 0.04 0.86

6 0.47 0.44 0.03 0.00 0.06 0.78

7 0.49 0.36 0.03 0.00 0.01 0.17

8 0.37 0.62 0.02 0.00 0.00 0.36

Table C. 12: Comparing the running times for the Ilp and the MST heuristic

𝑇𝑖𝑚𝑒𝑀𝑠𝑡

𝑇𝑖𝑚𝑒 𝐼𝑙𝑝

[%]

W T 3 4 5 6 7 8

2 0.74 1.22 0.18 0.12 0.11 0.08

3 0.50 0.36 0.01 0.03 0.02 0.06

4 2.03 1.09 0.02 0.56 0.41 0.19

5 1.10 1.82 0.02 0.01 0.04 1.14

6 1.02 2.25 0.04 0.00 0.07 1.38

7 0.84 0.81 0.03 0.00 0.01 0.20

8 0.62 0.72 0.02 0.00 0.00 0.44

112

Table C. 13: Comparing the running times for the Ilp and the Graph heuristic

𝑇𝑖𝑚𝑒𝐺𝑟𝑎𝑝ℎ

𝑇𝑖𝑚𝑒 𝐼𝑙𝑝

[%]

W T 3 4 5 6 7 8

2 9.55 31.13 24.72 8.67 16.63 10.03

3 5.71 7.98 1.11 3.51 2.68 6.35

4 30.38 31.60 1.96 74.42 58.45 13.15

5 24.07 53.91 1.73 0.79 5.11 146.02

6 33.81 64.83 3.40 0.27 7.61 163.74

7 26.07 45.82 1.68 0.19 1.29 27.90

8 21.87 72.86 1.19 0.15 0.20 62.90

113

Appendix D

Detailed description of the Auxiliary Graph Model of [22]

D 1. Description and example

Taking as input the network’s physical topology (number of nodes 𝑁 and set of arcs 𝐴), each

node’s functionalities (grooming and wavelength converting capabilities) and number of available

transceivers as well as wavelengths at disposal at each fiber link, an auxiliary graph 𝐺(𝑉, 𝐸) is created.

This graph is built in three layers: access (layer 2), lightpath (1) and wavelength (0), from top to

bottom. Each physical node has two ports (auxiliary graph nodes) on each layer, an input and an

output one. A port is characterized by 𝑉𝑖𝑙,𝑝

, where 𝑙 stands for the layer it belongs to, 𝑝 defines whether

it is an input port (𝑝 = 0) or an output one (𝑝 = 1), and 𝑖 traces back to the physical node. In turn, an

edge is represented as <𝑉,𝑉>, expressing a connection between two ports. An auxiliary graph edge

can have one of the following denominations:

Wavelength Bypass Edge (𝑊𝐵𝐸𝑖): edge from the input port to the output port on the wavelength

layer of every physical node. A connection that goes through one of these edges optically

bypasses the physical node. <𝑉𝑖0,0, 𝑉𝑖

0,1 >, 𝑖 ∈ 𝑁;

Grooming Edge (𝐺𝑟𝑚𝐸𝑖): edge from the input port to the output port on the access layer of a

given node with grooming capability < 𝑉𝑖2,0, 𝑉𝑖

2,1 >, 𝑖 ∈ 𝑁. A connection that goes through these

edges is routed in multi-hop fashion.

Mux Edge (𝑀𝑢𝑥𝐸𝑖): edge from the output port of the access layer to the output port of the

lightpath layer at each node < 𝑉𝑖2,1, 𝑉𝑖

1,1 >, 𝑖 ∈ 𝑁. A connection that goes through these edges is

forwarded in at least one already deployed lightpath;

Demux Edge (𝐷𝑚𝑥𝐸𝑖): edge from the input port of the access layer to the input port of the access

layer < 𝑉𝑖1,0, 𝑉𝑖

2,0 >, 𝑖 ∈ 𝑁;

Transmitter Edge (𝑇𝑥𝐸𝑖): edge from the output port of the access layer to the output port of the

wavelength layer < 𝑉𝑖2,1, 𝑉𝑖

0,1 >, 𝑖 ∈ 𝑁; Whenever a connection spans one of these edges, a

lightpath is established with origin at the correspondent physical node 𝑖;

Receiver Edge (𝑅𝑥𝐸𝑖): edge from the input port of the wavelength layer to the input port of the

access layer< 𝑉𝑖0,0, 𝑉𝑖

2,0 >, 𝑖 ∈ 𝑁; a receiver edge is always associated with a transmitter edge,

marking the endpoints of a new optical channel.

Wavelength Link Edges (𝑊𝐿𝐸𝑖𝑗): there is an edge from the output port of a node 𝑖 to the input

port of a node 𝑗 on the wavelength layer if the nodes are physically adjacent < 𝑉𝑖0,1, 𝑉𝑗

0,0 >

, 𝑖, 𝑗 ∈ 𝑁, (𝑖, 𝑗) ∈ 𝐴;

Lightpath Edges (𝐿𝑃𝐸𝑖𝑗): there is an edge from the output port of a node 𝑖 to the output port of a

node 𝑗 on the lightpath layer if there is an optical channel among the nodes < 𝑉𝑖1,1, 𝑉𝑗

1,0 >, 𝑖, 𝑗 ∈ 𝑁.

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Lightpath edges have a capacity associated 𝑐(𝐸) to express the current bandwidth occupation.

All other edges have an infinite capacity. Each edge has an assigned weight 𝑊(𝐸), according to its

type among those presented above. The weight of a path over the auxiliary graph is calculated as the

sum of the weight of all edges and the capacity as the minimum capacity among the capacities of the

edges crossed. The algorithm is fed with one traffic request at a time, 𝑇(𝑠𝑡 , 𝑑𝑡 , 𝑢𝑡 , 𝑟𝑡), a group of

𝑟𝑡 𝑂𝑑𝑢 − 𝑢𝑡 connections to satisfy between a given node pair (𝑠𝑡 , 𝑑𝑡). Whenever a connection or group

of connections is successfully satisfied, the changes to the network state are reflected onto the

auxiliary graph. The grooming, routing and wavelength assignment process is performed over the

graph‘s structure and on this topic, five operations can be conducted, the number of spanned existing

lightpaths referred to as 𝑒𝑙 and the number of newly created optical channels as 𝑛𝑙:

Route the traffic over a single existing lightpath from source to destination (𝑒𝑙 = 1, 𝑛𝑙 = 0):

𝑝 = 𝑀𝑢𝑥𝐸 + 𝐿𝑃𝐸 + 𝐷𝑚𝑥𝐸. The path’s capacity is 𝑐(𝑝) = 𝑐(𝐿𝑃𝐸);

Route the traffic over a set of 𝑎 existing lightpaths, in multi-hop fashion ( 𝑒𝑙 = 𝑎, 𝑛𝑙 = 0):

𝑝 = 𝑎 ∗ (𝑀𝑢𝑥𝐸 + 𝐿𝑃𝐸 + 𝐷𝑚𝑥𝐸) + (𝑎 − 1) ∗ 𝐺𝑟𝑚𝐸.The path’s capacity is

𝑐(𝑝) = 𝑚𝑖𝑛(𝐿𝑃𝐸𝑘) , ∀ 𝑘 ∈ [1, 𝑎].

Create a direct 𝑂𝑡𝑢 − 𝑘 lightpath from source to destination, spanning 𝑚 fiber links, to route the

traffic (𝑒𝑙 = 0 , 𝑛𝑙 = 1):

𝑝 = 𝑇𝑥𝐸 + 𝑚 ∗ 𝑊𝐿𝐸 + (𝑚 − 1) ∗ 𝑊𝐵𝐸 + 𝑅𝑥𝐸 . The path’s capacity is 𝑐(𝑝) = TS𝑘;

Create a set of 𝑏 new lightpaths, forming an optical path from 𝑠 to 𝑑 (𝑒𝑙 = 0, 𝑛𝑙 = 𝑏). Every newly

established optical channel carries an 𝑂𝑡𝑢 − 𝑘𝑗 , 𝑘𝑗 ∈ 𝐾 and spans 𝑚𝑗, 𝑗 ∈ [1, 𝑏] fiber links :

𝑝 = ∑

(𝑇𝑥𝐸 + 𝑚𝑗 ∗ WLE + (𝑚𝑗 − 1) ∗ WBE + RxE).𝑏𝑗=1 The path’s capacity is given by

𝑐 (𝑝) = 𝑚𝑖𝑛(TS𝑗) , ∀ 𝑗 ∈ [1, 𝑏].

Route the traffic over a mixture of 𝑎 existing lightpaths and 𝑏 newly created optical channels

(𝑒𝑙 = 𝑎, 𝑛𝑙 = 𝑏):

𝑝 = 𝑎 ∗ (𝑀𝑢𝑥𝐸 + 𝐿𝑃𝐸 + 𝐷𝑚𝑥𝐸 ) + (𝑎 − 1) ∗ 𝐺𝑟𝑚𝐸 +

∑ (𝑇𝑥𝐸 + 𝑚𝑗 ∗ WLE + (𝑚𝑗 − 1) ∗ WBE + RxE) 𝑏𝑗=1 . The path’s capacity

is 𝑐 (𝑝) = 𝑚𝑖𝑛(𝑐(𝐿𝑃𝐸𝑖), TS𝑗) , ∀ 𝑖 ∈ [1, 𝑎], 𝑗 ∈ [1, 𝑏] .

After determining which of the operations, if any, given the resource availability, is to be

conducted for the current request, it becomes necessary to reflect the changes onto the network and

the auxiliary graph:

(Step 1)

If 𝑐(𝑝) < 𝑟 ∗ 𝑇𝑆𝑢𝑡 satisfy 𝑥 = 𝑓𝑙𝑜𝑜𝑟 (c(p)

TS𝑢𝑡 ) 𝑂𝑑𝑢 − 𝑢𝑡 traffic demands and update the

remaining number of demands to 𝑟𝑡′ = 𝑟𝑡 − 𝑥 . Otherwise, satisfy 𝑥 = 𝑟𝑡 traffic

demands, and remove 𝑡 from the set of requests to attend;

(Step 2) Insert 𝑛𝑙 lightpath edges < 𝑉𝑠(𝑖)1,0 , 𝑉𝑑(𝑖)

1,1 > with capacity 𝑐(𝐿𝑃𝐸𝑖)=TS𝑖 − 𝑥 ∗ TS𝑢𝑡, ∀ 𝑖 ∈

[1, 𝑛𝑙];

(Step 3) Decrease the number of transmitters and receivers at the source and destination of

each newly created lightpath 𝑇𝑥𝑠(𝑖)

′ = 𝑇𝑥𝑠(𝑖)

− 1, 𝑅𝑥𝑑(𝑖)

′ =𝑅𝑥𝑑(𝑖)

− 1 , ∀ 𝑖 ∈ [1, 𝑛𝑙]. For each

𝑇𝑥𝑠(𝑖)

′ and 𝑅𝑥𝑑(𝑖)

′ whose value decreases to zero, remove the correspondent transmitter

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< 𝑉𝑠(𝑖)2,1 , 𝑉𝑠(𝑖)

0,1 > and receiver < 𝑉𝑑(𝑖)0,0 , 𝑉𝑑(𝑖)

2,0 > edges, respectively;

(Step 4) For every wavelength link crossed 𝑊𝐿𝐸𝑖𝑗 < 𝑉𝑖0,1, 𝑉𝑗

0,0 > decrease the number of

available wavelengths at the correspondent fiber link (𝑖, 𝑗), 𝑊𝑖𝑗′ = 𝑊𝑖𝑗 − 1. For every

zero valued 𝑊𝑖𝑗′ , remove the correspondent wavelength link edge;

(Step 5) Decrease the capacity of every spanned existing lightpath according to 𝑐(𝐿𝑃𝐸𝑖)′ =

𝑐(𝐿𝑃𝐸𝑖) − 𝑥 ∗ TS𝑢𝑡∀ 𝑖 ∈ [1, 𝑒𝑙]. For every lightpath with saturated capacity 𝑐(𝐿𝑃𝐸𝑖)′ <

TS𝑎 ,a = min(u) , ∀ 𝑢 ∈ 𝑈, remove the correspondent lightpath edge.

Figure D. 1: Description of the algorithm to update the auxiliary graph's state

The operation to be conducted is determined by the path or set of crossed edges with the

minimum weight. By carefully assigning weights to the edges, it is possible to direct the methodology’s

output to a certain goal. For instance, if one wishes to minimize the amount of electrical processing or

equivalently the number of virtual hops, it seems only fitting to penalize the utilization of grooming

edges. By doing so, it is made sure the remaining edges are preferred, having a higher probability of

being chosen for the shortest paths. Two grooming policies are applied, each with an associated

weight assignment:

Minimize the number of traffic hops (MinTH): This policy tries to route as many connections as

possible in direct lightpaths from source to destination, benefiting operations [1] and [3]. If these

options fail, the selected operation is that among [2], [4] and [5] that comprises the lowest

number of virtual traffic hops. The utilization of grooming edges is discouraged;

Minimize the number of lightpaths (MinLP): This policy tries to route as many connections as

possible over already established lightpaths, only recurring to operations that involve the

establishment of further lightpaths if all others fail. As so, operations [1] and [2] are always the

preferred ones. The utilization of transmitter and receiver edges is discouraged.

Minimize the number of wavelength links (MinWL): This policy tries to route as many connections

as possible over already established lightpaths to not consume further wavelength resources. As

so, operations [1] and [2] are always the preferred ones. If those fail, operations [3] and [5] with

𝒃 = 𝟏 are next in line.

To reflect these policies, the weight assignments are as follows, extracted from [22]:

Table D. 1: Weight Assignments for each Grooming Policy

Weight

Edge MinTH MinLP MinWL

𝑇𝑥𝐸 20 200 20

𝑅𝑥𝐸 20 200 20

𝐿𝑃𝐸 1 1 1

𝑊𝐿𝐸 10 10 1000

𝑊𝐵𝐸 0 0 0

𝐺𝑟𝑚𝐸 1000 20 0

𝑀𝑥𝐸 0 0 0

𝐷𝑚𝑥𝐸 0 0 0

The order in which traffic requests are selected impacts the final solution for it determines the

evolution in the consumption of network resources and the establishment of optical channels,

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conditioning the next attended requests routing options. Three metrics were used to settle an order in

the attendance of demands:

Maximum amount first (MAF): traffic request are attended from the one with the highest volume

of traffic 𝑟𝑡 ∗ TS𝑢𝑡 to the one with the lowest.

Least Cost first (LCF): each request is assigned a cost, calculated as the total volume of traffic

divided by the weight of the shortest path for routing the traffic on the graph 𝑟𝑡∗ TS𝑢𝑡

𝑊(𝑝) .

Maximum Utilization First (MUF): each request is assigned a utilization value, calculated as the

total volume of traffic divided by the number of hops of the shortest graph path on the physical

topology 𝑟𝑡∗ TS𝑢𝑡

𝐻(𝑝).

To make the algorithm as dynamic and updated as possible, for each request, the volume of

traffic considered was the one that could actually be attended as opposed to the one left to attend. To

do so, post routing each request, all shortest paths are recalculated as well as the amount of traffic

they can carry. Such behavior allows to calculate all metrics with regards to the current state of the

network.

A small ilustrative example is now presented, for greater clarity on the algorithm’s behaviour post

its definition. For simplicity, the weight considered for all edges is of one unit. All lightpaths work on the

40 Gbps line-rate, 𝑂𝑡𝑢 − 3. It is considered that there is only one wavelength available at each fiber

link and one transceiver at each network node. Requests to attend are, in order, 𝑇1(1,2, 𝑂𝑑𝑢 − 2,3) and

𝑇2(1,0, 𝑂𝑑𝑢 − 1,8). The network’s physical topology is presented, as well as a picture of state of the

auxiliary graph at each step.

To route the first request 𝑇1(1,2, 𝑂𝑑𝑢 − 2,3) two possible paths are available:

𝑝1 = 𝑇𝑥𝐸1 + 𝑊𝐿𝐸10 + 𝑅𝑥𝐸0 + 𝐺𝑟𝑚𝐸0 + 𝑇𝑥𝐸0 + 𝑊𝐿𝐸02 + 𝑅𝑥𝐸2 𝑊(𝑝1) = 7

𝑐(𝑝1) = 𝑚𝑎𝑝𝑂𝑇𝑁[3] = 32

𝑝2 = 𝑇𝑥𝐸1 + 𝑊𝐿𝐸10 + 𝑊𝐵𝐸0 + 𝑊𝐿𝐸02 + 𝑅𝑥𝐸2 𝑊(𝑝2) = 5

Figure D. 2: Network topology (left) and initial graph state

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𝑐(𝑝2) = 𝑚𝑎𝑝𝑂𝑇𝑁[3] = 32

Path 𝑝2 is the selected one given its lower weight and as so the request is routed over a newly

created lightpath between node 1 and node 2, whose capacity becomes 𝑐(𝐿𝑃𝐸12) = 32 − 3 ∗

𝑚𝑎𝑝𝑂𝑇𝑁[2] = 32 − 3 ∗ 8 = 32 − 24 = 8. Since the single available transmitter at node 1 and receiver at

node 2 were consumed, the correspondent edges are deleted. Also, the utilized wavelength links

between node 1 and 0 and between nodes 0 and 2 are removed. To route the second request

𝑇2(1,0, 𝑂𝑑𝑢 − 1,8), it is impossible to establish a direct lightpath for there are no transmitters at

disposal at node 1. The only available path is:

𝑝1 = 𝑀𝑢𝑥𝐸1 + 𝐿𝑃𝐸12 + 𝐷𝑚𝑥𝐸2 + 𝐺𝑟𝑚𝐸2 + 𝑇𝑥𝐸2 + 𝑊𝐿𝐸20 + 𝑅𝑥𝐸0 𝑊(𝑝1) = 7

𝑐(𝑝2) = 𝑚𝑖𝑛(𝑚𝑎𝑝𝑂𝑇𝑁[3], 𝑐(𝐿𝑃𝐸12)) = 𝑚𝑖𝑛 (32,8) = 8

The request is forwarded over the existing lightpath (1,2) and over a newly created lightpath from 2 to

0. Since there isn’t enough capacity to route the whole of the requests 8 ∗ 𝑚𝑎𝑝𝑂𝑇𝑁[1] = 8 * 2 = 16 >

𝑐(𝑝2) = 8 , a portion of the demands are blocked. 𝑥 = 𝑓𝑙𝑜𝑜𝑟 (𝑐(𝑝2)

𝑚𝑎𝑝𝑂𝑇𝑁[1]) = 𝑓𝑙𝑜𝑜𝑟 (

8

2) = 4 𝑂𝑑𝑢 − 1

connections are successfyully routed and the remaining four are left unattended.

The graph heuristic can easily be adapted to fit the cases of transparent and opaque network

scenarios. For the first all optical scenario, it is only necessary to remove the grooming edges from all

network nodes to assure that only operations [3] and [4] are conducted. For the opaque scenario, in

turn, it is necessary to make sure that, when selecting the shortest path in the graph, the candidate

paths can comprise at most one wavelength link. In order to do so, it becomes necessary to remove

from all nodes the wavelength bypass edges.

Figure D. 3: Path used to route the first request (left) and updated graph's state

Figure D. 4: Path used to route the second request (left) and updated graph's state