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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).
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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
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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
x
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
60
80
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Cr = 1.5
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Network cost comparison in translucent, mixed-line rate scenarios
Cr = 1.5
Cr = 2
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Network cost comparison in translucent, single-rate scenarios
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
0
2
4
6
8
10
12
14
1200 1600 2000 2400 2800 3200 3600 4000 4400
Tim
e [
s]
TTV [Gbps]
Computational times comparison in translucent, mixed-line rate scenarios
Cr = 1.5
Cr = 2
Cr = 2.5
200
700
1200
1700
2200
2700
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Co
st
TTV [Tbps]
84
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
200
400
600
800
1000
1200
1400
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Co
st
TTV [Tbps]
0
200
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800
1000
1200
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Co
st
TTV [Tbps]
100
200
300
400
500
600
700
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Co
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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
20
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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.
20
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91
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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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