optical transport networks with flexi-grid planning...canais com elevadas capacidades que poderão...

Optical Transport Networks with Flexi-Grid Planning

Alexandra Adelínovna Guerra Inácio

Thesis to obtain the Master of Science Degree in

Electrical and Computer Engineering

Supervisors:

Prof. João José de Oliveira Pires

Doctor João Miguel Santos

Examination Committee

Chairperson: Prof. José Eduardo Charters Ribeiro da Cunha Sanguino

Supervisor: Prof. João José de Oliveira Pires

Members of the Committee: Prof. Paulo Miguel Nepomuceno Pereira Monteiro

June 2019

Declaração

Declaro que o presente documento é um trabalho original da minha autoria e que cumpre todos os requisitos do Código de Conduta e Boas Práticas da Universidade de Lisboa.

Declaration

I declare that this document is an original work of my own authorship and that it fulfils all the requirements of the Code of Conduct and Good Practices of the Universidade de Lisboa.

i

Acknowledgements

Develop thesis at Coriant was a unique and overwhelming opportunity that I could not pass over. As

IST student, I already had contact with Coriant at brief presentation, which impressed me very positively.

The real contact with the company was a confirmation and even surpassing of all my expectations:

excellence, development, teamwork, organization, among other qualities Thus, in a first place, I would

like to thank Coriant and Eng. João Miguel Santos for guidance and for all given support. It was an

honour to me feeling as a member of a team.

I also acknowledge Instituto Superior Técnico and Eng. João José de Oliveira Pires, for giving me

an opportunity to take part of this project, and for all given support and supervision.

I express gratitude to Portuguese Navy for backing the hole process, particularly to my superiors and

supervisors, namely Eng. Bulcão Sarmento, Eng. Pereira Cavaco, Eng. Rodrigues Pinto, Eng. Mendes

Abrantes, Eng. Gil Viegas, Eng. José de Almeida and Eng. Mendes Simões.

At last, but not the least, I would like to acknowledge my parents, family, and João Pedro, for all

comprehension and companionship. Without them, all this effort would be meaningless.

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Resumo

A procura por soluções inovadoras na área de redes óticas foi fortemente impulsionada com o

aumento exponencial de tráfego durante as primeiras décadas do século XXI até aos seus novos

limites.

A gestão flexível da largura de banda está a ser atualmente integrada em soluções já existentes

sobre uma gestão de grelha fixa. O novo paradigma de redes elásticas de transporte ótico só foi

possível devido a desenvolvimento de novo equipamento, com especial enfoque em soluções de

deteção coerente e introdução de novos formatos de modulação. Adicionalmente, a implementação de

canais com elevadas capacidades que poderão transportar até 1 Tbps, os designados Super-canais,

levou à necessidade de rever as estratégias de roteamento atualmente implementadas nas redes

óticas.

Numa perspetiva estática, geralmente aplicável durante o processo de dimensionamento de novas

redes, a simulação e o processo heurístico são ferramentas importantes para identificar as melhores

soluções em problemas reais. No presente trabalho de investigação, foram comparados, por via de

simulação e através de uma abordagem heurística, diferentes algoritmos de roteamento, com diferentes

combinações de perfis de tráfego e topologias de rede.

Foi concluído que estratégias de ordenamento de pedidos que priorizam os caminhos mais

congestionados bem como estratégias de roteamento que consideram o número de 3R como critério

principal, complementado com a escolha dos caminhos com menor espetro, levam a melhores

resultados. No entanto, verificou-se também que a topologia e a distribuição do tráfego na rede têm

impacto nos resultados, devendo estas especificidades serem consideradas no processo de

planeamento.

Palavras-chave: Redes de transporte óticas, grelhas fixa e flexível, redes elásticas, ordenação de

pedidos, estratégias de roteamento, Super-canais

v

Abstract

In an exponentially growing traffic environment that characterizes the first decades of the 21st

century, the search for innovative technological solutions, compliant with dynamic client’s traffic

demands, is pushed to its new limits.

Fixed grid bandwidth management is being gradually combined with the flexible one that introduces

the new paradigm of elastic optical networks. This technological leap was possible with the development

of new equipment, with a highlight to the coherent detection solutions, and introduction of new

modulation formats. Also, the implementation of high capacity traffic channels, the Super-channels, with

capacities that can reach up to 1 Tbps, required new approaches of the routing strategies.

In static simulation scenarios, generally applicable at the dimensioning of new optical networks, it is

possible to derive best strategies that may be adopted at specific scenarios. In the present investigation,

there were compared different combinations of routing strategies, client traffic profiles, demand

orderings and optical networks. Heuristic approach was implemented, and the results compared.

It was concluded that demand orderings by the most congested link first and routing criteria that

considers the minimum number of regenerators as the first criteria and the minimum spectrum as an

untie criteria lead to best results. Thus, demand ordering and routing criteria algorithms have direct

influence at the performance networks, being be an important tool in the planning process. Therefore,

since networks with different topologies will react differently to client’s demands, it is important to

consider network and client’s specificities before implementation of extensive modifications.

Keywords: Optical Transport Network, Fixed and Flexible Grids, Elastic Optical Networks, Demand

Ordering, Routing Strategies, Super-channels

vii

Contents

ACKNOWLEDGEMENTS.................................................................................................................... I

RESUMO ........................................................................................................................................ III

PALAVRAS-CHAVE .......................................................................................................................... III

ABSTRACT ...................................................................................................................................... V

KEY-WORDS ................................................................................................................................... V

LIST OF FIGURES…........................................................................................................................... IX

LIST OF TABLES ……........................................................................................................................ XIII

LIST OF SYMBOLS............................................................................................................................XV

LIST OF ABBREVIATIONS ............................................................................................................... XVII

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

1.1. Motivation ................................................................................................................................ 1

1.2. Objectives and contributions ................................................................................................... 3

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

2. Overview of Optical Transport Networks.......................................................................................... 5

2.1. OTN Systems .......................................................................................................................... 6

2.1.1. OTN Hierarchy ................................................................................................................. 6

2.1.2. Optical Network Equipment ............................................................................................. 9

2.2. Multi-level modulations and Coherent Detection/ Reception Systems.................................. 13

2.2.1. Encode more bits per symbol ........................................................................................ 13

2.2.2. Transmit more symbols per second .............................................................................. 15

2.2.3. Coherent Detection ........................................................................................................ 16

2.3. Elastic Optical Transport Networks ....................................................................................... 17

2.3.1. Flexi-grid standard (ITU-T G.694.1) .............................................................................. 17

2.3.2. Super-channels (SC) ..................................................................................................... 21

3. Optical Transport Network Planning .............................................................................................. 24

3.1. Routing in Optical Networks .................................................................................................. 24

3.1.1. Routing Algorithms (Dijkstra and Yen) .......................................................................... 25

3.2. Static, semi-static and dynamic routing ................................................................................. 27

3.3. Multi-period planning ............................................................................................................. 28

3.4. Client Traffic Generation ........................................................................................................ 28

viii

3.5. Demand Ordering .................................................................................................................. 31

3.6. Demand Routing .................................................................................................................... 35

3.7. Wavelength/Spectrum Assignment ....................................................................................... 40

3.8. Optical Planner Software Description .................................................................................... 41

4. Results and Discussion .................................................................................................................. 46

4.1. Demand Ordering Strategies ................................................................................................. 48

4.1.1. Uniform Model ............................................................................................................... 48

4.1.2. Gravitational Model ........................................................................................................ 49

4.2. Demand Routing Strategies .................................................................................................. 52

4.2.1. Uniform Model ............................................................................................................... 52

4.2.2. Gravitational Model ........................................................................................................ 53

4.2.3. Detailed analysis with modulation scenarios (both models) .......................................... 55

5. Conclusions and Future Work ........................................................................................................ 60

5.1. Conclusions ........................................................................................................................... 60

5.2. Future Work ........................................................................................................................... 61

6. References ..................................................................................................................................... 63

Appendix A: Results ...................................................................................................................... A-1

A.1. Demand ordering - Uniform Distribution ............................................................................... A-1

A.2. Demand ordering – Gravitational Model ............................................................................... A-4

A.3. Demand Routing - Uniform & Gravitational .......................................................................... A-6

Appendix B: General Network Data .............................................................................................. B-1

B.1. European Optical Network (COST 239) ............................................................................... B-1

B.2. German Backbone Network (GBN) ...................................................................................... B-3

B.3. Portugal Backbone Network (PBN or PRT) .......................................................................... B-5

Appendix C: Auxiliary data used for Gravitational Model ..............................................................C-1

C.1. COST 239 .............................................................................................................................C-1

C.2. GBN ......................................................................................................................................C-3

C.3. PRT .......................................................................................................................................C-4

ix

List of Figures

Figure 2.1 – OTN network – switching at lambda and sub-lambda level [6] ........................................... 5

Figure 2.2 - Different services supported over the same wavelength by OTN [7]. ................................. 7

Figure 2.3 – OTN Hierarchy – Optical Transport Module [6]. .................................................................. 7

Figure 2.4 - OTN Mapping Hierarchy and new flex OTN Hierarchy in detail according ITU-T the Rec.

G.709. Changes are signalized with red color [8]. .................................................................................. 8

Figure 2.5 - OTN Network Layers [9]. ..................................................................................................... 9

Figure 2.6 – OA is an ideal device to enhance the range of DWDM system [10]. .................................. 9

Figure 2.7 - Transponder block diagram [12]. ....................................................................................... 10

Figure 2.8 – WSS is a 1 x N optical commutation device and allows to switch one or several channels

between input and output ports [12]. ..................................................................................................... 11

Figure 2.9 - OADM unit using optical switches and wavelength multiplexers [13]. ............................... 11

Figure 2.10 – ROADM – Express and add/drop switching [6]. .............................................................. 12

Figure 2.11 - C/D/C ROADM – different configurations [14]. ................................................................ 12

Figure 2.12 - OTM constitution: transponder, multiplexer and power amplifier [12]. ............................ 13

Figure 2.13 – QPSK is a four-level modulation format since symbols can take 4 different values (e.g.:

0,1,2,3). With a symbol rate of e.g. 2.5 Gbaud it is obtained a bit rate of 5 Gbps [16]. ........................ 14

Figure 2.14 - Example: two input signals (previously modulated by QPSK/QAM) are first modulated by

PDM (or PM) and then combined by the dual-carrier modulation [16]. ................................................. 15

Figure 2.15 – Digital Coherent Receiver - generic scheme [17]. .......................................................... 16

Figure 2.16 – Example of Cisco ® NCS 4000 400 Gbps WDM/OTN/Packet Universal Line Card –

relation between chart capability (Tbps) Spectral Efficiency (bit/s/Hz) and maximum reach (Lmax) for

different modulation schemes (ITU-T G.652 SMF – solid lines; ITU-T G.655 LEAF fiber – dashed lines)

[18] ......................................................................................................................................................... 17

Figure 2.17 – Example of multi-carrier 400 Gb/s and 1 Tb/s channels implementation [6]. ................. 18

x

Figure 2.18 – Flexi-grid with 12.5 GHz granularity has higher efficiency of the spectrum management,

allowing to transmit more channels at the same fiber and has additional capability to implement 400

Gbps and 1 Tbps Super-channels by grouping several channels in a flexible way [6]. ........................ 19

Figure 2.19 - An example of the use of the flexible grid [1]. .................................................................. 20

Figure 2.20 – Partitioning of the fiber spectrum: a) fixed grid spacing of 50 GHz; b) fixed grid spacing

of 37.5 GHz; c) Mixed channel spacing based on overlapping of 37.5 GHz and 50 GHz grids; d)

gridless partitioning [20]. ........................................................................................................................ 20

Figure 2.21 – SC implementation options – it can be constituted by several channels aggregated

together. From left to the wright: single carrier SC, dual-carrier SC, and multi-carrier [21]. ................. 22

Figure 3.1 - A wavelength-routed optical WDM network with lightpath connections [22]. .................... 25

Figure 3.2 – Spanning tree after the application of Dijkstra algorithm at different vertices of the graph

[24] ......................................................................................................................................................... 26

Figure 3.3 – Pseudocode for uniform model – generation of the input traffic ....................................... 30

Figure 3.4 – Pseudocode for gravitational model – generation of the input traffic ................................ 31

Figure 3.5 – Pseudocode for demand ordering policy Highest Rate First + Largest Distance (ID=0 or

DO_HRF) ............................................................................................................................................... 33

Figure 3.6 - Pseudocode for demand ordering policy Largest Distance + Highest Rate First (ID=1 or

DO_LD).................................................................................................................................................. 33

Figure 3.7 - Pseudocode for demand ordering policy Most Congested link + Random (ID=2 or

DO_MC-R) ............................................................................................................................................. 34

Figure 3.8 - Pseudocode for demand ordering policy Most Congested link + Highest Rate First (ID=3

or DO_MC-HRF) .................................................................................................................................... 34

Figure 3.9 - Pseudocode for demand ordering policy Most Congested link+Largest Distance (ID=4 or

DO_MC-LD) ........................................................................................................................................... 35

Figure 3.10 – Example of demand routing – three possible paths between nodes 1 and 4 with same

number of regenerators (3R). ................................................................................................................ 37

Figure 3.11 – Graph that exemplifies the possible topology of the network that was considered to

explain the demand routing algorithms in Table 3.4 and Figure 3-9. The numbers associated to

different links refer to the maximum spectral availability per lightpath. ................................................. 38

xi

Figure 3.12 – Demand routing algorithm 1 ............................................................................................ 38

Figure 3.13 - Demand routing algorithm 2 ............................................................................................. 39



Figure 3.16 - Demand routing algorithm A ............................................................................................ 40

Figure 3.17 - Demand routing algorithm B ............................................................................................ 40

Figure 3.18 - Demand routing algorithm C ............................................................................................ 40

Figure 3.19 – Flowchart of the OPS tool – general framework [3] [20] ................................................. 42

Figure 3.20 – OPS framework - RSA algorithm [3]. General structure was preserved. There were

introduced modifications at the algorithms at “Order the demands” and “Search for the k-th shortest-

path with available blocks [3] [20]. ......................................................................................................... 42

Figure 3.21 – Path segmentation in several lightpaths accordingly the modulation format maximum

reach. Node 3 integrates a regenerator (3R). ....................................................................................... 44

Figure 6.1 - Mean values of TBT (Gbps) for COST network at uniform model (yy axes) grouped by

different routing criteria (1,2,3,4,A,B,C) and sub ordered by different demand orderings (4,2,3,0,1) (xx

axes) ..................................................................................................................................................... A-1

Figure 6.2 - Mean values of TBT (Gbps) for GBN network at uniform model (yy axes) grouped by


axes) ..................................................................................................................................................... A-2

Figure 6.3 - Mean values of TBT (Gbps) for PRT network at uniform model (yy axes) grouped by


axes) ..................................................................................................................................................... A-2

Figure 6.4 - Mean values of TRC for COST network at uniform model (yy axes) grouped by different

routing criteria (1,2,3,4,A,B,C) and sub ordered by different demand orderings (3,2,4,0,1) (xx axes) A-2

Figure 6.5 - Mean values of TRC for GBN network at uniform model (yy axes) grouped by different


Figure 6.6 - Mean values of TRC for PRT network at uniform model (yy axes) grouped by different


xii

Figure 6.7 - – Mean values of TBT (Gbps) for COST network at gravitational model (yy axes) grouped

by different routing criteria (1,2,3,4,A,B,C) and sub ordered by different demand orderings (4,2,3,1,0)

(xx axes) ............................................................................................................................................... A-4

Figure 6.8 - Mean values of TBT (Gbps) for GBN network at gravitational model (yy axes) grouped by


axes) ..................................................................................................................................................... A-4

Figure 6.9 - Mean values of TBT (Gbps) for PRT network at gravitational model (yy axes) grouped by


axes) ..................................................................................................................................................... A-4

Figure 6.10 - Mean values of TRC for COST network at gravitational model (yy axes) grouped by


axes) ..................................................................................................................................................... A-5

Figure 6.11 - Mean values of TRC for GBN network at gravitational model (yy axes) grouped by


axes) ..................................................................................................................................................... A-5

Figure 6.12 - Mean values of TRC for PRT network at gravitational model (yy axes) grouped by


axes) ..................................................................................................................................................... A-5

Figure 6.13 - Mean values of TBT (Gbps) for COST network at uniform model (yy axes) grouped by

different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (4,2,1,3,C,A,B) (xx

axes). .................................................................................................................................................... A-6

Figure 6.14 - Mean values of TBT (Gbps) for GBN network at uniform model (yy axes) grouped by

different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (4,2,C,1,3,A,B) (xx

axes) ..................................................................................................................................................... A-6

Figure 6.15 - Mean values of TBT (Gbps) for PRT network at uniform model (yy axes) grouped by

different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (4,2,3,C,1,A,B) (xx

axes) ..................................................................................................................................................... A-7

Figure 6.16 - Mean values of TRC for COST network at uniform model (yy axis) grouped by different

demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (C,3,1,A,B,4,2) (xx axes) A-7

Figure 6.17 - Mean values of TRC for GBN network at uniform model (yy axis) grouped by different

demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (C,3,1,A,B,2,4) (xx axes) A-7

xiii

Figure 6.18 - Mean values of TRC for PRT network at uniform model (yy axes) grouped by different

demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (C,3,A,1,B,4,2) (xx axes) A-7

Figure 6.19 - Mean values of TBT (Gbps) for COST network at gravitational model (yy axes) grouped

by different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (4,2,1,3,C,A,B)

(xx axes) ............................................................................................................................................... A-8

Figure 6.20 - Mean values of TBT (Gbps) for GBN network at gravitational model (yy axes) grouped by

different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (4,2,C,1,3,A,B) (xx

axes) ..................................................................................................................................................... A-8

Figure 6.21 - Mean values of TBT (Gbps) for PRT network at gravitational model (yy axes) grouped by

different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (4,2,3,C,1,A,B) (xx

axes) ..................................................................................................................................................... A-8

Figure 6.22 - Mean values of TRC for COST network at gravitational model (yy axes) grouped by

different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (C,3,1,A,B,4,2) (xx

axes) ..................................................................................................................................................... A-8

Figure 6.23 - Mean values of TRC for GBN network at gravitational model (yy axes) grouped by

different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (C,3,1,A,B,2,4) (xx

axes) ..................................................................................................................................................... A-9

Figure 6.24 - Mean values of TRC for PRT network at gravitational model (yy axes) grouped by

different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (C,3,A,1,B,4,2) (xx

axes) ..................................................................................................................................................... A-9

Figure 6.25 – COST 239 network (11 nodes and 52 links) .................................................................. B-1

Figure 6.26 - German 17-node backbone network (DTAG), l: nodes with numbers, r: node distances to

its destinations by (Hinz, 2009) [29] ..................................................................................................... B-3

Figure 6.27 – Portuguese Backbone Network (PBN) [30] .................................................................... B-5

Figure 6.28 - Links of the PRT nodes (adjacency matrix) .................................................................... B-7

Figure 6.29 - Distances (km) between PRT nodes .............................................................................. B-8

xiv

List of Tables

Table 2.1 – SC optical transmission formats - OPS default values [3] ................................................. 23

Table 3.1 - Client rate distribution per traffic profile [20]. ...................................................................... 29

Table 3.2 – Main demand ordering policies applied during the simulation process. ............................ 32

Table 3.3 - Routing criteria (search for the best path) of OPS – Phase I. ID1 refers to the original

routing criteria implemented by (Santos, et al, 2015) [20]. ID2, ID3 and ID4 were developed during the

present investigation .............................................................................................................................. 36

Table 3.4 - Routing criteria (search for the best path) introduced during present investigation at OPS –

Phase II.................................................................................................................................................. 36

Table 3.5 – Input parameters for OPS - initial settings that were manually introduced (manual

configuration panel). .............................................................................................................................. 43

Table 3.6 – Relevant input data considered to perform simulation process [20] .................................. 45

Table 4.1 – Summary of important data relative to studied networks ................................................... 46

Table 4.2 - Format of the obtained results (example) ........................................................................... 47

Table 4.3 – Mean values of TBT (Gbps) and TRC obtained at uniform model for different networks and

demand orderings .................................................................................................................................. 49

Table 4.4 - Sequences of demand orderings for TBT and TRC results (from best to worst) ................ 49

Table 4.5 - Ratio between mean values and the minimum value for each demand ordering for different

networks at uniform model .................................................................................................................... 49

Table 4.6 - Summary of important data relative to studied networks and results obtained for TBT

(Gbps) for both models (uniform and gravitational) considering all demand orderings and routing

algorithms per each model. Population values based in values indicated in Appendix C. ................... 50

Table 4.7 Results obtained for the gravitational model – mean values of TBT (Gbps) and TRC for

different demand orderings.................................................................................................................... 50

Table 4.8 - Sequences of demand orderings for TBT and TRC results (from best to worst) ................ 50

Table 4.9 - Ratio between mean values and the minimum value for each demand ordering for different

networks at gravitational model ............................................................................................................. 50

xv

Table 4.10 - Mean values of TBT (Gbps) and TRC for different routing criteria (and five demand

orderings)............................................................................................................................................... 52

Table 4.11 – Ratio between mean values at different combination at the minimum value for different

networks at uniform model. a) TRC results different of zero obtained for PRT network were manually

manipulated; that is, for routing criteria B, 2 and 4, it was considered as the minimum value 1

regenerator (instead of 0) to avoid a division by 0 that would result in infinitive value (∞). .................. 53

Table 4.12 – TBT and TRC RC sequences (from best to worst) .......................................................... 53

Table 4.13 – Mean values of TBT (Gbps) and TRC values obtained at gravitational model for different

routing criteria ........................................................................................................................................ 54

Table 4.14 - Ratio between mean values at different combination at the minimum value for different

networks at gravitational model. ............................................................................................................ 54

Table 4.15 – Sequences by routing criteria, from best to worst results. ............................................... 54

Table 4.16 – Relative comparison of results obtained for TRC values for different routing criteria (and

all studied demand orderings) – uniform model versus gravitational model ......................................... 55

Table 4.17 – Total Blocked Traffic (Gbps) – mean values obtained for different networks and different

modulation scenarios (MS) .................................................................................................................... 55

Table 4.18 – Total Regenerator Count - mean values obtained for different networks and different

modulation scenarios (MS) (averaged all routing criteria and all demand orderings per MS) .............. 56

Table 4.19 – Total Blocked Traffic – demand ordering sequences from best to the worst results for

each type of network, model and modulation scenario (MS). Specific cases analysed also by different

routing criteria (RC). .............................................................................................................................. 57

Table 4.20 - Total Regenerator Counter – demand ordering sequences from best to the worst results

for each type of network, model and modulation scenario (MS). Specific cases analysed also by

different routing criteria (RC). ................................................................................................................ 58

Table 4.21 – Total Blocked Traffic – routing criteria (RC) sequences from best to the worst results for

each type of network, model and modulation scenario (MS) ................................................................ 58

Table 4.22 - Total Regenerator Count – routing criteria (RC) sequences from best to the worst results

for each type of network, model and modulation scenario (MS) ........................................................... 59

Table 6.1 – TBT (µ - mean value of all results under selected criteria) ............................................. A-10

xvi

Table 6.2 – TRC (µ - mean value of all results under selected criteria) ............................................. A-11

Table 6.3 - Distances (km) between COST 239 nodes – modelled (approximated values from Google)

.............................................................................................................................................................. B-1

Table 6.4 - COST 239 topology and links (equivalent to Figure 6.25) (adjacency matrix) .................. B-2

Table 6.5 – Distances (km) between GBN nodes ................................................................................ B-3

Table 6.6 – Links of the GBN nodes (adjacency matrix) ...................................................................... B-4

Table 6.7 - Links (Distances (km)) between PBN nodes – modelled - 26 nodes and 36 links ............ B-6

Table 6.8 – Relevant populational data of COST 239 cities – populational density, urban population

and municipal population (data available at Google) ...........................................................................C-1

Table 6.9 – Results for Expected Traffic, 𝐸𝑖𝑗 (popi*popj /dij2) for COST and considering available data

(approximated values). .........................................................................................................................C-1

Table 6.10 – Results of cumulative expected traffic, 𝑐𝑖𝑗 for COST (cumulative sum, at each table row,

of results obtained in Table 6.9) (approximated values). .....................................................................C-2

Table 6.11 – Results of probability of expected traffic, 𝑝𝑖𝑗 ( (popi*popj /dij2) / 𝑐𝑖𝑗) for COST. ..............C-2

Table 6.12 - Cumulative probability of expected traffic obtained accordingly proposed formulation for

gravity model for the modelled distances, for COST. ...........................................................................C-2

Table 6.13 – Population for gravitational model with PRT network [31] ..............................................C-4

Table 6.14 – Distance (km) between cities used in the gravitational model for the PRT network .......C-5

xvii

List of Symbols

Symbol Definition Unit

(𝑖, 𝑗) Connection / link between node 𝑖and node 𝑗

𝑐𝑖 Cumulative expected traffic for city 𝑖

𝐷 Traffic Matrix (also client traffic demands)

𝑑𝑖𝑗 Distance between the cities 𝑖 and 𝑗 𝑘𝑚

𝐸𝑖𝑗 Expected traffic at each connection or link (𝑖, 𝑗)

𝑃𝑖𝑗 Cumulative expected traffic probability at each connection or link (𝑖, 𝑗)

𝑝𝑖𝑗 Expected traffic probability at each connection or link (𝑖, 𝑗)

𝑝𝑜𝑝𝑖 Population of city 𝑖

𝑝𝑜𝑝𝑖 Population of city 𝑗

𝑥 Traffic at the first year

λ Refers in this case to a lightpath, which is conceptual (see Section 4)

𝑘 Unselected set of vertices

𝑣𝑠 Visited node / vertex

sd Source node

td Target node

rd Bit rate

𝑠 Route node

𝑡 Terminal node

𝑑 Demands (d ∈ D) where each demand is represented by a source

node sd, target node td and bit rate rd

𝐺 Graph that represents network topology; 𝐺 = (𝑉, 𝐸)

𝑉 Set of nodes / vertices of the graph G (remaining vertices 𝑣 𝜖 𝑉 and

𝑉 = 𝑣1, 𝑣2, … , 𝑣𝑛)

𝐸 Set of links / edges of the graph G, where 𝐸 = (𝑒1, 𝑒2, … 𝑒𝑛)

𝐵𝐼𝑁 New Bandwidth Demands (the same as 𝐷)

xix

List of Abbreviations

A/D Add / Drop

ADM Add / Drop Multiplexer

AON All-Optical Network

AS Available Spectrum

ASK Amplitude Shift Keying Modulation

ATM Asynchronous Mapping Procedure

AWG Arrayed Waveguide Grating

AWGN Additive White Gaussian Noise

BBR Bandwidth Blocking Ratio

BPSK Binary Phase Shift Keying

BVT Bandwidth Variable Transponders

CapEx Capital Expenditures

DWDM Dense Wavelength-Division Multiplexing

CapEx Capital Expenditures

CD Chromatic Dispersion

C/D Colorless and Directionless

C/D/C Colorless, Directionless and Contentionless

CORONET Core Optical Network of United States of America (USA)

CohD RX Coherent Detector Receiver

COST European Optical Network

CP-QPSK Coherent Polarization-Multiplexed Quadrature Phase Shift Keying

CR Churn Ratio

CWDM Coarse Wavelength-Division Multiplexing

DC Dual Carrier

DO Demand Ordering

DP Dual Polarization

DSP Digital Signal Processing

DWDM Dense Wave Division Multiplexing

EDFA Erbium Doped Fiber Amplifier

E/O/E Electrical-Optical-Electrical (or Electrical to Optical and again to Electrical

domain conversion)

EOL End of Life

EON Elastic Optical Network

FAR Fixed Alternate Routing

FEC Forward Error Correction

FF First-Fit

xx

FIN Finland Backbone Network

FOADM Fixed Optical Add Drop Multiplexer

FR Fixed Path Routing

FSK Frequency-shift Keying

Gbaud Giga symbols per seconds

GbE Giga bit Ethernet

GBN German Backbone Network

Gbps (or Gb/s) Giga bit per second

GFP Generic Framing Procedure (ITU-T Rec. G.7041)

HO-ODU High-order Optical Channel Data Unit

ILP Integer Linear Programming

IP Internet Protocol

IP/MPLS Internet Protocol / Multi Protocol Label Switching

ITU International Telecommunication Union

ITU-T International Telecommunication Union – Telecommunication Sector

LASER Light Amplification by Stimulated Emission of Radiation

LB Legacy Bandwidth

LO Local Oscillator

LO-ODU Low-order Optical Channel Data Unit

LRF Largest Client Rate First

LSPS Longest Shortest Path First

MATLAB MATrix LABoratory

MCM Multi-Carrier Modulation

MCS Multicast Switches

MLM Multi-Level Modulation Format

MPLS Multi-Protocol Label Switching

MS Modulation Scenarios

NE Network Element

NTWK Network

OA Optical Amplifier

OADM Optical Add/Drop Multiplexer

OCh Optical Channel (with full functionality)

OD Optical Demultiplexer

ODU Optical Channel Data Unit

ODUflex Flexible Optical Data Unit

ODUk Optical Data Unit-k

OFDM Orthogonal Frequency-Division Multiplexing

OFTS Optical Fibre Telecommunication Systems

OM Optical Multiplexer

OMS Optical Multiplex Section

xxi

ONE Optical Network Element

O/E/O Optical-Electrical-Optical (or Optical to Electrical and again to Optical domain

conversion)

OOK On/Off Keying (modulation)

OP Orthogonal Polarization

OpEx Operational Expenditures

OPS Optical Planner Software

OPU Optical Channel Payload Unit

OSNR Optical Signal-to-Noise-Ratio

OTH Optical Transport Hierarchy

OTM Optical Terminal Multiplexer

OTN Optical Transport Network

OTS Optical Transmission Section

OTU Optical Channel Transport Unit

OXC Optical Cross-Connect

PDM Polarization Division Multiplexing

PM Polarization Multiplexing

PM-QPSK Polarization Multiplexed Quadrature Phase Shift Keying

PRT Portuguese Backbone Network

PSK Phased-shift Keying

QAM Quadrature Amplitude Modulation

QPSK Quadrature Phase Shift Keying (modulation)

RC Routing Criteria

ROADM Reconfigurable Optical Add/Drop Multiplexer

RSA Routing and Spectrum Assignment

RWA Routing and Wavelength Assignment

SA Spectrum Assignment

SBVT Sliceable Bandwidth Variable Transponders

SC Super-channel

SDH Synchronous Digital Hierarchy

SMF Single-Mode Optical Fiber

SONET Synchronous Optical Network

SSSP Single Source Shortest Path

Tbps (also Tb/s) Tera bit per second

TBT Total Blocked Traffic

TDM Time Division Multiplexing

TRC Total Regenerator Count

VOA Variable Optical Amplifier

WA Wavelength Assignment

WB Wave Blockers

xxii

WDM Wavelength Division Multiplexing

WSS Wavelength Selective Switch

3R Reshaping, Retiming and Regeneration. Refers to regenerators.

1

1. Introduction

1.1. Motivation

In an exponentially growing traffic environment that characterizes the first decades of the 21st

century, the telecommunication operators of Optical Transport Networks (OTN) are pushed to provide

innovative technological solutions, compliant with dynamic client’s traffic demands. Every year the limits

of the provided capacities are surpassed, being OTN nowadays able to deal with enormous amounts of

information and work in a challenging environment.

An OTN is a fundamental component of the telecommunication networks that supports a wide variety

of different client signals, like IP/MPLS1, Ethernet, SDH/SONET2 and other protocols. Typically, OTN is

a long-distance telecommunication transport network where the communication is performed at

transparent3 optical domain through optical fibres and it is supported by Dense Wave Division

Multiplexing (DWDM) technology (multichannel system). Thus, OTN is a digital wrapper technology,

defined by an Optical Transport Hierarchy (OTH), performed under ITU-T4 normalization (G.709, G.872,

G.959), and destined to provide high capability channels.

Total network capacity enabled by traditional optical technology is typically upper-bounded to 96

channels of 100 Gbps [1] per each optical fiber, where each channel occupies a fixed spacing of 50

GHz, which is called a fixed-grid solution. It is foreseen that fixed-grid based optical networks will not

have the capability to sustain the exponential traffic growth [2] [3] [4]. To obviate this limitation, ITU-T

G.694.1 has redefined the frequency grid enabling the capability of supporting a variety of fixed and

flexible (or flexi-grid) channel spacings, ranging from 12.5 GHz up to 100 GHz [1]. This innovation

allowed Super-channels, technique that combines multiple optical signals into a single spectral window,

to have variable and adjustable dimensions and to improve the spectral efficiency and reduce the

penalties caused by filtering in the traversed nodes.

Independently of using Super-channels and flexi-grid, higher transmission capabilities typically result

in the additional accumulation of impairments from the optical fiber that, in turn, limit the maximum

distance that is possible to be achieved without complete signal regeneration, thus requiring higher

number of optical interfaces. Hence, and considering that the Super-channels can be tuned to different

configurations (number of optical carriers, bit rate per carrier, spectrum occupied), it should be possible

to efficiently manage the relationship between the capacity of the established connections and the

respective regeneration usage. Flexi-grid and Super-channels are two examples of disruptive

techniques that are being introduced in OTN with the purpose of, in a short time, increase the

1 IP/MPLS – Internet Protocol / Multiprotocol Label Switching 2 SDH/SONET - Synchronous Digital Hierarchy / Synchronous optical networking 3 Transparent networks are those that operate entirely at the optical domain. Opaque and semi-transparent networks operate entirely or partially at the electrical domain, requiring optical to electric conversions (e.g. SDH/SONET). 4 ITU-T – International Telecommunication Union – Telecommunication Standardization Sector

2

transmission capacity over optical fiber. Specifically, it is foreseen that the maximum channel capacity

will increase up to 400 Gbps and beyond at single wavelength [5].

Considering this engineering problematic, there is a need to make readjustments to the processes

followed in Optical Transport Network planning. To promote the best practices, it becomes important to

analyse the impact of different factors in the usage of the available network resources for a large set of

scenarios. The start point of the network planning generally consists in the analysis of the physical

network topology and the characterization of the traffic model. Generally, networks have measuring

points at the nodes that allow to determine precisely the traffic at each node / point and, subsequently,

to perform statistical modelling of the obtained data. In static scenarios, the traffic compilation for all

possible pairs of sources and destinations, and for a certain period, results in a traffic matrix (in dynamic

scenarios, it is not feasible to perform this type of analysis due to data unpredictability). Then, there are

evaluated different strategies concerning routing, wavelength assignment and traffic grooming, among

other specific aspects (such as static or dynamic traffic, etc.). Finally, planning also depends on the time

horizon and the amount of resources that are available to be allocated at each period along the life cycle

of the network.

In this context, routing is an optimization process, based on some specific criteria, that calculates the

best feasible paths (set of links)5, that will be crossed by lightpaths, aiming such way to solve all traffic

requests that exists in a studied network. In the other hand, traffic is the amount of data that is being

exchanges through the network at a given period. This traffic is wrapped (or encapsulated) and is

groomed accordingly established by OTN standardization, providing high bandwidth efficiency. Each

demand (or request) is a source-destination pair that will be transmitted through the network accordingly

some established algorithms. Wavelength assignment consists on the assignment of the wavelength to

each lightpath in the network.

Present investigation is focused specifically in evaluating three factors: traffic distribution, demand

ordering algorithms, and demand routing algorithms. Whereas the first factor defines how the nodes

exchanging demands are selected, the second one stipulates the order by which those demands are

served, and the third one specifies the criteria employed to determine the optical path for each of those

demands. Uniform and gravitational traffic distribution models will be used to compare how the limited

network resources are consumed when the demands are more or less geographically concentrated.

Different ways to define the sequence by which demands are ordered are investigated to determine if

any a-priori knowledge of the network is useful to increase the number of satisfied demands. A similar

approach will be used regarding the routing strategies. The scenarios investigated are characterized by

different properties, such as 1) network topology; 2) spectral grid format; 3) types of available Super-

channels; 4) client traffic rates. The planning algorithms can be characterized by the 1) demand ordering

algorithms; 2) and routing and spectrum assignment algorithms. To evaluate network performance, both

blocked demands and installed regenerators will be used as measurable results. The former

measurement is useful to identify how much of the offered load was eventually satisfied by the planning

5 The compilation of best feasible paths results in routing matrix.

3

procedures employed, whereas the latter quantifies how much additional cost (in regenerators) will this

performance be dependent on. It is important to underline that both Capital Expenditures (CapEx) and

Operational Expenditures (OpEx) represent the decisive factors when building telecommunication

networks. In this context, satisfied demands and required regenerators can be somewhat viewed as

OpEx and CapEx figures.

1.2. Objectives and Contributions

The main purpose of this thesis is to study the influence of different traffic ordering algorithms, traffic

distributions, and routing criteria in the planning of flexible optical transport networks with Super-

channels. The performance of the planning process is evaluated in terms of blocked traffic and total

amount of installed regenerators over different network topologies. The new functionalities are directly

implemented and evaluated on an existing software framework, here named Optical Planner Software,

previously developed and authored by Coriant.

To achieve the abovementioned objectives, there were implemented new methods being this way

the main contributions in the scope of this thesis:

Three demand ordering algorithms based on link congestion;

Six demand routing algorithms based on the combination of different criteria, which include

spectral occupation and number of feasible lightpaths;

Demand distribution based on a gravitational model.

It was performed analysis of the collected results obtained via extensive computer simulations, with

systematization of conclusions about how they may influence the design of OTN networks.

1.3. Thesis Outline

This thesis is structured into five main chapters.

The first phase consists in the introduction and framework of the work (Chapter 1). It also referrers

to the state of the art of the related scientific literature that is relevant to contextualize the subject matter

(Chapter 2). Thus, it consists in performing a description of existent flexi-grid optical transport networks

(OTN) and of the new technologies of data optical transmission supported at multi-level modulations.

The second phase of the investigation, more operational one, corresponds to the third Chapter and

describes the Optical Planner Software developed by Coriant, related concepts, and the introduced

modifications. Furthermore, it is also targeted an analysis of different routing strategies, namely: 1) static

and semi-static traffic routing; 2) demand ordering; 3) client traffic generation. The developed algorithms

were applied to different network topologies and refer to 1) alternative demand ordering methodologies;

2) different traffic generation at the network (uniform and gravitational); 3) and different demand routing

strategies.

The third and final phase of the investigation discusses the obtained results from the developed

algorithms and identifies more suitable algorithms for a more practical and efficient exploration of the

4

available resources (Chapter 4). It also states the final conclusions and there are made some

considerations about the future work (Chapter 5).

5

2. Overview of Optical Transport Networks

Optical Transport Network (OTN) describe a set of technologies that can be used to build optical

networks. As illustrated in Figure 2.1, in the area D marked by dashed line, OTN is composed by

electrical and optical (photonic) layers. Optical Network Elements (ONE) are elementary blocks that

constitute the OTN, connected by optical fibre links, and are able to provide transport, multiplexing,

routing, management, supervision, and survivability of optical channels, in order to manage OTN client

signals that are originated at services layer (Recommendation G.872 ITU-T). Thus, OTN provides an

independent client specific aspects transport, i.e., the client layer suffers an interlayer adaptation (or

encapsulation) to be compatible with the optical channel layer. This property allows to manage the client

signal itself as a “black box” and only consider specific aspects at optical channel layer.

Figure 2.1 – OTN network – switching at lambda and sub-lambda level [6]

Figure 2.1 shows an OTN-based network that supports packet and Time Division Multiplexing (TDM)

clients. Optical Channel Data Unit (ODU) containers, at the transport layer, perform lambda level

networking where further grooming is not required, whereas Low-order ODUs (LO-ODUs) allow

additional grooming for better rates and higher efficiency. In its turn, multiple LO-ODUs containers form

a higher rate High-order ODU (HO-ODU) containers, at transport layer. Thus, there are performed both

photonic and electronic switching, that complement each other and increase the network efficiency since

optical signals that surpass network nodes are switches at the wavelength level (lambda level), when

the granularity of the transported signal is close to wavelength capacity, and when there is a termination,

the composed signal can be entirely or partially switched at the electronic level (or at sub-lambda level).

These modular network element architectures allow to support client’s mixed services and specific traffic

6

distribution, providing the required flexibility with different configurations and grooming options at

different levels.

OTN provide support for optical networking using Wavelength Division Multiplexing (WDM). Thus,

WDM is a technology that allows to put data (or a number of optical carrier signals) from different sources

into the same optical fiber, allowing the creation of multi-channel systems. Multiplexing is an especially

used technique since it is more economical to transmit data at higher rates over a single fiber versus

transmit data at lower rates over a single fiber. WDM is performed by using different wavelengths of

laser6 light and allows to achieve higher ranges and capacities at the network without laying more fiber.

WDM systems permits users to preserve their own backbone networks since WDM optical multiplexers

(OM), optical demultiplexers (OD) and optical amplifiers (OA) are capable to perform the interface with

external or/and public OTN. Thus, the capacity of the link can be increased only by upgrading the OM

and OD at each terminal/end of the line, which is very attractive as a technological solution.

Dense WDM (DWDM) systems7 are used in more demanding networks, where there are required

higher capacities, since they are able to provide large number of wavelengths and allow long

transmission distances (up to 1200-3500 km), being used for a long-range data transmission. In the

other hand, DWDM systems are relatively expensive and complex (if compared to WDM).

Present investigation is centred only at physical layer8 characteristics and specifically at the optical

frequency plan, contextualized at DWDM frequency grid (centred at 193.1 THz) and formulated

according specifications defined at ITU-T G.694.1 [1].

2.1. OTN Systems

2.1.1. OTN Hierarchy

OTN flexibility allowed to perform development of innovative solutions, without the need of disruption

with already implemented solutions. Thus, OTN is capable to integrate and converge, into the same

transport network, different networking protocols and traffic that is originated at the services layer

(SONET/SDH, Video, 10 GbE, etc.). Client’s data is encapsulated and sent in fixed frame sizes, allowing

to transport both synchronous and asynchronous services (Figure 2.2) [7]. OTN also allows an

existence of lines, typically designated transponders, with a capacity of 100 Gbps lines or more.

6 LASER - Light Amplification by Stimulated Emission of Radiation

7 There are three types of WDM systems: normal WDM (WDM), coarse WDM (CWDM) and dense WDM (DWDM). However, only DWDM is relevant at OTN, since there are some limitations associated to WDM and CDWM systems in terms of range, spacing of the wavelengths, number of channels, and the ability to amplify the multiplexed signals in the optical space.

8 According ITU-T G.871 there are different aspects concerning to OTN systems and technology, related with development, study and normalization processes, such as architectural aspects, structures and mapping, equipment functional characteristics, management aspects, physical layer characteristics and general aspects. All these aspects contribute to achieve integrated, organized, and interoperable outcomes from different entities that concur at the telecommunication fields.

7

Figure 2.3 represents the OTN hierarchy defined by G.709. Optical Transport Module structure is

transported through optical line interface and it is divided in electrical and optical layers (Figure 2.3).

Figure 2.2 - Different services supported over the same wavelength by OTN [7].

Figure 2.3 – OTN Hierarchy – Optical Transport Module [6].

At the electrical (or digital) layer, the Optical Channel Payload Unit (OPU) contains the payload

frames (client data) that are encapsulated / wrapped using the Generic Framing Procedures (GFP)9.

The Optical Channel Data Unit (ODU) is the basic payload that is electronically groomed and switched

within OTN network with a specific overhead with several information (optical path-level monitoring,

alarms, etc.). Optical Channel Transport Unit (OTU) overhead adds bytes to provide optical section layer

Path Monitorization, among other information and represents a physical interface or port, such as an

OTU2 (10 Gbps), OTU3 (40 Gbps) and OTU4 (100 Gbps). Here, it is also added the Forward Error

Correction (FEC) that allows the system tolerate lower Optical Signal-to-Noise-Ratio (OSNR), thereby

reducing the number of required regenerators and the cost of the network.

Grooming of client’s data, performed at the electrical layer, is referenced by Optical Multiplexing

Hierarchy and it is showed at Figure 2.4, where each container (ODU0, ODU1, ODU2, etc.) is optimized

9 GFP is “used to adapt diverse packet protocols at the link layer to be transported and […] facilitates interoperability of equipment of different vendors” [36].

8

for different client’s signals. Low Order ODU (LO-ODU) encapsulation refers to a direct encapsulation

of the client’s signal, whereas High Order ODU (HO-ODU) encapsulation refers to the encapsulation of

the low order containers. For example, 1000BASE-X client can be encapsulated into one ODU0 (low

order ODU). In its turn, eight containers ODU0 may be encapsulated into one ODU2 (high order ODU)10.

Figure 2.4 - OTN Mapping Hierarchy and new flex OTN Hierarchy in detail according ITU-T the Rec. G.709. Changes are signalized with red color [8].

OTU is then mapped to a wavelength at the optical (or analog) layer. The optical line that transports

the client’s signal constitutes the Optical Channel (OCh) (Figure 2.3 and Figure 2.5). As illustrated at

Figure 2.5, Optical Multiplex Section (OMS) lays between two devices with multiplexing and

demultiplexing functions that are connected by a fiber. Within OMS, there can exist one or several

Optical Transmission Sections (OTS), connecting two devices, Optical Network Elements (ONE) [7]. At

this layer there is also exist different overheads, to provide management, supervision, fail detection, and

other functions. However, the overheads of the optical layer are transported at a physically separated

channel, the Optical Supervisory Channel. The OTN interfaces are defined at ITU-T G.709 standard.

The mapping of OPUk, ODUk and OTUk is performed under previously defined bit rates and capabilities.

At the optical layer, the Optical Transport Module interfaces are defined in a more complex way and will

not be described here since they are not the scope of this work11.

10 Detailed relationship between different multiplexing and mapping structures can be accessed at ITU-T Recommendation [75].

11 For further information see ITU-T G.709 standard [75].

9

Figure 2.5 - OTN Network Layers [9].

2.1.2. Optical Network Equipment

Optical equipment is necessary to implement OTN DWDM solutions. Some of the main key blocks

that are directly related with the present investigation are described very briefly in the following

paragraphs. The key blocks that integrate the electrical layer are the regenerator and the ODU switch.

Relatively to the optical layer, there will be described optical amplifier (OA), Wavelength Selective Switch

(WSS), reconfigurable optical add/drop multiplexer (ROADM) and optical terminal multiplexer (OTM).

There are other optical elements like optical couplers, optical splitters and combiners, filters, attenuators,

isolators, transmitters, etc. that will not be described in the present report, since they do not constitute

the main scope of the present investigation.

Optical amplifiers (OA) are devices that provides direct in-line amplification of optical signals, without

the need of conversion to an electrical domain, independently of data rate, and are implemented in OTN

networks in lengthy links (hundreds of kilometres) (Figure 2.6). The gain is relatively flat (due to

implementation of Variable OA (VOA) so that they can be cascaded for long distance use. Nowadays,

in-line OA are typically installed at every 80-120 km and they are generally composed by two EDFA

(and other secondary components), as showed in figure below. In case of usage of two different bands

(C and L), they are separated before the in-line optical amplifier and different EDFA are used for each

band. The supervision channel is used to control the performance of optical amplifiers, and it is

transported separately from the traffic wavelengths.

Figure 2.6 – OA is an ideal device to enhance the range of DWDM system [10].

10

Regenerators are typically used in long-distance communication systems, in order to deal with

transmission impairments that are not eliminated by OA (see Figure 2.5). Therefore, periodic

regeneration is usually required to regenerate/restore the original waveform and perform the

synchronization of the signals. Regenerator first converts the optical signal to electrical domain, then

supress the noise (3R functions12) and in the end converts again the “clean” signal to the optical domain,

delivering it to the network. In WDM systems, each wavelength requires its own opto-electric amplifier,

which verifies to be very expensive since there are many wavelengths to process simultaneously and

due to high cost of the equipment. Thus, in project design of OTN systems, the number of regenerators

is one of the key factors to be minimized (CapEx) [11].

In opposition to regenerators and OA, that maintain the signal at the OTN scope (see Figure 2.1),

optical transponder units perform operations between OTN and the Services Layer. Thus, they perform

O/E/O conversions, mapping, multiplexing and grooming operations. Optical transponder units are

elementary blocks that generally integrate bigger structures like OTM, Optical Add/Drop Multiplexer

(OADM) and ROADM. They support full C and are designed to interoperate with any open DWDM line

systems at ITU-T grid. There are two types of OTU: transponders (one input and one output, Figure 2.7)

and muxponders (one output port and multiple input ports). OTN switching is a more flexible, but also

more expensive solution, if compared to transponders and muxponders. It enables any client to be

mapped to any line interface (multiple inputs and multiple outputs). This solution is driven essentially by

the necessity of grooming (aggregation) of lower speed client signals onto high-speed line interfaces,

increasing such way the efficiency of the bandwidth’s management.

Figure 2.7 - Transponder block diagram [12].

Another key element is the WSS that dynamically route, block and attenuate all DWDM wavelengths

within a network node where each DWDM wavelength input from the common port can be independently

switched (routed) to any one of the N multi-wavelength ports (1:N or N:1, i.e., multiplexing or

demultiplexing functions). This process can be performed dynamically through remote control and it is

possible to perform attenuation and equalization operations at the channels. WSS and OA, among

others, are elementary blocks that integrate OADM/ROADM’s, explained further13.

12 3R functions are reshaping (equalises and amplifies), retiming (generates the clock signal from the received signal and uses it to sample the signal) and regeneration (decides and line codes).

13 The most common building blocks that are used to implement ROADMs are WSS, 1xN and MxN All-Optical Switches (OXC), NxM Multicast Switches (MCS), optical amplifiers, fixed and tunable filters, wave blockers (WB), AWG Multiplexers and optical splitters / couplers [6] [12].

11

Figure 2.8 – WSS is a 1 x N optical commutation device and allows to switch one or several channels between input and output ports [12].

OADM is a device that is used in DWDM systems for multiplexing and routing different optical

channels into or out of a SMF. An OADM may be considered as a specific type of Optical Cross-Connect

(OXC) where the node degree is two and it is the key component of All-Optical Networks (AON).

Typically, an OADM consists of three parts: an optical demultiplexer (OD), an optical multiplexer (OM)

and a method of reconfiguring the paths between OD, OM, and a set of ports for adding and dropping

signals. In the figure below, the optical switch allows to add/drop specific wavelengths. The signal(s)

can be selectively downloaded, uploaded or simply passed through the OADM without the need of O/E

or E/O conversions, independently of data rate and data protocol, being in this way an effective mean

for data transmission. Since it is also associated to reductions of network equipment, it leads to an

improvement at the system capacity and in the reduction of overall system cost.

Figure 2.9 - OADM unit using optical switches and wavelength multiplexers [13].

In the other hand, ROADM has wavelength switching that allows a dynamic wavelength

management, meaning that optical channel can be flexibly added/dropped by network operator under

software control through the switching function built into transport node (see Figure 2.10). The concept

of degree in ROADM means that network is mesh-like and each node behaves as a junction point,

where a wavelength can reach any adjacent node through the switching function, as long as

transmission distance is not an issue. Each degree represents a direction in which the node connects

to another node.

12

Figure 2.10 – ROADM – Express and add/drop switching [6].

ROADMs evaluated to be colorless, directionless and contentionless (C/D/C): colorless means that

wavelength can be set under software control and is not fixed by physical add/drop port on the ROADM;

directionless means that wavelength can be added or dropped from any direction (under software

control); and contentionless means that multiple copies of the same wavelength are allowed on a single

add/drop structure; the control plane allows implementation of automatized controls using software

control plane. Thus, at ROADMs the service can be assigned its color and direction without any

restrictions as long as the wavelength color is available at the network level for that direction. In the

basic ROADM design, the reconfigurability is limited to routing the wavelength and the add/drop

structure is fixed. The colored add/drop limitation is not due to transmitters or receivers, but it is caused

by the add/drop structure (wavelength splitter).

Figure 2.11 - C/D/C ROADM – different configurations [14].

OTM terminates the optical paths within optical networks (terminates and demultiplexes

wavelengths) and adapts client’s signals originated at Services Layer, to the format required for

transmission within the Transport Layer, aiming the generation of a good quality signal at the output.

OTM multiplex discrete optical carriers over a single fiber and accepts both synchronous (SONET) and

asynchronous transmission formats. It can be deployed in a point-to-point, ring, or mesh architectures.

An OTM have an optical interface, may or not have an electrical interface, and includes transmitter,

receiver, and a duplex interface to the client network. OTM is generally constituted by transponders

(wavelength’s conversion to ITU standard), by a multiplexer (combination of wavelengths) and by an

OA (power amplification). An OTM with dynamic wavelength assignment (e.g. tuneable source) is useful

in a network with a dynamic traffic load. This type of OTM can be reconfigured/retuned to new

13

wavelengths that reach different destinations. New traffic demands can then be met in a flexible manner

so that a better utilization of existing network resources is obtained.

Figure 2.12 - OTM constitution: transponder, multiplexer and power amplifier [12].

2.2. Multi-level Modulations and Coherent Detection/ Reception

Systems

The need to increase the fiber capacity originated technological investigation and development in six

main key fields: 1) increase of the fiber core area; 2) increase of the number of fiber cores; 3) increase

of the repeater bandwidth (e.g. flexi-grid); 4) introduction of next-generation FEC’s; 5) impairments

compensation (chromatic dispersion, polarization-mode dispersion, self-phase modulation, cross-phase

modulation, laser phase noise, etc.); 6) and increase of spectral efficiency ( [15]. Studies related to the

increase of the spectral efficiency produced better practical results if compared to other investigation

fields. Presently the technological solutions are already being implemented, despite it is not yet a

completely developed technology. This topic will be briefly described hereafter since it is important for

the present investigation. The demand for increased fiber capacities, higher performance, reach

increase and cheaper cost of bit-transport at long-haul fiber (>1,000 km), associated to available

technological solutions, lead to the development of coherent systems.

2.2.1. Encode More Bits per Symbol

The traditional and the simplest modulation method of optical data is the On/Off Keying (OOK), which

is the cheapest solution. OOK is the simplest form of ASK14 modulation, where the amplitude of the

optical data is codified in two values accordingly to the transmitter symbol (high power level and low

power level). At OOK/ASK modulation the symbol rate (e.g. 10 Gbaud) is equal to the bit rate (e.g. 10

14 ASK - Amplitude Shift Keying Modulation; the most affected by the noise interference.

14

Gbit15). Since current opto-electronic technologies are limited to 64 Gbaud, which is not enough to

transmit modern data rates16, it requires more bits per symbol, leading to the employment of multi-level

modulation formats.

Figure 2.13 – QPSK is a four-level modulation format since symbols can take 4 different values (e.g.: 0,1,2,3). With a symbol rate of e.g. 2.5 Gbaud it is obtained a bit rate of 5 Gbps [16].

The fundamental digital modulation methods are phased-shift keying (PSK), frequency-shift keying

(FSK)17, amplitude shift-keying (ASK) and quadrature amplitude modulation (QAM)18. In all these

methods and its variants, each symbol is assigned to a unique binary pattern and a correspondent

number of binary bits19, being generally represented by constellation diagrams. Despite the existence

of a diversity of modulation formats, the most common modulations used at long-haul optical

transmission systems are PSK and QAM, with some variants (quadrature phase-shift keying (QPSK),

8-QAM, 16-QAM, etc.). QPSK (or 4-PSK) is a four-level modulation format, where symbols can take 4

different values and 2 bits are encoded at each symbol, as it is illustrated Figure 2.13. For example, if

compared to 2-PSK (or binary PSK, BPSK and functionally equivalent to 2-QAM), with spectral efficiency

of 1 bit/second/Hz) and QPSK (functionally equivalent to 4-QAM), with spectral efficiency of 2

bit/second/Hz, 16-QAM allows higher spectral efficiencies (send more bits per second) whereas the

occupied bandwidth remains the same, allowing spectral efficiency of 4 bits/second/Hz [16]. For the

same number of signal levels (M), M-QAM have higher spectral efficiency if compared to M-PSK, with

a counterpart that it is associated to lower signal to noise ratio.

15 Gbaud - giga symbols per seconds.

16 Modern systems generically are characterized by 2.5,10, 40 Gbps wavelength channels and 100 Gbps, 400 Gbps and beyond next generation channels.

17 FSK requires higher bandwidth (two times ASK bandwidth), and it is more sensitive to transmission interferences, which is not suitable at optical systems solutions.

18 QAM is in fact a combination of PSK and ASK techniques.

19 Channel capacity (C) is related with bandwidth (B) through Nyquist definition C = 2B log2 M , where M = 2N is the number of discrete signal levels and N is number of bits. For binary signals (only two levels), C=2B. This equation can be related to Shannon Bound for AWGN non-fading channel (or Shannon limit for information capacity), where

C = Blog2(1 +S

N) [51].

15

2.2.2. Transmit More Symbols per Second

It is possible to increase even more the spectral efficiency20 and the bit rate of the system through

implementation of additional modulation formats over the already implemented QPSK/QAM modulation

formats using the polarization division multiplexing (PDM)21 and dual-carrier modulation. At PDM, light

beams are left and right circularly polarized while being transmitted through the optical fiber. Dual-carrier

modulation is a specific case of multi-carrier modulation (MCM) and consists in transmitting data by

dividing it into several bit streams with a lower bit rate, generally closed spaced, and that will modulate

individual carriers, having several advantages such as resilience to interference, resilience to narrow

band fading and multipath effects. OFDM22 is an example of MCM that uses closely spaced carriers,

orthogonally separated, avoiding such way interferences between them (selective fading, interference,

inter-symbol and inter-frame interference, etc.).

Figure 2.14 - Example: two input signals (previously modulated by QPSK/QAM) are first modulated by PDM (or PM) and then combined by the dual-carrier modulation [16].

As an example, 16-level Quadrature Amplitude Modulation (16-QAM) format encodes four bits in one

of the 16 symbols. If compared to BPSK format, and considering 32 Gbaud electronics (symbol rate),

16-QAM quadruples the number of bits per second achieving 128 Gbit/s (100 Gbit/s of effective carrier).

However, if it is considered PM-16QAM format, a multilevel modulation, with double number of bits per

second (256 Gbit/s), it is possible to achieve an effective carrier rate of 200 Gbit/s. Further, it is possible

to achieve a 400G channel rate by multiplexing two 200G carriers in the wavelength domain forming

Dual-Carrier (DC) 400G channel (DC-PM-16QAM). Note that the spacing between these two carriers

may be adjusted allowing an increase of spectral efficiency (Figure 2.14). However, it is important to

refer that it is not feasible to expect very high modulation schemes, since the additional techniques will

lose gradually its spectral efficiency, since they require higher signal to noise ratios. For higher order

modulations, such as PM-QPSK or PM-16QAM, the spectral efficiency is higher (4 bit/s/Hz and 8

20 In WDM systems the spectral efficiency is calculated by dividing data rate of a single channel by the channel bandwidth. So, for example, a 100G Polarization-Multiplexed Binary Phase Shift Keying (PM-BPSK) signal fixed at within 100 GHz grid will have its spectral efficiency of 1 bit/s/Hz.

21 PDM is also denoted as polarization multiplexing (PM), dual polarization (DP) or orthogonal polarization (OP).

22 OFDM - Orthogonal Frequency-Division Multiplexing

16

bit/s/Hz), however, the amount of optical power (if considering non-linear penalties) is lower for each bit

within modulated symbol.

2.2.3. Coherent Detection

There are two main types of detectors: direct and coherent detectors. In the direct detection, the

incoming signal is detected directly with the photodiode (O/E conversion) and only amplitude of the

signal can be obtained. In the coherent detection the signal is mixed with local oscillator (LO) beam,

tuned to ITU-T grid, before being detected by the photodiode, preserving such way both the amplitude

and the phase of the signal. Then, LO is used by coherent detector (CohD RX) to extract from the

interference signal the information contained in the phase, amplitude and polarization of the optical

signal and convert it into electrical domain by a bank of photodiodes (Figure 2.15). T Already in the

electric domain, Digital Receiver compensates waveform distortion due to chromatic dispersion and

optical nonlinear effects in the optical fibers. It also performs adaptive equalization, demodulation (signal

mapping) and error correction decoding (symbol estimation and FEC). Clock recovery and retiming

operations and low-pass filtering are also integrated in DSP.

Figure 2.15 – Digital Coherent Receiver - generic scheme [17].

Presently, coherent optical communications are primarily oriented to the digital signal processing

(DSP) and compensation of phase perturbations in optical systems with phase modulation [17].

Coherent detection combined with DSP has better performance and reach advantages over direct

methods such as greater wavelength selectivity, increased sensitivity in the reception stage, greater

distances in optical links and higher spectral efficiency, among other benefits like electronic dispersion

compensation at the receiver end and higher rates. It is possible to see at Figure 2.16 that higher spectral

efficiencies and higher capacity channels (PM-16QAM), that uses higher number of symbols, are

obtained at the expense of the maximum reach, that decreases inversely. In the other hand, modulation

schemes like PM-BPSK have higher reach.

17

Figure 2.16 – Example of Cisco ® NCS 4000 400 Gbps WDM/OTN/Packet Universal Line Card – relation between chart capability (Tbps) Spectral Efficiency (bit/s/Hz) and maximum reach (Lmax) for different modulation schemes (ITU-T G.652 SMF – solid lines; ITU-T G.655 LEAF fiber – dashed lines) [18]

2.3. Elastic Optical Transport Networks

As explained in previous paragraphs, the increasing demand for traffic at OTN (and at higher bit

rates), required the implementation of innovative solutions. One of the innovations is related with a more

efficient management of the spectrum [6]. This idea is described briefly in the following paragraphs.

Different migration strategies were being proposed to perform a non-disruptive transition to flexi-grid

networks, however, as referred in introduction chapter, present investigation will focus only a specific

subject of this transition, as it will be explained further in Chapter 3.

2.3.1. Flexi-grid Standard (ITU-T G.694.1)

The optical spectrum that is used for transmission in optical fibers rely at region between 1.3 and 1.6

μm, that comprises C band that presents lower losses and is generally exploited for very long

transmissions. The C band is centred at 1552.52 nm frequency and comprises tabled frequencies

between approximately 1525 nm and 15265 nm (accordingly recommendation ITU-T G.694.1). DWDM

technology that is used to perform the transmission of several signal carriers (at different wavelengths)

onto a single fiber is capable to use a fixed 50 GHz grid spacing in optical frequency (also called fixed

grid), which allows to transmit 87 channels23. Higher bit rates that are available at optoelectronic devices

allow to increase the channel capacity up to 100 Gbps per wavelength, which correspond, at fixed grid,

to a 2 bit/s/Hz spectral efficiency [6].

23 Note that C band has a 4380 GHz bandwidth, obtaining this way 87 channels. However, recent developments allow to implement 96 channels [6].

https://www.cisco.com/c/dam/en/us/products/collateral/optical-networking/network-convergence-system-4000-series/datasheet-c78-736495.docx/_jcr_content/renditions/datasheet-c78-736495_3.jpg

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Due to increase of traffic at OTN, it is foreseen that in near future the optical spectrum will be a scarce

resource. New signal transmission techniques were being developed, supported by coherent detection

techniques, resulting in a reduction of occupied spectrum by optical signals and implementation of 33

GHz channels capable to transmit 100 Gb/s. Higher transmission bit rates, such as 200 Gb/s, are

possible if higher modulation formats, such as QAM (16-QAM, etc.), are implemented. However, as

explained in Sections 2.2.2 and 2.2.3, these modulation formats are characterized by lower transmission

distances. One way to avoid this limitation is to use multi-carrier signals with the same or higher symbol

rate than 100 Gb/s signal to obtain higher rate channels (400 Gb/s and 1 Tb/s, as illustrated in Figure

2.17). In the other hand, these higher capacity channels require larger channel spacing, breaking the

standard 50 GHz grid per channel policy (400 Gb/s requires 75 GHz channel spacing and 1 Tb/s requires

175 GHz channel spacing, as exemplified in Figure 2.17).

Figure 2.17 – Example of multi-carrier 400 Gbps and 1 Tb/s channels implementation [6].

Thus, it became necessary to implement a new grid that would allow to accommodate channels with

higher spectrum requirements and with higher spectral efficiencies and, simultaneously, with more

dynamic spectrum allocation policies. The implementation, by ITU-T, of the flexible frequency grid (flexi-

grid), that represents a finer grid associated to a variable frequency slot allocation of optical connections

was possible partially due to the development of new-generation transponders with new modulation

schemes, enabling adjustable and flexible (or elastic) management of the spectrum. Figure 2.18

illustrates the impact of flexi-grid if compared to fixed-grid. For the same spectrum occupation, flexi-grid

can support 8x200 Gb/s channels (more two if compared to fixed-grid), that are narrower positioned,

and allows to group channels to obtain higher capacity channels (super-channels), that may be carried

as single entities through the OTN. In the other hand, the implementation of smaller granularities of 12.5

GHz, allowed to implement more precise dimensioning of the channels slots, with 12.5 GHz, 37.5 GHz

and 50 GHz spacings, resulting, consequently, in a more efficient and adjusted to real necessities

channels24.

24 Capacity gains of 30-100% are obtained in simulations for flexi-grid networks [47].

19

Figure 2.18 – Flexi-grid with 12.5 GHz granularity has higher efficiency of the spectrum management, allowing to transmit more channels at the same fiber and has additional capability to implement 400 Gbps and 1 Tbps Super-channels by grouping several channels in a flexible way [6].

Elastic Optical Networks (EON) and associated elastic structure brings the “fitted for the need”

concept, where the traffic management can be made through an allocation of frequency slots that are

effectively needed (“elastic allocation”), instead of being limited to predefined traffic channels. In this

concept, several number of contiguous frequency slots can be assigned through the route, being

characterized by some specific spectrum width and effective filter bandwidth and not by fixed boundaries

(as in fixed-grid WDM). In the other hand, higher order modulations and multi-carrier signals permit to

obtain higher rate channels, if compared to fixed-grid. The main advantages of flexi-grid, if compared to

fixed grid, are a better spectral efficiency, possibility to implement advanced modulation schemes and

capacity to perform dynamic adjustments at both traffics (“sub-wavelength” and “super-wavelength”)

[19]. Finally, the introduction of flexibility in the grid allows mixed bit rates or mixed modulation formats,

optimizing this way the bandwidth management.

Relatively to the optical layer of the OTN, ITU-T G.694.1 has defined the frequency grid to support a

variety of fixed and flexible channel spacings, from 12.5 GHz up to 100 GHz (and wider) [1]. According

ITU-T G.694.1, at the fixed grid, and for the channel spacing of 12.5 GHz, the allowed channel

frequencies are defined by expression (1) (where n is a positive or negative integer including 0)25:

𝟏𝟗𝟑. 𝟏 + 𝒏 × 𝟎. 𝟎𝟏𝟐𝟓 (1)

At flexible grid, the allowed channel frequencies are defined by the expression (2) (where n is a

positive or negative integer including 0 and 0.00625 is the nominal central frequency granularity in THz;

m is a positive integer and 12.5 is the slot width granularity in GHz). Different combinations are allowed

restrained to frequency overlaps that shall not occur [1]. Figure 2.19 and Figure 2.20 illustrates the

associated idea of gridless concept.

25 The DWDM fixed grid for higher channel spacings (25 GHz, 50 GHz, 100 GHz and integer multiples of 100 GHz) are defined at by ITU-T G. 694.1 Standard.

20

𝟏𝟗𝟑. 𝟏 + 𝒏 × 𝟎. 𝟎𝟎𝟔𝟐𝟓 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑠𝑙𝑜𝑡 𝑤𝑖𝑑𝑡ℎ 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑏𝑦 𝟏𝟐. 𝟓 × 𝒎 (2)

Figure 2.19 - An example of the use of the flexible grid [1].

Figure 2.20 – Partitioning of the fiber spectrum: a) fixed grid spacing of 50 GHz; b) fixed grid spacing of 37.5 GHz; c) Mixed channel spacing based on overlapping of 37.5 GHz and 50 GHz grids; d) gridless partitioning [20].

As it is possible to observe at Figure 2.19 and Figure 2.20, the partitioning of the fiber spectrum at

fixed grid is performed by the allocation of fixed slots (50 GHz or 37.5 GHz, as applicable), while the

mixed channel spacing is based on overlapping of 37.5 GHz and 50 GHz grids. As illustrated by the

example of Figure 2.20, both fixed and mixed grid partitioning are less efficient than the gridless

partitioning of the spectrum. Note that the flexible (or elastic) management of the spectrum is possible

in all cases, since it depends of the modulation formats that are feasible to implement. However, the

elasticity fits better at grids with smaller granularities.

Relatively to the electronic layer, and at the OTN hierarchy level, there was a need to adapt the

mapping process. It was implemented in 2009 the new standardization by ITU-T the Rec. G.709 as it is

illustrated in the Figure 2.4. The changes are illustrated with red color. There were considered new low

order and high order mapping packages (ODU0, ODUflex, ODU2e, ODU4 and OTU4). Thus, lower order

ODU became capable to map any non-OTN signals that afterwards are mapped at high order to OTN

signals. The ODU0, ODU2e and ODU4 were added to allow additional flexibility, whereas ODUflex is

capable to map any bit rate client flow (dissociating this way the physical network from the client type

signal).

During the present investigation it was only considered a gridless scenario in the demand routing

process, i.e., there were considered 50 GHz, 37.5 GHz, and 50 / 37.5 GHz grid partitions simultaneously.

This option was motivated by the results obtained by investigation developed by (Santos, 2015, page

B128, Figure 10), that shows that the consequences of using gridless approach when deploying the

21

Super-channel services, and independently of the legacy bandwidth values, are almost negligible (slight

increase of 1.3% in favour of fixed-grid and 1.5% in favour of gridless). As explained by Santos, this

important result means that predefined frequency grids could be an adequate solution to support Super-

channel signals without incurring in heavy performance penalties, which is particularly important if the

applied transmission formats are based on mixed (37.5/50 GHz) grids, which are harder to manage.

2.3.2. Super-channels (SC)

A third complementary technique to the multi-level modulation and coherent technologies is the

implementation of Super-channels (SC). At transport level, SC allow to aggregate or groom different

client’s signals with different bit rates in the same lightpath (or bigger “pipe”), enabling this way EONs

and support to next-generation high-speed services. Note that grooming operation is performed at

electronic layer (or Grooming Layer), as it was described at 2.1.1. paragraph (see Figure 2.4), where

client’s signals are mapped successively to Low Order ODU (ODU0, ODU1, ODUflex, etc.), then to High

Order ODU, to OTU, and finally they are converted to an optical signal.

Thus, SC is a combined signal with desired capacity provisioned for specific operational cycle that

packs multiple optical signals into a single spectral window with variable and adjustable dimension to

improve the spectral efficiency and/or reduce the penalties caused by ROADMs (Figure 2.21) [3]. As

illustrated at Figure 2.21, there are different SC implementation options, like the implementation of single

carrier SC, dual-carrier SC and multi-carrier SC. For the same bandwidth (in this example, 462.5 GHz,

which corresponds to 384 Gbaud electronics26), the higher is the number of the carriers, the higher is

the number of required modulators and lasers. Single carrier channel is the simplest solution to

implement, however it does not allow, due to inbuilt hardware/electronic limitations, flexibility to allocate

smaller granularity bandwidths that are required at flexi-grid. In the other hand, the multi-carrier SC, that

in the example of Figure 2.21 is composed by twelve 100G waves, in spite of requiring higher number

of components (twelve times the number of lasers and modulators), if compared to a single carrier

option, allows to operate at required speeds and provides greater flexibility, since individual waves may

be joint in different combinations, and modulation formats can be assigned on a wave-by-wave basis.

SC technology is supported by sliceable bandwidth variable transponders (SBVT) that allow several

optical interfaces that may be configured and operated separately or jointly. However, SBVT are still a

matter of study and are not a completely matured technology.

26 Presently, 320 Gbaud is only a theoretical value considering electronics industry roadmaps. The current

electronics is in the order of 32-64 Gbaud.

22

Figure 2.21 – SC implementation options – it can be constituted by several channels aggregated together. From left to the wright: single carrier SC, dual-carrier SC, and multi-carrier [21].

Grooming operations, and the subsequent implementation of SC, allow to increase the efficiency of

the bandwidth usage (reach, O/E conversions, power consumption and cost) since they reduce the

unused spectrum, scale bandwidth, without operation procedures’ escalation and optimize DWDM

capability and reach27 [6]. Finally, implementation of SC allows to integrate legacy services already

circulating at the fixed grid networks.

During present investigation there were considered different optical transmission format structures

for SC that were used by (Santos, 2014) [3] in previous evaluation of OPS based investigation

associated to analysis of Spectrally-Efficient Super-channel Formats in Brownfield Networks with

Legacy Services accordingly table below, where it was considered 12.5 GHz granularity to obtain the

total occupied spectrum of the client signals. It is relevant to observe that, Table 2.1 reflects the

relationship that exists between different modulation formats and the maximum reach as it was

illustrated previously at Figure 2.16, that is, modulations with higher efficiency of the spectrum (e.g. 16-

QAM vs CP-QPSK28) are associated to lower maximum reach. It is also possible to observe that for the

same modulation format, higher occupied spectrum (and grid) of different SC is associated respectively

to higher maximum reach, which is related with lower efficiency of higher grid formats (e.g. 50 GHz vs

37.5 GHz).

27 It is interesting to find that a single 1 Tbps carriers (not yet developed) have higher fiber impairments if compared to multi-carrier solution (SC).

28 CP-QPSK - Coherent Polarization-Multiplexed Quadrature Phase Shift Keying.

http://www.upgrademag.com/web/wp-content/uploads/2015/01/Figure2.jpg

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Client (Gbps)

Modulation Optical Carriers Grid

(GHz) Spectrum (GHz) Max Reach (km)

100 CP-QPSK 1 50 50 2500

100 CP-QPSK 1 37.5 37.5 2000

200 CP-QPSK 2 50 100 3000

200 CP-QPSK 2 37.5 75 2400

200 16-QAM 1 50 50 600

200 16-QAM 1 37.5 37.5 500

300 CP-QPSK 3 50 150 3100

300 CP-QPSK 3 37.5 112.5 2500

300 8-QAM 2 50 100 1200

300 8-QAM 2 37.5 75 1000

400 CP-QPSK 4 50 200 3200

400 CP-QPSK 4 37.5 150 1600

400 16-QAM 2 50 100 750

400 16-QAM 2 37.5 75 625

Table 2.1 – SC optical transmission formats - OPS default values [3]

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3. Optical Transport Network Planning

Planning of optical transport networks (OTN) is required before the actual implementation of the final

solution and aims the identification of the best possible solution among different possible scenarios and

existent options, reducing this way CapEx and OpEx costs at long term. The migration of OTN from

fixed-grid to flexi-grid (and, consequently, EON) brought several concerns that were already being

investigated over several years. There are generally preferred non-disruptive solutions, which allow the

integration of legacy services. Present investigation is focused on a specific topic of this migration

process, physically associated to optical layer (transport layer) and concerns about the way different

routing algorithms, demand ordering and demand routing strategies may affect the efficiency of the

delivery of the traffic. This study is subject to specific traffic distributions and network models.

3.1. Routing in Optical Networks

A routing strategy refers to computation mechanism of the routes from source node to destination

node, where the network topology can be represented by a graph 𝐺 = (𝑉, 𝐸), where 𝑉 represents a set

of nodes and 𝐸 the set of links that connect them. It is important to refer that in context of OTN, nodes

are materialized by in Network Elements such as ROADM and OTM (and another equivalent NE), as

described at Chapter 2. In the optical transparent and translucent networks, routing is a key control and

operational feature at the optical layer. It is directly related to the path selection and wavelength

assignment process, which is generally designated Routing and Wavelength Assignment (RWA) or

Routing and Spectrum Assignment (RSA). The RWA/RSA problem refers to process of designating

lightpaths to connect the source node to the destination node and assigning it wavelengths/spectrum

slots and it is typically formulated in two separate steps: routing and wavelength/spectrum assignment

(however, there are different approaches). Generally, the problem consists in minimizing the set of

lightpaths while maximizing the number of established connections and consequently minimize the

blocked connections. In addition to the amount of lightpaths (which materialize into a given number of

O/E/O interfaces), there is also the need to consider some specific blocking ratio, i.e., the percentage

of the traffic that will not be routed through the network. Here, traffic can be represented by a traffic

matrix 𝐷 containing several demands (𝑑 𝜖 𝐷), where each demand is represented by a source node 𝑠𝑑,

target node 𝑡𝑑 and bit rate 𝑟𝑑 (or data transmitted by the demands which correspond to OTN signals).

Traffic blocking can occur due to several reasons, but it is mostly impacted by the limited link capacity

and the wavelength/spectrum continuity constraint.

In optical fiber DWDM networks, each lightpath represents an optical signal, transmitted at a specific

wavelength/spectrum, carrying information across the network. Since the lightpath is only converted to

the electrical domain at its boundary points, it is constrained to wavelength/spectrum-continuity over the

links used (as illustrated in Figure 3.1). This constraint imposes that two different optical signals that are

routed through common paths (even partially) cannot be assigned the same wavelength (frequency). In

elastic optical networks, the routing problem is also related with spectrum assignment, i.e., Routing and

Spectrum Assignment (RSA), since in flexible grid the channels are designated according the required

25

and available spectrum. In fact, RWA is a subcase of RSA. Whereas the latter requires selecting a set

of contiguous frequency slots of 12.5 GHz, the former is limited to selecting only one slot corresponding

to a fixed 50 GHz occupation.

The RWA/RSA problem has been widely studied and its theoretical formulation was made in several

investigation works; thus, theoretical formulation (e.g. using Integer Linear Programming, ILP) will not

be analysed and it is considered out of the scope of the present investigation. As detailed during this

chapter, the routing algorithm (RSA) studied in the present investigation consists of three steps, for a

given network topology and traffic profile, and with the final purpose of maximizing the efficiency of the

whole routing process: 1) demand ordering taking into account the generated client traffic and the

network topology (3.4 and 3.5); 2) demand routing, i.e., select the most favourable path(s) accordingly

specified criteria for the traffic requests (3.6); 3) wavelength assignment to the calculated routes (3.7).

Figure 3.1 - A wavelength-routed optical WDM network with lightpath connections [22].

The routing is responsible for mapping the logical topology over the physical one. The main purpose

of the routing algorithms is to find, for some specific physical topology represented by graph 𝐺 = (𝑉, 𝐸)

and for some specific traffic matrix 𝐷, a set of paths that satisfy the requests and simultaneously

determine the capacity of all links/connections of the network. There are several calculation

criteria/metrics that allow to reach the destination nodes, as for example: 1) minimize the cost of the

network (and of the associates links); 2) minimize the traffic associated to the most loaded link; 3)

minimize the number of hops associated to regenerators (3R) when the paths/links are calculated; 4)

minimize the distance of the paths; 5) maximize the capability of the protection of the links, among other

criteria. The generality of the routing strategies includes an algorithm that calculates the shortest paths

in order to determine the path that lead to lower result associated some specific metric.

3.1.1. Routing Algorithms (Dijkstra and Yen)

Dijkstra algorithm is a greedy algorithm to solve a single source shortest path (SSSP) problem that

computes the shortest path, length, cost or other measuring unit, from the source 𝑠𝑑 (𝑠𝑑 𝜖 𝑉) to the

remaining vertices 𝑣 (𝑣 𝜖 𝑉) (or nodes) of some studied directioned (or unidirectioned) graph 𝐺 = (𝑉, 𝐸),

where 𝑉 is the number of vertices (𝑉 = 𝑣1, 𝑣2, … , 𝑣𝑛) and 𝐸 are the associated edges (𝐸 = (𝑒1, 𝑒2, … 𝑒𝑛),

26

where each edge, 𝑒 𝜖 𝐸, has associated a non-negative weight cost (weighted graph). (It is also

considered that at all vertices are connected to the remaining ones by at least one path). Generally, the

main metrics (or criteria) used to define the shortest path are either distance or processing time;

however, other metrics may be used. In present investigation it was used the distance criteria (i.e. the

search was performed for the shortest feasible distance). This algorithm starts at node 𝑣𝑠 (the first visited

vertex / node) and selects, from an unselected set of vertices 𝑘, the 𝑣 vertex that has the lower

distance/cost/etc. relatively to 𝑣𝑠, that may be reached only via the already visited nodes, and which is

declared to be the shortest one relatively to 𝑣𝑠. Then, 𝑣 is checked and added to the list of processed /

selected nodes and the process repeats until all vertices are processed and added to the list of the

visited nodes. Thus, the output of the algorithm is a set (series) of lengths, in a form of a tree (i.e. a

graph with only one path between every two nodes), of shortest paths (or minimum total lengths) from

a given source vertex 𝑣𝑠 (𝑣 𝜖 𝑉) to all other vertices 𝑣. The algorithm, however, can be stopped once the

shortest path to the destination vertex (or node) has been found [23].

Figure 3.2 – Spanning tree after the application of Dijkstra algorithm at different vertices of the graph [24]

Yen algorithm have the main purpose to order and calculate the shortest (loopless) k-paths between

two nodes (with positive costs) and its k-1 derivations. Thus, Yen algorithm computes first the single-

source k-shortest path between a pair of non-negative weighted edges (nodes) of some graph G, using

any shortest path algorithm to find the shortest path (k-path). Then, Yen algorithm computes k-1

deviations (or spurs) of the best path. Or in other words, Yen algorithm identifies first the shortest path

between a pair of nodes and then explores subsequent k derivations of the shortest path.

Yen algorithm constructs a tree built from the k-shortest paths, where the initial node is the route and

the leaves are the k copies that lead up to the terminal node. All paths between the route and the end

node are unique and correspond to the k shortest paths. Thus, Yen algorithm calculates successively

the k-1 shortest paths, until all the paths are identified, performing following operations:

1. The path between the route (s) until the node v of the tree (it may occur that s=v), being

possible that the path from s to v may be or not common to the found shortest-path.

https://www.google.pt/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjJxefZmOneAhXGyYUKHRegACkQjRx6BAgBEAU&url=https://cis.temple.edu/~giorgio/cis307/readings/graph.html&psig=AOvVaw0g5Ve0umdFNz0nborg_pz7&ust=1543017064813031

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2. The shortest path from v until the terminal node, t, provided that it does not use the previously

found paths. This way, the algorithm identifies all possible derivation at v.

3.2. Static, Semi-static and Dynamic Routing

Static routing (or non-dynamic routing) of the demands generally refers to routing that is performed

considering a stationary scenario, not affected by operational flows that may affect real circumstances

and may be considered as multicommodity flow problem where due to high complexity of the problem

originated by different variables and constraints, the solution is generally obtained by non-linear

approach. Static routing applies to permanent or long-term connections or to planning of future networks,

where paths need to be previously designated and are generally considered immutable during all

simulation process. Therefore, in static model, the purpose is generally to minimize some pre-defined

cost parameters like the number of wavelengths (or spectrum) or networks resources (like regenerators,

transmitters, transponders/muxponders, number of fibers and the number of other types of related

interfaces, like ROADM, etc.). In alternative, the purpose may be the establishment of a maximum

number of connection requests (input traffic) considering network (with pre-defined topology) as being

limited to a maximum capacity of number of wavelengths per fiber, which is the problem that is

investigated in the present work. For example, it was concluded by Sengezer & Karasan (2010) [25] that

the initial demand sorting (by shortest demands first vs longest demands first) affects the percentage of

the successfully routed demands, concluding that de longest demand first distribution achieves lower

blocking demand ratio.

In static routing, there are generally applied route-finding techniques like Dijkstra algorithm (shortest

cost path) or other metrics. However, static routing is unable to employ new paths in case of failure of

some of the link along the chosen path. There are two routing algorithms: fixed path routing (FR)

algorithm and fixed alternate routing (FAR) algorithm. Whereas the first one calculates only the best

feasible path (best solution of Dijkstra algorithm, i.e., the shortest path first), the second one, proposes

several feasible routes, sorted from the best to worse solution, that will be assigned (or tried) sequentially

in case of unavailability of the best solution. In this last case, Yen algorithm is implemented instead of

Dijkstra and the connections are only blocked if all paths fail.

In semi-static routing, it is considered that traffic is incremental, i.e., the establishment of the

lightpaths is made sequentially and cumulatively, accordingly the arrival of the requests for connection,

and indefinitely since they will remain until the end of the simulation process or considered period. Semi-

static routing can be viewed as a sequence of several static routing periods, where the occupied capacity

is always cumulative. When the demands are grouped in specific time intervals, the semi-static

scenarios are also known as multi-period.

In opposite, dynamic routing refers to dynamically managed network, where the paths are calculated

during the operation of the network or the network simulation. Networks’ topology changes and dynamic

traffic model are calculated over the time to allow the simulation of establishment or extinction of links

and arrival and departure of demands (or calls), i.e., connections (lightpaths) that may be released after

some finite amount of time. Dynamic routing is especially suitable for complex topologies, it is

28

independent of network size and allows automatic construction of routing tables along time. However, it

is more difficult to implement (e.g. higher computational complexity), it is less secure, and it requires

additional resources. Thus, it is more suitable to random and unpredictable traffic patterns.

Since the main emphasis of the present investigation was to analyse the influence of the demand

ordering/routing and traffic distribution at the behaviour of the network, a static scenario was considered.

It was considered a high average input traffic of 130 Tbps and no exit bandwidth (i.e., the connections

are cumulatively occupied without no release of any capacity) since the purpose was to obtain the

maximum outflow of the traffic, by analysing the total blocked traffic and total regenerator count, i.e., the

number of regenerators that were needed to implement the studied combination.

3.3. Multi-period Planning

The implementation of optical networks is generally made along some defined horizon (e.g. 10 years

forecast) mainly driven by the high investment costs and operational restraints. Therefore, multi-period

planning is a comprehensive approach to the routing strategy, that allows to understand in advance the

impact of the selection of some specific demanding policies at the performance of the network29.

Generally, it is considered a progressive increasing of the traffic30, and the modifications are made in a

gradual and a cost-effective way. Thus, new demands may be virtually generated each year (added to

the network), but also some demands may be dropped (or subtracted). Churn ratio (CR) defines the

ratio between the added and the dropped demands (bandwidth).

The Optical Planner Software that was used in the present investigation is prepared to consider the

incremental traffic (CR=0) [20] where the optimum solution is calculated progressively for each period,

allowing to understand the associated network costs, and/or blocking probabilities. However, at the

present investigation, multiperiod planning was not considered since it is essentially focused on an end-

of-life (EOL) planning. In addition, and because there is no grooming or reuse of equipment, evaluation

of the demand and routing algorithms does not benefit from multi-period planning.

3.4. Client Traffic Generation

In a real network operation and considering the transport (optical) layer of optical transport networks

as it was referred at Chapter 2, the client traffic is a random process, despite being characterized by

average values along time. However, in simulation process, it is important to consider different traffic

profiles to understand its implications in the performance on the networks.

29 For example, flexi-grid network efficiency (based on SBVT deployment) suggest being more cost-effective (CapEx and OpEx approaches) if compared to fixed-grid solutions, especially for higher annual rates of traffic demand, even at long-haul networks, where the cost offset is not immediately compensated.

30 Greenfield scenario is a specific case, prior to year 1, that considers that there is no previously installed equipment, which is applied, for example, to new entrant operators.

29

Traffic generation model can be developed stochastically. Different simulation tools were developed

to test and evaluate performance of the network, considering realistic behaviours of the network

supported by random generators and statistical distributions [26]. Different distributions can be used

such as Uniform, Gaussian, Poison and Exponential distributions. Other characteristics of the network

traffic distribution may be modelled differently (on-off sources, traffic replay tools, etc.). However, in sake

of simplicity and knowing in advance the characteristics of client traffic profiles of interest, these

distributions were not considered.

In the present investigation, there were considered traffic profiles for client rate distributions

according Table 3.1, implemented by Santos (2015) [20] and it was considered an extensive use of

Super-channels to reach higher bandwidths that characterize EONs. The main considered demands are

100, 200, 300 and 400 Gbps (SC) in different proportions and different bandwidths ratio for different

profiles (A, B, C, D, E, F and G). The A profile represents an evenly distributed traffic, whereas profiles

B, C, D and E, polarizes the traffic to one specific client types. Profiles F and G polarizes the traffic

evenly in two different client rates.

Traffic Profile 100 Gbps 200 Gbps 300 Gbps 400 Gbps

A 25% 25% 25% 25%

B 85% 5% 5% 5%

C 5% 85% 5% 5%

D 5% 5% 85% 5%

E 5% 5% 5% 85%

F 45% 45% 5% 5%

G 5% 5% 45% 45%

Table 3.1 - Client rate distribution per traffic profile [20].

The generation of traffic was performed accordingly two traffic distribution models: uniform and

gravitational model. Whereas the uniform model was previously implemented at initially delivered

version of the OPS, it was necessary to implement the gravitational model algorithm during the present

investigation. It is possible to see further in Section 3.8 that the generation of the traffic is performed in

the OPS before the RSA algorithm and corresponds to the block designated “Generate and route SC

demands” at Figure 3.19.

Uniform model considers an equitable distribution of the traffic along different nodes, i.e., the

probability of some traffic demand being attributed during the simulation process to some specific node

is equitable or uniformly distributed (all nodes have the same probability to generate traffic). Gravitation

model intends to reflect the non-equal distribution of traffic that is verified at some cities’ nodes. For

example, it is intuitively reasonable to consider that city of Paris with its municipal population higher than

2.2 million people generates much more traffic that Copenhagen, that has a 600 thousand municipal

population. The expected traffic (𝐸𝑖𝑗) at each connection / link (𝑖, 𝑗) (link is established from node 𝑖 to

node 𝑗) is calculated accordingly the generic expression of gravitational model accordingly expression

30

(3), where 𝑝𝑜𝑝𝑖 is the population of the city 𝑖, 𝑝𝑜𝑝𝑗 is the population of city 𝑗 and 𝑑𝑖𝑗 is the distance

between the cities 𝑖, 𝑗 [27].

𝐸𝑖𝑗 ~ 𝑝𝑜𝑝𝑖 ∙ 𝑝𝑜𝑝𝑗

𝑑𝑖𝑗2 (3)

In its turn, the cumulative expected traffic (c) for each city 𝑖 may be formulated accordingly the following

expression:

𝑐𝑖 = ∑ 𝐸𝑖𝑗𝑛𝑗=1 (4)

The expected traffic probability (𝑝𝑖𝑗) at each connection / link (𝑖, 𝑗) is obtained by the following

formulation, where 𝑛 represents the number of nodes that exist in the network:

𝑝𝑖𝑗 =𝐸𝑖𝑗

𝑐𝑖 ~

𝑝𝑜𝑝𝑖∙𝑝𝑜𝑝𝑗

𝑑𝑖𝑗2

∑ 𝐸𝑖𝑗𝑛𝑗=1

(5)

Finally, the cumulative expected traffic probability31 at each city 𝑖 is obtained by the following

formulation:

𝑃𝑖 = ∑ 𝑝𝑖𝑗𝑛𝑗=1 ~ ∑

𝐸𝑖𝑗

𝑐𝑖

𝑛𝑗=1 (6)

As an example, and considering COST network topology, the corresponding distances between the

nodes (Appendix B.1) and the municipal population associated to the nodes (cities) (Appendix C.1), see

tables with different results obtained at Appendix C.1 (approximated values). Note that the values that

are obtained for the cumulative expected traffic, the expected traffic probability and the cumulative

expected traffic probability are not symmetric (because the sums are performed cumulatively ordered

from one node to the next one). Thus, the explained calculations are applicable only in one direction

(from 𝑖 → 𝑗).

Figures 3.3 and 3.4 detail the performed pseudocode that was modified at OPS algorithms/blocks.

Data used to implement COST, PRT and GBN networks with gravitational model is indicated at

Appendices B, C and D.

UNIFORM MODEL

*** Add Input Traffic (extract) ***

nodeij = rand (network dimension) // randomly select the node pairs (integer numbers i and j)

Figure 3.3 – Pseudocode for uniform model – generation of the input traffic

GRAVIATIONAL MODEL

*** Main (extract) - Calculate cumulative traffic for node i,j ***

31 Note that the cumulative distribution function of a real-valued random variable 𝑋 is given by 𝐹𝑋(𝑥) = 𝑃(𝑋 ≤ 𝑥).

31

cumulative expected traffici = 0

for (i =0; i < network dimension; i++)

for (j=0; i < network dimension; i++) & ( j ≠ i )

cumulative expected traffici = cumulative expected traffici

+ (populationi * populationj)/(distancei,j)2

// see equation 5 at Appendix E

for (j=0; i<network dimension; i++) & ( j ≠ i )

cumulative expected traffic probability at connectioni,j =

+ cumulative expected traffic probability at connectioni,j-1

+(populationi * populationj)/ (distancei,j2* total partial probability)

// see equation 7 at Appendix E

*** Add Input Traffic (extract) ***

nodei,j = integer rand (network dimension) // randomly select the node pairs

aux = rand (1) //variable to symbolize the probability to adjust to gravitational model

index=0 //auxiliary variable

// find nodei,j that has cumulative probability equal or higher than cumulative expected traffic

// probability at connectioni,j1

while (index < network dimension)

while (aux < cumulative expected traffic probability at connectioni,j1) & ( index ≠ i )

index++ ;

j=index;

Figure 3.4 – Pseudocode for gravitational model – generation of the input traffic

3.5. Demand Ordering

Demand ordering refers to a process that sorts the traffic demands that will be processed first and

occurs before the RWA/RSA process. This process generally is supported by specific algorithms that

will order the demands based on specific parameters: distance, bit rate, congestion, etc. Therefore, the

demand ordering can be performed through none criteria, i.e., the random process. Since different

methods may be used to implement demand ordering algorithm, with their own

advantages/disadvantages, the outcome may be different, which in its turn will influence the

performance of RWA algorithm and, in the end, the efficiency of the traffic distribution and levels of

blocking ratio.

Present investigation focuses in the influence of the ordering policies in the efficiency of the routing

algorithms and its effect on the maximum exploitation of the available resources (bandwidth) at the

optical network. Thus, it is possible to consider some specific priority-based rules that will influence the

order of the demand processing. The investigation performed by (Santos, et al, 2015) [20], studied the

effects of ordering first the longest path (distance) or largest client data rate, at German Backbone

Network (GBN), Pan-European Sparkle and Telecom Italia (TI) networks. It was concluded that

generally, the longest path first ordering lead to the better results in terms of total load of the network

32

and the final costs. In the present investigation, additional combinations were considered and evaluated

as described in Table 3.2. Highest Client Rate First means that the client demands with the highest data

rate will be ordered before remaining demands (i.e., these demands will have lower index). Largest

Distance orders first the demands associated to the paths with higher distance (km). Most congested

link ordering considers first the demands that are associated to the most occupied links, which involves

pre-routing calculations.

ID Main demand ordering policy Untie policy

0 DO_HRF Highest Client Rate First Longest Distance First

1 DO_LD Longest Distance First Highest Client Rate First

2 DO_MC-R Most Congested Link First Random

3 DO_MC-HRF Most Congested Link First Highest Client Rate First

4 DO_MC-LD Most Congested Link First Largest Distance First

Table 3.2 – Main demand ordering policies applied during the simulation process.

Demand ordering refers to the “order of demands” block of the RSA algorithm (Figure 3.20), as it will

be explained further in Section 3.8, and it is performed before the routing algorithm. The “Highest Client

Rate First + Largest Distance” and “Largest Distance and Highest Client Rate First combinations” have

been already implemented at the OPS planner (see Table 3.2). During the present investigation, there

were developed algorithms for “Most Congested Link First + Random”, “Most Congested Link First +

Highest Rate First” and “Most Congested Link First + Largest Distance First” combinations and the

results analysed. Figures below presents the pseudocode that illustrate the introduced modifications at

OPS.

Demand orderings associated to “Most Congested Link First” policy (ID2, ID3 and ID4) have pre-

routing algorithm (see Figures 3.7, 3.8 and 3.9) that consists in calculation of the occupation level of

links that constitute each analysed path (sum of the occupied slots per each link), where it is considered

the most occupied link. Thus, it will be considered first the demand that is associated to the most

congested path (and associated worst link).

DEMAND ORDERING 0 HIGHEST RATE FIRST + LARGEST DISTANCE

while (demand counter < total demands)

{

best_demand.rate = 0

best_demand.distance = 0

for (index=1; index ≤ all unprocessed demands; index++)

{

if (demand.rateindex ≥ best_demand.rate)

if (demand.rateindex = best_demand.rate) //if there is a tie

if (demand.distanceindex > best_demand.distance)

best_demand = demandindex

else

33


}

demandindex = processed

demand counter++

}

Figure 3.5 – Pseudocode for demand ordering policy Highest Rate First + Largest Distance (ID=0 or DO_HRF)

DEMAND ORDERING 1 LARGEST DISTANCE + HIGHEST RATE FIRST


{

best_demand.rate = 0

best_demand.distance = 0


{

if (demand.distanceindex ≥ best_demand.distance)

if (demand.distanceindex = best_demand.distance) //if there is a tie

if (demand.rateindex > best_demand.rate)


else


}


demand counter++

}

Figure 3.6 - Pseudocode for demand ordering policy Largest Distance + Highest Rate First (ID=1 or DO_LD)

DEMAND ORDERING 2 MOST CONGESTED LINK + RANDOM


{

best_demand = 0

best_link_occupation=0


{

// 1st pre-routing of all demands in the shortest path and

// sum all the occupied slots per each link:

for (i=0; i<number of links; i++) //for shortest path of the demand

if (linkij == occupied)

link_occupationij ++

}

for (all linksi,j)

{

//2nd find the most congested link:

if (link_occupationij > best_link_occupation)


34

best_link_occupation = link_occupationij

}


demand counter++

clean pre-routing

}

Figure 3.7 - Pseudocode for demand ordering policy Most Congested link + Random (ID=2 or DO_MC-R)

DEMAND ORDERING 3 MOST CONGESTED LINK + HIGHEST RATE FIRST


{

best_demand = 0



{






}

for (all linksi,j)

{


if (link_occupationij ≥ best_link_occupation)

if (demand.rateindex > best_demand.rate)



else



}


demand counter++

clean pre-routing

}

Figure 3.8 - Pseudocode for demand ordering policy Most Congested link + Highest Rate First (ID=3 or DO_MC-HRF)

DEMAND ORDERING 4 MOST CONGESTED LINK + LARGEST DISTANCE FIRST


{

best_demand = 0


35


{






}

for (all linksi,j)

{


if (link_occupationij ≥ best_link_occupation)

if (demand.distanceindex > best_demand.distance)



else



}


demand counter++

clean pre-routing

}

Figure 3.9 - Pseudocode for demand ordering policy Most Congested link+Largest Distance (ID=4 or DO_MC-LD)

3.6. Demand Routing

The routing of the demands is based on previously computed k-shortest paths for each node pair

based in Yen algorithm and correspond to block designated “Compute k-shortest paths for each node

pair” of OPS platform as indicated in Figure 3.19 (it uses Dijkstra algorithm to perform the support

calculations). The objective of the implemented Yen algorithm is to minimize the total path distance.

During present investigation there were considered three shortest paths at all performed calculations.

Then, there are computed, for each path and transmission format, the number of regenerators (see

corresponding block at Figure 3.19, Section 3.8).

Thus, demand routing integrates the RSA algorithm of OPS platform as it is illustrated in Figure 3.20

and refers to the “Search for the k-th shortest-path with available spectrum that minimizes regenerator

count / spectrum occupied / interface count” block as it will be explained further in Figure 3.19, Section

3.8. Thus, when the three shortest paths are calculated, there are calculated, for each path, total costs

associated to each identified path, which are the number of regenerators, the number of interfaces and

the total occupied spectrum. The demand routing uses the three shortest paths and selects the one that

minimizes some designated criteria.

36

Essentially, the implemented demand routing algorithm consists in the following steps:1) search for

the best path, i.e., it is identified the one that minimizes some specific criteria, accordingly Tables 3.3

and 3.4 (it is also considered the combination of lightpaths with the same spectrum); 2) if solution is

found, deploy the best path while doing the wavelength assignment; 3) update link occupation (both

directions); 4) if no feasible path found, the demand is blocked. The developed algorithms used to

implement the demand routing criteria are indicated in Table 3.3. Thus, in the first criteria (ID1), the

routing algorithm uses the shortest path that minimizes the number of regenerators (3R) along the path

and in case of tie, uses the path with lower occupied spectrum. Again, if tie occurs, the demand routing

algorithm will select the path that has the lowest cost, that is, the path that has the lower number of

interfaces, which in present investigation corresponds to the number of hops or lightpaths (product of

number of interfaces per modulation and the number of the required regenerators per path). Further

routing criteria (ID2, ID3 and ID4), implemented during present investigation, use the same criteria of

ID1, but implemented with reversed orderings, as detailed in Table 3.3. There were performed

simulations with all types of demand routing criteria, as it will be explained further in Section 3.8.

ID 1st criteria 2nd criteria 3rd criteria

1 lowest 3R lowest spectrum lowest cost (nº of interfaces)

2 lowest spectrum lowest 3R lowest cost (nº of interfaces)

3 lowest 3R lowest cost (nº of interfaces) lowest spectrum

4 lowest spectrum lowest cost (nº of interfaces) lowest 3R

Table 3.3 - Routing criteria (search for the best path) of OPS – Phase I. ID1 refers to the original routing criteria implemented by (Santos, et al, 2015) [20]. ID2, ID3 and ID4 were developed during the present investigation

After initial simulations performed with routing criteria indicated in Table 3.3 (corresponding results

are integrated at final results presented in Chapter 4), it was possible to conclude that criteria ID1 and

criteria ID2 lead, on average, to the lowest values of total blocked traffic (TBT) and total regenerator

count (TRC)32, output metrics of the OPS platform. There were developed complementary criteria to

analyse further the influence of the demand routing criteria by the lower number of regenerators (3R) as

summarized in Table 3.4.

ID 1st criteria 2nd criteria

A lowest 3R maximum spectral availability per lightpath of the path

B lowest 3R maximum average spectral availability per lightpaths of the path

C lowest 3R shortest number of lightpaths at the path

Table 3.4 - Routing criteria (search for the best path) introduced during present investigation at OPS – Phase II

The criteria (A) as indicated in Table 3.4, refers to a routing performed firstly by the lowest number

of regenerators (3R) among the available shortest paths and then, in case of tie, choses the path that

32 Definitions of TBT and TRC are included in Section 3.8

37

has the highest available spectrum per lightpath (which is correlated with wavelength/spectrum

continuity constraint as it was explained in Section 3.1). To explain better this idea, consider the paths

1, 2 and 3 shown in Figure 3.10. Thus, routing criteria A will first calculate the number of regenerators

that exist at different paths, resulting in this case that it is equal to two for all paths, obtaining this way a

tied solution. Next, routing algorithm identifies for each path the minimum available spectrum per

lightpath (in the Figure 3.10 there are considered lightpaths with spectral availabilities of 50 GHz, 100

GHz and 200 GHz). In this case, it is obtained for path 1 the minimum spectral availability per lightpath

of the path of 100 GHz (400 GHz > 200 GHz > 100 GHz), for path 2 - 50 GHz (200 GHz > 50 GHz) and

for path 3 - 100 GHz (200 GHz > 100 GHz). Thus, the maximum available spectrum per path is obtained

for paths 1 and 3 (that correspond to the less congested paths). Since there is a tie, the routing algorithm

will choose the first analysed one, which in this case is the path 1 (first-fit criteria). Note that, and as

described at Chapter 2, 3R node implicitly considers the transition (or conversion of the signal) from

optical to electronic layer of OTN, while at transparent node demands travel only at optical layer. As

referred previously, these nodes are generally implemented by ROADMs or OTM (in case of the source

or destination nodes).

Figure 3.10 – Example of demand routing – three possible paths between nodes 1 and 4 with same number of regenerators (3R).

38

Figure 3.11 – Graph that exemplifies the possible topology of the network that was considered to explain the demand routing algorithms in Table 3.4 and Figure 3-9. The numbers associated to different links refer to the

maximum spectral availability per lightpath.

Criteria B, accordingly Table 3.4, refers to the routing algorithm that uses as untie criteria the path

with the highest average value of the available spectrum. Thus, considering again the example of Figure

3.10, the average value of the available spectrum at path 1 is ~233.3 GHz. For path 2 it will be 100 GHz

and for path 3 it will be ~133.3 GHz. Thus, since there is a tie for the first criteria (lower number of 3R)

between all considered paths, path 1 will be chosen since it has the maximum average available

spectrum (233 GHz > 133 GHz > 100 GHz).

Criteria C, as indicated in Table 3.4, uses as untie criteria the path with lowest number of lightpaths.

Considering the example of Figure 3.10, all paths are constituted by three lightpaths (despite path 1 has

higher number of nodes). Thus, the routing algorithm (OPS platform) will choose the first processed /

identified path (first-fit criteria), which in this case was the path 1.

Figures below illustrate the pseudocode for the implemented algorithms.

DEMAND ROUTING 1 1) lowest 3R; 2) lowest spectrum; 3) lowest cost (nº of interfaces)

{

if (nº 3R at the found path ≤ nº 3R fount for best path-1)

if (nº 3R found path = nº 3R fount for best path-1) // there is a tie

if (spectrum found path ≤ spectrum best path-1)

if (spectrum found path = spectrum best path-1) // there is a tie

if (nº interfaces found path < nº interfaces best path-1)

best path = best path-1

else best path = best path-1


}

Figure 3.12 – Demand routing algorithm 1

DEMAND ROUTING 2 1) lowest spectrum; 2) lowest 3R; 3) lowest cost (nº of interfaces)

{


39




if (nº interfaces found path < nº interfaces best path-1)




}

Figure 3.13 - Demand routing algorithm 2

DEMAND ROUTING 3 1) lowest 3R; 2) lowest cost (nº of interfaces); 3) lowest spectrum;

{



if (nº interfaces found path ≤ nº interfaces best path-1)

if (nº interfaces found path = nº interfaces best path-1)

if (spectrum found path < spectrum best path-1)




}


DEMAND ROUTING 4 1) lowest spectrum; 2) lowest cost (nº of interfaces); 3) lowest 3R;

{



if (nº interfaces found path ≤ nº interfaces best path-1)

if (nº interfaces found path = nº interfaces best path-1)

if (nº 3R at the found path < nº 3R fount for best path-1)




}


DEMAND ROUTING C or 5 1) lowest 3R; 2) maximum spectral availability per lightpath;

{



calculate minimal available spectrum at the available slots of the lightpaths of

the studied path

if (max spectral availability path < max spectral availability best path-1)

40



}

Figure 3.16 - Demand routing algorithm A

DEMAND ROUTING B or 6 1) lowest 3R; 2) maximum mean spectral availability per lightpath;

{


if (nº 3R found path = nº 3R fount for best path-1 ) // there is a tie

1st for the available identified path calculate the number of available slots per

each lightpath and sum the correspondent available spectrum

2nd calculate the mean value (total available spectrum / nº available slots

if mean available spectrum path < mean available spectrum best path-1



}

Figure 3.17 - Demand routing algorithm B

DEMAND ROUTING C or 7 1) lowest 3R; 2) shortest number of lightpaths;

{



calculate the number of the lightpaths for the identified available lightpath

if (nº available lightpaths path < nº available lightpaths best path-1)



}

Figure 3.18 - Demand routing algorithm C

3.7. Wavelength/Spectrum Assignment

As explained in Chapter 2, (D)WDM technology allows to carry several signals at the same fiber, but

at different wavelengths. Therefore, after the lightpaths are routed they must be assigned to a specific

wavelength or spectrum. Note that the performed algorithm during present investigation was Spectrum

Assignment problem. In addition, there is also a need to consider the wavelength continuity constraint,

since generally it is desirable to consider, in a CapEx point of view, scarce conversion resources.

There are different methods to proceed with wavelength/spectrum assignment. The most used are

Random and First-Fit. The Random method determines first which wavelengths/spectrums are available

and chooses randomly one between the possible solutions. The First-Fit method chooses the lower

index of available wavelength/spectrum (in ascending or descending order of lightpath occupation), with

purpose to leave the upper end of the wavelength space / spectrum slot, with longer wavelengths,

41

associated to higher probability to be available [28]. There are several other assignment algorithms that

aim to reduce the overall blocking probability for new connections (Least Used/SPREAD, Least Loaded,

etc. are other examples of RWA). Due to its simplicity and efficiency, in the present study, spectrum

assignment is performed using the First-Fit criteria, as it was implemented by (Santos, 2015) [20].

As additional note, OPS platform supports routing of the legacy services by random and first-fit

methods. However, in present investigation, it was considered the inexistence of the legacy services,

thus this consideration does not influence the performed investigation.

3.8. Optical Planner Software Description

Optical Planner Software (OPS) used to perform all simulations was developed by Coriant®. It was

written in C language and may be operated by software such as Microsoft Visual Studio tool. The

flowchart of the planning tool is illustrated in Figure 3.19 and Figure 3.20 [3] - at the first one it is

illustrated the general flowchart of the OPS framework and at the second one it is illustrated the RSA

algorithm. The general structure of the OPS tool was not modified during present investigation – only

small modifications at the algorithms (blocks) were introduced.

The implemented methods, that lead to modifications in the RSA algorithm, were evaluated

considering (as accordingly it was being described in previous sections): three reference network

topologies, seven client rate distributions, two traffic distributions, three types of frequency grids, five

demand ordering algorithms and seven demand routing algorithms. It was considered a greenfield

scenario, i.e., it was considered an absence of the legacy bandwidth (LB=0) (in opposition to brownfield

scenario). It is possible to simulate this option in a pre-defined input option “maximum legacy bandwidth”

of the OPS platform as indicated in Table 3.5.

There were used two important measuring parameters that correspond to OPS platform outputs and

that have a purpose to measure the performance of the network planning and associated ordering and

routing algorithms, namely the total blocked traffic and the total regenerator count. Total blocked traffic

(TBT) refers to metric that calculates the amount of traffic that was not routed due to filled (overloaded)

network capacity for considered paths, where network capacity refers to the capacity of the three

shortest paths calculated for corresponding demand. Since the input client traffic is equal for all

simulations, there is no need to consider the ratio of blocked traffic as measuring parameter (that

corresponds to the ratio between the total blocked traffic versus the total generated/input traffic). (Note

that total generated traffic is randomly generated for seven client’s profiles and two distribution models

and it has a maximum capacity of 130 Tbps (BIN). The demands that are successfully routed correspond

to the total active traffic and ones that are blocked correspond to total blocked traffic. That is, the sum

of total active traffic and total blocked traffic is a random value, equal or lower than 130 Tbps.)

Total regenerator count (TRC) refers to the required number of regenerators that were employed in

the routing (and assigning) of the fulfilled demands.

42

Figure 3.19 – Flowchart of the OPS tool – general framework [3] [20]

Figure 3.20 – OPS framework - RSA algorithm [3]. General structure was preserved. There were introduced modifications at the algorithms at “Order the demands” and “Search for the k-th shortest-path with available

blocks [3] [20].

43

The initial input parameters of OPS platform and the corresponding values were defined as indicated

in Table 3.5. The analysed networks were COST 239, GBN and PRT, characterized at Appendices B,

C, D, E, F and G (refers to “network name” input of the OPS platform in Table 3.5). Although

implemented heuristics are prepared to be used with networks of any dimensions and characteristics,

these networks were chosen due to their relatively simple structure and relatively low number of nodes

(11 nodes and 52 links for COST 239, 13 nodes and 21 links for GBN and 26 nodes and 36 links for

PRT), which allowed feasible computational simulations time periods (considering the available

hardware). Since it was considered static scenario (as explained in Section 3.2), only one period per

network scenario was simulated. The input “maximum legacy bandwidth” was considered as zero since

as previously explained, it was simulated a greenfield scenario. The average entry load (bandwidth) was

fixed at 130 Tbps in order to evaluate the performance of the algorithms under heavy load conditions.

The average exit load (bandwidth) parameter refers to dropped bandwidth, a set of demands that exit

the network. Since it was only considered a single period and the purpose of the simulation process was

to compare the efficacy of different implemented algorithms the maximum exit bandwidth per period was

fixed in 0 Tbps (That is, it was supposed that all input load was completely distributed). There were also

performed by OPS platform some pre-defined initializations, such as optical transmission format

structures for SC (as previously explained in Section 2.3.2 in Table 2.1).

Parameter name Input values Parameter name Input

values

Network name COST/GBN/PRT Maximum legacy bandwidth (in Tbps) 0

Maximum number of candidate paths

3 Average entry bandwidth per period (in Tbps)

130

Number of periods per network scenario

1 Average exit bandwidth per period (in Tbps)

0

Number of trials per network scenarios

50

Table 3.5 – Input parameters for OPS - initial settings that were manually introduced (manual configuration panel).

There were performed some initial trials considering different “number of trials per network scenarios”

(e.g. 10, 20, 30, etc.). After comparison of different results, it was decided to fix the variable at 50 trials

since the corresponding results showed to be statistically steady (i.e., for the same input values at OPS,

the output was statistically very similar). There were not considered higher values due to inacceptable

correspondent computational processing time (higher than 2 hours). It is also important to refer that

each trial by itself correspond to a mean value of 50 cycles/trials.

Thus, after input network topology processing (COST, GBN or PRT), which corresponds to “Read

Network Topology” block as illustrated in Figure 3.19, OPS tool calculates, based in Yen algorithm, the

k-shortest paths for all node pairs associated to the network with the purpose of minimizing the total

path distance, considering a maximum of 3 paths (k=3) (Yen algorithm explained in Section 3.1.1). Next

follows the computation of the minimum number of regenerators (3R) required per each path (previously

calculated k-paths) and each modulation format, considering the maximum reach of the client signals

as shown in Table 2.1 (incrementing regenerator count associated to each path and for different

44

modulation formats). Paths whose individual links surpass the maximum reach of the client signals are

considered unfeasible and there are calculated alternative paths [20]. In addition, possible lightpaths

per path are calculated accordingly illustrated in Figure 3.21. The lightpaths 1 and 2 are not constrained

to same wavelength / spectrum (do not have to be at the same frequency). However, the lightpath 1 that

go through three nodes (123 and 34) is subject to wavelength/spectrum constraint. Client traffic

demands (D or, as referred by (Santos,2015) [20], New Bandwidth Demands, BIN) are randomly

generated with discrete distributions of traffic patterns/profiles indicated in Table 3.1 and node pairs are

randomly selected accordingly it was selected uniform or gravitational model (as explained in Section

3.4). During this computational process, it is also calculated the number of hops / interfaces for each

path and each modulation format. Thus, path exemplified at figure 3.21 have two hops (nodes 2 and 3)

between the source node (1) and the destination node (4), but only one regenerator (at node 3).

Figure 3.21 – Path segmentation in several lightpaths accordingly the modulation format maximum reach. Node 3 integrates a regenerator (3R).

Then, RSA algorithm performs the ordering and routing of the created demands (as described

previously in Sections 3.5 and 3.6) and spectrum assignment (Section 3.7), selecting this way, for each

demand, the transmission format and respective path. It is important to refer that each transmission

format (i.e. the optical carriers belonging to a given SC signal) are carried over one single path being

treated as a single entity in the network. Thus, some of implemented transmission formats (Table 2.1)

may be or not available for selection depending on the adopted frequency grid. The path assignment

and selection is only performed if among calculated shortest paths there exist available spectrum for a

given modulation format and it manages to minimize the selected (at some specific cycle) routing criteria

(as defined in Table 3.3 and Table 3.4). Then, first-fit policy is used to assign the demands to the free

spectrum slots in each lightpath, starting from the lowest free indexes. If the demand is blocked, i.e., it

was not found path with available spectrum resources for the specific demand, TBT will be updated. If

the demand is successfully assigned, TRC count will be updated accordingly the characteristics of the

assigned path. This closes the cycle and the demand is assigned as treated and RSA moves to the next

request [20].

In the final phase, OPS platform generate several .txt format files with the results of different identified

scenarios accordingly the following combinations: type of network (COST, PRT and GBN), type of

modulation, traffic distribution (seven different combinations as explained in Section 3.4 in Table 3.1)

and demand order (as explained in Section 3.5 in Table 3.2). It was developed an auxiliary software in

MATLAB to automatize the processing and compilation of the produced information and generation of

graphics that are presented in the results chapter (Appendix A:).

45

Other relevant parameters considered are indicated in Table 3.6 (the same as assumed by (Santos,

2015) [20]). The per-hop reach penalty was not considered since it is out of the scope of present

investigation and because it was used a simplified model for the estimation of the performance of the

algorithms.

Designation of the variable Value Description

Per-hop reach penalty 0 m Distance penalty due to node traversing33

Slot 12.5 GHz Spectrum slot in the fibre

Slot count 384 Number of frequency slots (12.5GHz) in the total fibre spectrum

Fibre spectrum 4800 GHz Total spectrum available for transmission in a fibre

Large slot 50 GHz Largest slot size for an optical signal

Small slot 37.5 GHz Smallest slot size for an optical signal

Speed of light 200000000 Speed of light in the optical fibre

Fibre reach 1000 km Fibre maximum reach

OMS link 4.8 THz Available spectrum at each OMS link (equivalent to 96 wavelengths of 50 GHz)

Table 3.6 – Relevant input data considered to perform simulation process [20]

33 It was assumed that when trespassing a node, the signal doesn’t suffer any distortion.

46

4. Results and Discussion

The results are obtained after extensive simulation of the OPS framework in three different network

topologies, namely COST, GBN and PRT, as specified in Appendices B, C, D, E, F and G (Section 3.8

clarifies the reason behind the selection of these networks). Some of the details about these networks

are listed in Table 4.1. Detailed results are transcribed in Appendix A. The input parameters of the

planning tool (OPS platform) are the ones indicated in Table 3.5. As previously referred (Section 3.8),

the average entry load (bandwidth) is fixed at 130 Tbps in order to evaluate the performance of the

algorithms under heavy load conditions. Both uniform and gravitational traffic distribution models are

applied. Since operators typically add capacity without removing any of the existing demands

(incremental scenario), only one planning period is assumed (as explained in Section 3.8). As detailed

in Section 2.3.2., different transmission formats were considered that allow transmission capacities

ranging from 100 Gbps to 400 Gbps, depending of different combinations of modulation types, number

of carriers and spectral occupation. Thus, client demands (100 GHz, 200 GHz, 300 GHz and 400 GHz)

are mapped to possible transmission formats (CP-QPSK, 16-QAM or 8-QAM), as detailed in Table 2.1.

It is not aloud mixing mapping to support each client demand individually (e.g., 400 GHz cannot be

supported by one 16-QAM optical carrier and two CP-QPSK optical carrier). The spectrum is occupied

in a continuous sequence in 12.5 GHz slots for each optical carrier and it is not fragment into separate

/ multiple slots. It was considered only gridless scenario (grids 50 GHz, 37.5 GHz and 50/37.5 GHz are

considered simultaneously), introducing flexibility to manage the grid (see Section 2.3.1) and supported

by minimum channel spacing of 12.5 GHz and tuning granularity of 6.75 GHz. As explained in Section

3.8, TBT and TRC measures were considered to evaluate the analysis. Note that all results for TBT are

expressed in Gbps. The results presented in this section are obtained by averaging over 50 independent

runs, each with a different set of demands (also explained in Section 3.8). In addition, and due to the

multiplicity of scenarios, results presented in Section 4.1 are also averaged over different modulation

scenarios and traffic profiles. Section 4.2 provides an analysis with separation between modulation

scenarios. Some complementary, but not essential, figures, tables and data that allow better

understanding of the results are provided in Appendices A, B and C.

Network nº nodes nº

unidirectional links34

Ratio (nº nodes / nº links)

Mean distance35

(km)

Mean distance (km)

/ nº nodes

Mean distance (km)

/ nº links

COST 11 52 0.2 462 42.0 8.9

GBN 13 38 0.3 216 16.6 5.7

PRT 26 72 0.4 203 7.8 2.8

Table 4.1 – Summary of important data relative to studied networks

34 In presented table, links refer to a unidirectional connection between two nodes. Thus, and as for example connections “Viena to Zurique” and “Zurique to Viena” are considered in this case as two different links.

35 Mean distance refers to the average distance between the nodes.

47

Initial analysis of the topological elements of the three networks, and considering maximum reach

for different modulation formats, as indicated in Table 2.1, conduces to some relevant findings. COST

network has 22 links, from the total number of 52 links, that fit to all possible modulation formats without

maximum reach constraint (which is 500 km and corresponds to 16-QAM modulation format) and without

requiring regenerators implementation. However, the remain links have associated distances between

500-1000 km (26 links) and 1000-1260 km (4 links). Thus, if minimum number of regenerator

implementation is prioritized, then lower spectral efficiencies will be preferred (CP-QPSK). In opposition,

if higher spectral efficiencies will be prioritized (QAM), then additional number of regenerators will be

required. In the case of GBN, all link distances fit to the reach constraint. In case of PRT there are 8

(unidirectional) links (associated to “Lisboa Funchal”, “Funchal Ponta Delgada”, “Funchal

Portimão” and “Lisboa Ponta Delgada” connections) that will require implementation of

regenerators if 16-QAM modulation format is used. Note that the regenerator and interface counts are

performed for each modulation format and each feasible path (and associated links) as a hole and not

by each wavelength (see Section 3.8 for detailed explanation).

During the discussion it will be used the expression “saturation level”, which refers to a ratio between

the number of demands and the number of the nodes at some network. Thus, a network with “higher

level of saturation” is the one where the distribution of the demands per each node is higher if compared

to the other analysed one.

Modulation Scenario a)

(0,1,2)

Demand Ordering

(0,1,2,3,4)

Routing Criteria

(1,2,3,4,A,B,C)

Traffic Distribution

(0,1,2,3,4,5,6) TBT (Gbps) TRC

0 0 1 0 Results Results



etc. etc. etc. etc. etc. etc.

a) Results were compiled to an Excel sheet (using an additional program developed in MATLAB) with format exemplified in this table, where the Modulation Scenario is a designation used by OPS to mention the used Spectral Grid.

Table 4.2 - Format of the obtained results (example)

Thus, for each combination of spectral grid (designated by OPS as modulation scenario), demand

ordering, routing criteria and traffic distribution, there were obtained specific results for TBT and TRC

(note that each result represents the average value of 50 trials, as referred in Section 3.8). Thus, Section

4.1 refers to results obtained for different demand orderings, averaging all possible combinations.

Sections 4.2.1 and 4.2.2 refer to results obtained for different routing algorithms and averaging all

possible combinations. Finally, Section 4.2.3 analyse in detail all combinations that refer to modulation

scenarios and different routing algorism, in order to understand if there are significant differences.

48

4.1. Demand Ordering Strategies

4.1.1. Uniform Model

Results obtained for the five demand ordering algorithms (Table 3.2), and uniform distribution, are

illustrated at Appendix A.1 and summarized in Table 4.3. It was considered initially only the previously

implemented demand routing algorithm (ID1). However, afterwards, all demand routing algorithms were

performed to allow a comprehensive analysis, as described in Section 3.6.

It is possible to verify in Table 4.3 that, in average, the total blocked traffic (TBT) is higher for GBN

(~2.8x104 Gbps) and COST (~2.3x103 Gbps) networks than for PRT network (~9.2x102 Gbps). This can

be explained by the fact that GBN and COST are smaller networks, with 13 and 11 nodes, respectively,

if compared to PRT network, with 26 nodes36. Additionally, the results are worse for GBN since this

network has the smallest number of links (38), if compared to COST (52) and PRT (72) networks. Since

the generated input client traffic is equal for all simulated scenarios / networks (130 Tbps), when it is

featured the uniform distribution model to distribute the same amount traffic the smaller networks will

have higher ratio of number of demands per each node and link (“higher level of saturation” of the

network).

Relatively to the demand ordering, it is possible to conclude from Table 4.4 that GBN and COST

networks, demand orderings 0 and 1 have in average worse performance, if compared to other demand

orderings, meaning that in these networks the most congested link first is the best ordering criteria. For

PRT network, the best results are obtained when the highest rate first (demand orderings 0, 4 and 1) is

used. However, this result is not very significant, since the variations are not relevant, as it is possible

to observe in Table 4.5. These results may be explained by the fact that since the injected traffic was

the same for all networks, that leads, in average, to GBN and COST networks being more congested

networks, when compared to PRT network. Since the level of “saturation” at GBN and COST is higher,

the spectrum become a scarcer resource, leading to better results when demand orderings 2, 3 and 4

are adopted. Thus, it is possible to conclude that at highly congested networks, the demand ordering by

the most congested link first can generally increase the performance of the routing algorithm. However,

the problem is more complex, depending on more variables, and this conclusion cannot be generalised.

Network / Demand Ordering 0 1 2 3 4

TB

T COST 2.7x103 3.1x103 1.8x103 2.0x103 1.8 x103

GBN 3.3x104 3.1x104 2.4x104 2.6x104 2.7 x104

PRT 8.4x102 9.2x102 9.9x102 9.4x102 8.9x102

TR

C COST 50 53 47 47 47

GBN 34 35 26 27 29

PRT 3 3 3 3 3

36 Note, however, that present investigation is not focused in distinguishing different possible equipment that may

be installed at different nodes (transponders, regenerators, etc.). SBVT are a good example of equipment to be used to implement gridless spectrum partitioning.

49

Table 4.3 – Mean values of TBT (Gbps) and TRC obtained at uniform model for different networks and demand orderings

Network /Demand Ordering TBT TRC

(not relevant differences)

COST 2,4,3,0,1 X,X,X,0,1

GBN 2,3,4,1,0 2,3,4,1,0

PRT 0,4,1,3,2 (not relevant

differences) X,X,X,X,X

Table 4.4 - Sequences of demand orderings for TBT and TRC results (from best to worst)

Network / Demand Ordering 0 1 2 3 4

TB

T COST 1.5 1.7 1.0 1.1 1.0

GBN 1.3 1.2 1.0 1.1 1.1

PRT 1.0 1.1 1.2 1.1 1.1

TR

C COST 1.1 1.1 1.0 1.0 1.0

GBN 1.3 1.4 1.0 1.0 1.1

PRT 1.0 1.0 1.0 1.0 1.0

Table 4.5 - Ratio between mean values and the minimum value for each demand ordering for different networks at uniform model

Relatively to the results obtained for the total regenerator count (TRC), the highest values of total

regenerator count (TRC) were obtained for COST (~48) and GBN (~29) networks. These results are

explained by the fact that the average distance between nodes associated to these networks is higher

(especially for COST network), if compared to PRT network, for which there were obtained the smallest

values of TRC (~3). It was verified that the number of TRC at PRT network is not affected significantly

by the demand orderings, reinforcing the conclusion that it is not “saturated” enough (that is, since the

generated input client traffic is distributed over higher number of nodes, if compared to COST and GBN

networks, the simulation doesn’t conduce to comparable replenishment of the network). These results

also reinforce that COST and GBN networks, for the same level of input traffic, have lower routing

performance (or routing capability) if compared to PRT, due to their different topology. Both for COST

and GBN networks, the demand orderings 0 a 1 reveals to be the worst results (degradation varying

between 10% and 30% relatively to the best results), supporting the conclusion that at highly saturated

networks, the most efficient demand ordering is associated to the most congested link first algorithm

(demand orderings 2,3,4).

It is also interesting to observe that for COST and GBN networks, the demand ordering sequence

for TBT is coincident with the obtained sequences for TRC values, which means that the worst demand

orderings not only increase the total blocked traffic but also increases the number of regenerators (3R).

4.1.2. Gravitational Model

The summary of the results obtained for the gravitational model are described in the tables below

and Appendix A.2 (besides different distribution of the traffic, gravitational in this case, other algorithms

were kept equal relatively to one’s describer in Section 4.1.1).

50

Mean

Population (x103)

TBT (uniform

model)

TBT (gravitational

model)

TRC (uniform

model)

TRC (gravitational

model)

COST 2062 2.3x103 3.2x104 49 31

GBN 776 2.8x104 7.0x104 30 40

PRT 816 9.2x102 4x104 3 2

Table 4.6 - Summary of important data relative to studied networks and results obtained for TBT (Gbps) for both models (uniform and gravitational) considering all demand orderings and routing algorithms per each model.

Population values based in values indicated in Appendix C.

Network / Demand Ordering

0 1 2 3 4

TB

T COST 3.5x104 3.4x104 3.0 x104 3.2 x104 2.9 x104

GBN 7.5x104 6.9x104 6.7 x104 7.1 x104 6.7 x104

PRT 4.5x104 4.0x104 3.7 x104 4.0 x104 3.9 x104

TR

C COST 40 43 24 24 25

GBN 39 42 40 40 39

PRT 2 2 1 2 2

Table 4.7 Results obtained for the gravitational model – mean values of TBT (Gbps) and TRC for different demand orderings

Network / Demand Ordering TBT TRC

COST 2,4,3,1,0 2,3,4,0,1

GBN 2,4,1,3,0 4,0,2,3,1 (not relevant variations)

PRT 2,4,3,1,0 X,X,X,X,X (not relevant variations)

Table 4.8 - Sequences of demand orderings for TBT and TRC results (from best to worst)

Network / Demand Ordering

0 1 2 3 4

TB

T COST 1.2 1.1 1.0 1.1 1.0

GBN 1.1 1.0 1.0 1.1 1.0

PRT 1.2 1.1 1.0 1.1 1.0

TR

C COST 1.7 1.8 1.0 1.0 1.0

GBN 1.0 1.1 1.0 1.0 1.0

PRT 1.6 1.9 1.0 1.2 1.8

Table 4.9 - Ratio between mean values and the minimum value for each demand ordering for different networks at gravitational model

It is possible to conclude from Table 4.6 that in average, the total blocked traffic (TBT) is higher in

the gravitational model that in the uniform model although the mean values obtained for different

networks are at the same order of magnitude. Thus, PRT network has much worse results (at least 100

times) if compared to the results obtained at the uniform model. COST results increase 10 times and

GBN 1.5 times. This may be explained by the fact that COST and GBN network were already highly

saturated networks at uniform model and the transition to the gravitational model did not have the same

impact as it happened at PRT network. This leads to a conclusion that gravitational formulation of a

problem, generally more alike to the real scenarios, accelerates the saturation of the network and

reveals the importance of consider carefully different factors associated to specific characteristics of the

51

analysed networks (such as the traffic origins and terminations) during the planning process of optical

networks.

It is also possible to conclude that demand orderings 0 and 1, for all networks, lead in average to

worse results of TBT, if compared to demand orderings 2, 3 and 4 (Table 4.7). It is interesting to see

that the biggest variations occur for demand orderings 0 and 1 (uniform ratio vs gravitational ratio as

indicated in Table 4.5 and Table 4.9). Thus, it is possible to conclude that when networks need to work

under heavy load conditions (as it was simulated in order of 130 Tbps) concentrated at specific nodes

of the network (in opposition to uniformly distributed traffic), the scarcest resource becomes the number

of the available links, leading to preferable demand ordering option be the most congested link first, that

in the present investigation correspond to demand orderings 2, 3 and 4. However, the differences are

not very significant. Thus, before the implementation of demand ordering 2,3, and 4 it is important to

analyse at each specific case the correspondent cost-benefit since these demand orderings are more

complex to implement since they require additional computational processes (pre-routing made

calculation of the most congested link, as explained in Section 3.5).

Relatively to the total count of regenerators (TRC), it is possible to conclude that in average (see

Table 4.6) the TRC values are higher for uniform model. This may be explained by the fact that in

gravitational model, associated to higher TBT, the most congested nodes aren’t capable to distribute all

the traffic in the same proportion as in uniform model (where the traffic is more equally distributed),

generating this way higher values of TBT and, in its turn, proportional lower levels of regenerators (lower

TRC). Analysing Table 4.7, Table 4.8 and Table 4.9, it is possible to observe that there is a significant

reduction of number of regenerators at COST network, when demand orderings 2,3 and 4 are

implemented if compared to demand orderings 1 and 2 (and correspondent TRC variation of 24/24/25

to 40/43). This means that in COST network, the routing by most congested links first will have higher

impact at TBT and TRC counts if compared to higher rate first or largest distance first orderings, which

may be explained by topological characteristics of the network (higher mean distances) and gravitational

distribution of the traffic in certain cities. Results for PRT also reveal that demand ordering 2 and 3

conduced to lower number of TRC. Note that in this particular network, there are specific cities (Funchal

and Ponta Delgada) are situated more than 1000 km away from the most loaded nodes (Lisbon and

Porto), meaning that for this link, even with lower load at each link, there will be some traffic that need

to be considered and implying the existence of regenerators in case if higher modulation schemes and/or

higher bit rates are used (see Table 2.1), that are associated to lower reach distances or implementation

of higher number of regenerators37 (at least one or two, depending of the existence of traffic at these

nodes). For GBN network, the variations are not relevant for different demand orderings, meaning that

demand orderings do not influence significatively the obtained results.

37 As an example, a 200 Gbps client channel can be implemented with CP-QPSK modulation (2 optical carriers),

obtaining a reach of 3000 km (50 GHz grid) or with 16-QAM modulation (1 optical carrier), obtaining a reach of 600 km (50 GHz grid). Thus, if both are implemented, two regenerators will be required in the first case and only one regenerator will be required in second case.

52

In a hole, it is possible to conclude that the demand ordering has lower impact in TRC results than

in TBT results (specially, if compared to the impact that routing criteria have at these metrics, as it will

be explained further). In average, COST and GBN networks lead to highest values of TRC if compared

to PRT, which is again related with higher mean link distances.

4.2. Demand Routing Strategies

Results obtained for the uniform and gravitational models combined with all studied demand routing

algorithms and all demand orderings are summarized at Appendix A.3.

4.2.1. Uniform Model

Average (mean) results of TBT and TRC, for different routing criteria (as explained in Section 3.6)

are presented in Table 4.10. Note that these results integrate all demand orderings obtained by

averaging all results for each routing criteria.

Network / Routing Criteria

A B C 1 2 3 4

TB

T COST 3.7x103 3.6x103 3.4x103 2.1x103 4.5x102 2.1x103 4.5x102

GBN 3.1x104 3.3x104 3.0x104 3.0x104 2.2x104 3.0x104 2.2x104

PRT 1.0x103 9.3x102 6.7x102 1.0x103 9.2x102 9.8x102 9.1x102

TR

C COST 8 8 4 4 156 4 156

GBN 8 9 5 4 90 4 90

PRT 0 1 0 0 8 0 8

Table 4.10 - Mean values of TBT (Gbps) and TRC for different routing criteria (and five demand orderings)

It is possible to observe that routing criteria has higher influence in results than demand ordering for

all networks since the variations of the results are relatively higher.

It is also possible to conclude that the implementation of new routing criteria has larger influence in

mean values of TBT results for COST network, but they do not have very significant role for GBN and

PRT networks (as it is possible to see in the Table 4.10 and Table 4.11). This can be explained by the

fact that the ratio between the number of nodes and the number of links at COST network is the lowest

one, associated to higher mean distances, leading to a conclusion that in this case the employed routing

criteria have more influence that in other networks. Mean values of TRC do not vary significantly, with

the exception for routing criteria 2 and 4, for all networks. Note that, and as explained in Section 3.6,

routing criteria 2 and 4 are the ones that route by the lowest spectrum occupation first, while the remain

routing criteria (1,3,A,B,C) prioritize the minimum number of 3R. Thus, at routing criteria 2 and 4, links

with lower occupation will be preferred to others, independently if they are associated to higher distance

or higher number of interfaces (as explained in Section 3.6). Considering that, it is a logical consequence

that the results obtained for TRC values are expressively higher. Note that in average, the mean TRC

results displayed in Table 4.10 are lower than the ones displayed in Table 4.3. This is caused by the

fact that the last ones were obtained by averaging different routing criteria, including 2 and 4 criteria,

damping this way other results.

53

Network / Ratio relatively to minimum mean value

Routing Criteria A B C 1 2 3 4

TB

T COST 8.3 8.2 7.7 4.7 1.0 4.8 1.0

GBN 1.4 1.5 1.4 1.4 1.0 1.4 1.0

PRT 1.5 1.4 1.0 1.5 1.4 1.5 1.4

TR

C COST 2.0 2.0 1.0 1.0 41.7 1.0 41.7

GBN 1.9 2.1 1.1 1.0 22.6 1.0 22.6

PRT 0 1 ª) 0 0 8 ª) 0 8 ª)

Table 4.11 – Ratio between mean values at different combination at the minimum value for different networks at uniform model. a) TRC results different of zero obtained for PRT network were manually manipulated; that is, for routing criteria B, 2 and 4, it was considered as the minimum value 1 regenerator (instead of 0) to avoid a division

by 0 that would result in infinitive value (∞).

Nevertheless, routing criteria 2 and 4 lead to better TBT results for all networks if compared to other

routing criteria (the differences are not significant, but they exist, for GBN and PRT networks). As a

reverse of the medal, these routing criteria induces significant increase of the TRC mean values,

indicating that these routing criteria increase traffic saturation at the cost of longer routes. Since routing

criteria 2 and 4 route by the lowest spectrum occupation first, the longer paths may be preferred to the

shorter ones, increasing such way the number of TRC count. This leads to a conclusion that routing

algorithms that prioritize the spectrum option (2, 4), instead of 3R (A, B, C, 1, 3), generally should be

avoided, specially, in heavily loaded networks.

The most interesting result is obtained for the PRT network for the routing criteria C that originated

the lowest value of mean TBT, and simultaneously any TRC. It is also observed that for COST and GBN

networks, routing criteria C, 1 and 3 lead to relatively low average values of TBT and low number of

TRC, indicating that minimizing by 3Rs and either the interface count or the number of hops are

acceptable options.

Network / Routing Criteria TBT TRC

COST 2,4,1,3,C,B,A 3,1,C,B,A,4,2

GBN 2,4,1,3,C,A,B (not relevant

variations) 3,1,C,A,B,4,2

PRT C,4,2-B,3,1,A (not relevant

variations) 3,1,C,A,B,4,2

Table 4.12 – TBT and TRC RC sequences (from best to worst)

4.2.2. Gravitational Model

Approximated values obtained for all routing criteria at the gravitational model are summarized in

tables below. Note that these results integrate all demand orderings obtained by averaging all results

for each routing criteria. It is possible to conclude that routing criteria do not affect almost at all the

average values of TBT for all networks at gravitational model. However, and as previously referred in

54

Section 4.1.2, the average levels of TBT values, for all routing criteria, are expressively higher at

gravitational model if compared to uniform model.

Network / Routing Criteria

A B C 1 2 3 4

TBT

COST 3.3x104 3.3x104 3.3x104 3.5x104 2.8x104 3.5x104 2.8x104

GBN 7.2x104 7.2x104 7.1x104 7.3x104 6.5x104 7.3x104 6.5x104

PRT 4.0x104 4.0x104 4.0x104 4.1x104 4.1x104 4.1x104 4.1x104

TRC

COST 10 13 4 3 93 3 93

GBN 6 12 4 5 124 5 124

PRT 1 1 1 1 5 1 5

Table 4.13 – Mean values of TBT (Gbps) and TRC values obtained at gravitational model for different routing criteria

Relatively to the TRC values, the obtained variations are in the same order of magnitude as the ones

obtained for the uniform model. However, it is possible to conclude that there is significant reduction,

comparatively to the uniform model, of the number of regenerators, excluding the results obtained for

COST with routing algorithms 2 and 4 (routing by the lowest spectrum first). Thus, although there is a

higher concentration of the request at specific nodes (equivalent to more populated cities), the routing

and the selection of paths will end up at the same links (that will be more heavily loaded), requiring this

way approximately the same or even lower number of regenerators. In the other hand, and even more

important, since there exist higher level of total of blocked traffic, there will be demands that will not even

be able to reach the network since they will be blocked at the very beginning (before being delivered to

the network), contributing this way to a reduction of TRC count.

Network / Ratio relatively to minimum mean value

Routing Criteria A B C 1 2 3 4

TB

T COST 1.1 1.2 1.2 1.2 1.0 1.2 1.0

GBN 1.1 1.1 1.1 1.1 1.0 1.1 1.0

PRT 1.0 1.0 1.0 1.0 1.0 1.0 1.0

TR

C COST 3.3 4.3 1.3 1.0 31.0 1.0 31.0

GBN 1.5 3.0 1.0 1.3 31.0 1.3 31.0

PRT a) 1.0 1.0 1.0 1.0 5.0 1.0 5.0

Table 4.14 - Ratio between mean values at different combination at the minimum value for different networks at gravitational model.

The obtained sequences for TBT and TRC values, as illustrated in Table 4.15, are compliant with

the withdrawn conclusions.

Network / Routing Criteria TBT

(not relevant variations) TRC

COST 4,2,1,3,C,A,B 1,3,C,A,B, 2,4

GBN 4,2,C,A,B,1,3 C,3,1,A,B, 2,4

PRT A,B,C,1,2,3,4 C,3,A,1,B, 4,2

Table 4.15 – Sequences by routing criteria, from best to worst results.

Comparing the obtained results both for uniform and gravitational models (and considering all

demand orderings by averaging per each routing algorithm), the best routing algorithms happens to be

55

the routing algorithms 1, 3 and C. While the routing algorithms 1 and 3 are the ones that combine 3R

with lowest spectrum (by this order), the C routing algorithm combines 3R minimization with the shortest

number of lightpaths. It is also important to refer that the relative results (best/medium/worst) obtained

for uniform and gravitational models were the same, indicating that the implementation of the

gravitational model is not significantly important to understand the influence of different demand

orderings and routing algorithms in the efficiency of the network.

ID 1st criteria 2nd criteria 3rd criteria UM GM

1 min 3R min spectrum min cost Best Best

2 min spectrum min 3R min cost Worst Worst

3 min 3R min cost min spectrum Best Best

4 min spectrum min cost min 3R Worst Worst

A min 3R Max spectral availability/lightpath

N/A Medium Medium

B min 3R Max mean spectral availability/lightpath

N/A Medium Medium

C min 3R shortest number lightpaths

N/A Best Best

Table 4.16 – Relative comparison of results obtained for TRC values for different routing criteria (and all studied demand orderings) – uniform model versus gravitational model

4.2.3. Detailed Analysis with Modulation Scenarios (Both

Models)

A more detailed analysis of different spectral grids, designated in OPS platform as “modulation

scenarios”, conduces to some interesting conclusions (that are synthetized at Appendix A.3, in Tables

6.1 and 6.2). Note that different modulation scenarios are defined in the OPS as an “in-build”

configuration of the main cycle. Table 4.17 and Table 4.18 synthetize the results obtained for different

combinations of average values of TBT and TRC results.

TBT (mean values)

Model Network/ spectral grid (or modulation scenario)

MS=0 (50 GHz) MS=1 (37.5 GHz) MS=2 (50/37.5 GHz)

UNI

COST 5.33x103 1.25 x103 2.28x102

GBN 3.34x104 2.60 x104 2.49 x104

PRT 2.28x103 2.56x102 2.08 x102

GM

COST 4.02x104 2.93x104 2.75x104

GBN 7.33x104 6.85x104 6.85x104

PRT 4.93x104 3.64x104 3.62x104

Table 4.17 – Total Blocked Traffic (Gbps) – mean values obtained for different networks and different

modulation scenarios (MS)

56

TRC (mean values) Model NTWK MS=0 (50 GHz) MS=1 (37.5 GHz) MS=2 (50/37.5 GHz)

UNI

COST 53 35 57

GBN 19 37 35

PRT 3 1 4

GM

COST 25 30 38

GBN 22 49 48

PRT 2 0 3

Table 4.18 – Total Regenerator Count - mean values obtained for different networks and different modulation scenarios (MS) (averaged all routing criteria and all demand orderings per MS)

As presented in Table 4.17, the average values of TBT obtained both for uniform and gravitational

models, for different networks, are higher for modulation scenario 0 (i.e. 50 GHz grid) and are lower for

modulation scenario 1 (37.5 GHz grid), leaving the modulation scenario 2 (50 GHz/37.5 GHz grid) in the

middle of both. Thus, smaller granularity (37.5 GHz) and mixed granularity (50 GHz/37.5 GHz grid) have

better performance if compared to the higher granularity (50 GHz). And, in its turn, the mixed granularity

is slightly better than the smaller one. Considering the previously discussed concepts in Chapter 2,

particularly paragraph 2.3, it is understandable that networks with flexible or smaller grids will have better

(lower) TBT results, since the available spectrum is more efficiently used. In the other hand, comparing

the three networks between them, the PRT network has, in terms of TBT results, the worst behaviour in

the presence of the gravitational model, whereas GBN has the lowest variation, leaving the COST

network in the middle, which is in line with results previously discussed in Sections 4.1, 4.2.1 and 4.2.2.

Regarding the values of TRC, they are generally higher for modulations 1 and 2, and lower for

modulation 0. This may be explained by the fact that the smaller and mixed grids are associated to

shortest reach distances (as it was detailed in Section 2.3.2 and in Table 2.1), which will induce higher

number of regenerators when smaller grids are used (37.5 GHz and 50/37.5 GHz). However, it is

possible to observe (Table 4.18) that in some cases the number of regenerators is lower when smaller

grid is used, which may be observed in results obtained for uniform model (all networks) and PRT both

uniform and gravitational models. It is possible to observe (Table 4.17) that associated TBT results are

also lower, if compared to the results obtained for 50 GHz grid. These results may be explained by the

fact that smaller grid is more efficient to manage the traffic, increasing the total capacity of the optical

fiber and delivering more traffic to the destination nodes (and resulting in lower TBT). Since the mean

traffic at each node is uniformly distributed, the total load per node is lower and the shortest paths are

more frequently used, generating lower number of regenerators. Better results of TRC obtained for PRT

in gravitational model for smaller grid may be explained by the fact that the most loaded nodes are

associated to lower mean distances (that correspond to Lisbon and Porto cities) and are, in average,

geographically situated closer to the remain nodes (opposingly, for example, to Porto Santo).

Comparing uniform vs gravitational TRC results, it is possible to observe that COST and PRT results

of TRC are lower for gravitational model (53-35-57 / 25-30-38 for COST and 3-1-4 / 2-0-3 for PRT),

whereas in GBN the TRC results are lower for uniform model (19-37-35 / 22-49-48), specially for smaller

57

and mixed grids. It is expectable to obtain lower TRC results in gravitational model (and not in uniform

model) since in general cases the TRC values are inversely proportional to TBT values, that is, if the

total blocked traffic is higher, than, the corresponding proportion of traffic that won’t be introduced in the

network will not require any regenerator. However, GBN results are not in line with this generalization,

being higher in gravitational model. This may be related with the fact that the obtained TBT results for

GBN in gravitational model are expressively higher if compared to other networks, resulting in also

corresponding higher TRC values. Finally, it is important to highlight the significant difference in TRC

results in COST network obtained for MS=0 (53 in uniform model and 25 in gravitational model), followed

by results obtained for MS=2 (57 vs 38). This difference may be explained by the fact that the mean

distance between the nodes of COST network is the highest one, if compared to other networks and the

associated ratio between number of nodes and links is the lower one (see Table 4.1). Thus, when

gravitational model is implemented combined with a 50 GHz grid (associated to higher reach distances),

the obtained relative reduction is the highest one (if compared to other grids or networks). Follows

immediately the mixed grid, with associated reach distances that are situated between the 50 GHz grid

and the 37.5 GHz.

In order to analyse the results in more detail, it is possible to sort the obtained TBT and TRC results,

for each modulation scenario, by different demand orderings, from best to the worst (see Table 4.19 and

Table 4.20). It is possible to observe in Table 4.19 that for almost all cases and independently of the

used model, the average values of TBT are lower if demand orderings 2 and 4 are used, whilst demand

orderings 0 and 1 lead in average to worse results. Demand ordering 3 leads to average results,

generally in the middle of other demand ordering. This leads to a conclusion that generally the demand

ordering does not influence significantly the TBT results when different grids are implemented. TRC

results obtained for different demand orderings (Table 4.20) also reveal, almost for all cases, that the

demand ordering does not influence the results obtained for different grids (or modulation scenarios).

The bigger variations are observed for results obtained for PRT network. However, these high variations

are caused by very low levels of the obtained regenerators (see for example Table 4.3 and Table 4.7),

resulting that small differences (one or two units) will lead to apparently significant differences. For this

reason, results obtained for PRT network are not considered relevant in this analysis.

TBT (Demand Ordering (DO) from best to worst) Model NTWK MS=0 (50 GHz) MS=1 (37.5 GHz) MS=2 (50/37.5 GHz)

UNI

COST DO: 4-2-3-0-1 DO: 4-2-3-0-1 DO: 4-2-3-0-1

GBN DO: 2-3-4-1-0 DO: 2-3-4-1-0 DO: 2-3-4-1-0

PRT

DO: 1-0-4-3-2 @RC=1,2,3,4 DO: 3-4-2-0-1 @RC=A,B,C

DO: 0-1-4-3-2 @RC=1,2,3,4 DO: 3-4-2-0-1 @RC=A,B,C

DO:0-1-4-X-X @RC=1,2,3,4,A,B DO: 4-3-2-0-1 @RC=C

GM

COST DO: 2-4-3-1-0 DO: 4-2-3-1-0 DO: 4-2-3-1-0

GBN DO: 4-2-1-3-0 DO: 2-4-1-3-0 DO: 2-4-1-3-0

PRT DO: 2-4-3-1-0 DO: 2-4-1-3-0 DO: 2-4-3-1-0

Table 4.19 – Total Blocked Traffic – demand ordering sequences from best to the worst results for each type of network, model and modulation scenario (MS). Specific cases analysed also by different routing criteria (RC).

58

TRC (Demand Ordering (DO) from best to the worst) Model NTWK MS=0 (50 GHz) MS=1 (37.5 GHz) MS=2 (50/37.5 GHz)

UNI

COST DO: 4-2-3-0-1 DO: 3-4-2-0-1 DO: 3-2-4-0-1

GBN DO: 2-3-4-0-1 DO: 2-3-4-0-1 DO: 2-3-4-0-1

PRT DO: 3-1-2-0-4 DO: 2-0-1-3-4 DO=1-3-4-0-2

GM

COST

DO: 2-3-4-1-0 @RC=2,4 DO inverse @remain RC



GBN

DO: 0-2-4-3-1 @RC=2,4 DO:2-4-1-3-0 @RC=A,B,C,1,3

DO: 0-3-4-2-1 @RC=2,4 DO insignificant inverse @remain RC

DO: 1-3-4-2-0 @RC=2,4 DO inverse insignificant @remain RC

PRT

DO: 2-3-0-4-1 @RC=2,4 DO insignificant variations @remain RC

DO: zero @all RC

DO: 2-3-0-4-1 @RC=2,4 DO ~zero @remain RC

Table 4.20 - Total Regenerator Counter – demand ordering sequences from best to the worst results for each type of network, model and modulation scenario (MS). Specific cases analysed also by different routing criteria (RC).

Relatively to the influence of the routing criteria (RC) at the TBT values for different modulation

scenarios, it is possible to conclude that for COST and GBN networks, the main tendency is that RC’s

2 and 4 lead to lower (better) results (as it was previously concluded). However, this is not so linear for

PRT network, since despite for MS=0 maintains the trend, for MS=1 and MS=2 the results are steady,

and the sequences approximately inverted. For TRC values the worst results are obtained precisely for

routing criteria 2 and 4 without any exception (COST, GBN and PRT) and there is a strong tendency for

the lower (best) values being obtained with routing criteria C,3,1. It is interesting to observe that the

results for different combinations and networks are almost equal for MS=0 for, whereas they start to be

different when smaller grid granularity (M=1) is introduced. In conclusion, and supported by results of

Table 4.21 and Table 4.22, it is possible to say that TBT results are influenced significantly when different

combinations of routing algorithms/criteria and different grids (modulation scenarios) are implemented.

However, the obtained TRC results are not influenced significantly by different combinations of routing

criteria and different grids. It is also possible to conclude that routing criteria influence more the results

if compared to the results obtained for different demand orderings combined with different modulation

scenarios. It is also interesting to observe that routing criteria C (combination of lowest 3R (1st) and

shortest number of lightpaths at the path (2nd)) leads to better results in many studied scenarios.

TBT (RC from best to worst)

Model NTWK MS=0 (50 GHz) MS=1 (37.5 GHz) MS=2 (50/37.5 GHz)

UNI

COST RC: 2-4-1-3-C-A-B RC: 4-2-3-1-B-A-C RC: C-2-4-A-B-1-3

GBN RC: 4-2-1-3-C-A-B RC: 2-4-1-3-C-A-B RC: 2-4-C-A-1-3-B

PRT RC: C-2-4-3-1-B-A RC: C-B-A-3-4-2-1 RC: B-A-C-2-3-4-1

GM

COST RC: 2-4-A-C-B-3-1 RC: 4-2-X-X-X-X-X RC: 4-2-X-X-X-X-X

GBN RC: 2-4-C-X-X-X-3 RC: 4-2-A-C-B-3-1 RC: 2-4-B-A-C-3-1

PRT RC: 2-4-C-1-3-B-A RC: A-B-C-1-2-4-3 RC: A-C-3-1-B-2-4

Table 4.21 – Total Blocked Traffic – routing criteria (RC) sequences from best to the worst results for each type of network, model and modulation scenario (MS)

59

TRC (RC from best to worst)

Models NTWK MS=0 (50 GHz) MS=1 (37.5 GHz) MS=2 (50/37.5 GHz)

UNI

COST RC: C-3-1-B-A-4-2 RC: 3-C-1-A-B-4-2 RC: A-B-3-C-1-4-2

GBN RC: C-1-3-B-A-4-2 RC: 1-3-C-A-B-2-4 RC: C-3-1-A-B-2-4

PRT RC: C-3-1-A-B-4-2 RC: A-B-C-1-3-2-4 RC: 1-C-3-A-B-4-2

GM

COST RC: 1-3-C-A-B-2-4 RC: C-3-1-A-B-2-4 RC: C-1-3-A-B-2-4

GBN RC: C-3-1-A-B-4-2 RC: C-3-1-A-B-4-2 RC: 3-C-1-A-B-4-2

PRT RC: C-3-1-A-B-2-4 RC: zero @all RC RC: C-A-B-3-1-4-2

Table 4.22 - Total Regenerator Count – routing criteria (RC) sequences from best to the worst results for each type of network, model and modulation scenario (MS)

60

5. Conclusions and Future Work

5.1. Conclusions

In this work, the influence of different traffic ordering algorithms, traffic distributions, and routing

criteria is studied in the planning of flexible optical transport networks with Super-channels. The

performance of the planning process was evaluated in terms of blocked traffic (TBT) and total amount

of installed regenerators (TRC) over different network topologies. The new functionalities were directly

implemented and evaluated on an existing software framework, here named Optical Planner, previously

developed and authored by Coriant.

There were implemented new methods, namely 1) three demand ordering algorithms based on

combination of different criteria; 2) six demand routing algorithms based on the combination of different

criteria; 3) demand distributions were based on uniform and gravitational models.

The analysis of the collected results obtained via extensive computer simulations allowed to conclude

that at heavily congested networks demand ordering and routing criteria algorithms denote more impact

when the network is characterized by lower ratio between the number of nodes and links and higher

mean link distances. Thus, highly connected networks with lower mean distances (e.g. PRT) will have

better behaviour (in terms of average levels of TBT and TRC results) when subjected to the same input

load (traffic), whereas networks with higher mean distances will require higher number of regenerators

to support the traffic (e.g. COST and GBN).

With regard to different demand orderings, and for both TBT and TRC counts, analysis of the results

obtained for GBN and COST with uniform traffic model allow to conclude that demand ordering

strategies based on most congested links first can be an important tool to improve the performance of

the routing algorithm, allowing to obtain enhancements in the efficiency up to 30-40%. When networks

need to deal with high volume of traffic concentrated at specific nodes of the network, as it happens in

gravitational model, the number of the available links gains an increased importance as a lacking

resource and lead, in average, to a preferable demand ordering option to be, with especial relevance

for the TBT results, the most congested link first, reinforcing the results obtained in the uniform model,

but this time, extensible to all studied networks.

Implementation of routing criteria algorithms, in comparison to the demand ordering algorithms, has

higher impact in the results, being associated to higher variations in TBT and TRC average counts (with

special incidence in this last one). It was observed both for uniform and gravitational models that routing

criteria that prioritized spectrum occupation (routing criteria 2 and 4), conduced to somewhat lower TBT

results, but simultaneously to expressively higher values of TRC, leading to a conclusion that these

routing algorithms should be avoided if lower number of regenerators and lower total blocked traffic are

the goals to achieve. Routing criteria C, 1 and 3, based on minimization of the number of regenerators

and either lower number of interfaces or hops are acceptable options to consider if higher efficiencies

are sought. It was also concluded that the relative results (best/medium/worst) obtained for uniform and

gravitational models were the same, indicating that the implementation of the gravitational model is not

significantly important to understand the influence of different demand orderings and routing algorithms

61

in the efficiency of the network. However, gravitational model is actually a very important tool in cases

where it is important to estimate the absolute values of TBT and TRC, since it approximates the results

to real scenarios.

Detailed analysis of the results for different modulation scenarios lead to a conclusion that smaller

grids, especially if implemented in networks characterized by lower mean distances between the nodes,

allow to obtain higher efficiencies, leading this way to lower TBT and TRC results. Networks

characterized by higher mean distances between the nodes also benefit with smaller grid partitioning,

however implementation of routing criteria need be analysed more carefully. Thus, if the TBT is

expressively high, the TRC count may not reflect the true number of the regenerators that is really

required, since in a simulation process these demands will be blocked before being delivered to the

network. It was also observer that implementation of different grids influences mainly the TRC results,

being this way an important tool to consider in a planning process, which is closely related with the fact

that shorted grids are associated to shortest reach distances.

Finally, it is important to refer that implementation of routing criteria is the factor that influence the

most the TBT and TRC results, if compared to implementation of demand orderings and different

modulation scenarios. Thus, a careful analysis of the topological elements of networks, combined with

the implementation of suitable routing criteria may be the win-win solution to a problem.

5.2. Future Work

The work developed in this thesis can be further extended into multiple directions. Refer to the

following list as a set of possible studies:

Evaluation of the demand ordering and routing algorithms in multi-period planning with traffic

churn38. The use of Super-channels implies a spectrum occupation that is not limited to single

50 GHz slot. In this sense, spectrum left vacant due to the removed traffic demands may not be

enough for the demands of the next period.

Consider different traffic loads. In this work, a fixed entry load of 130 Tbps was assumed. This

was done to represent a heavy loaded network. However, the algorithms studied could have a

different performance when subjected to a lighter or even heavier traffic load.

Include high baud-rate signals39 into the optical signal options to carry the client traffic. The high-

baud rate formats (e.g., 60 Gbaud/s, 90 Gbaud/s) can increase the bit-rate but use a single

optical carrier, which occupies a wider spectrum slice. There is a trade-off regarding reach with

38 Considering a multi-period planning, traffic churn or churn ratio is a coefficient between the dropped and added

bandwidth (set of old and new demands) in each period (as it was referred in Section 3.3).

39 High-baud rate signal is a high capacity wavelength (channel), where the increased capacity is obtained by

using higher baud rates combined with adjustable spectral window, allowing to obtain simultaneously lower impact in reach (if compared to implementation of high-level modulation schemes).

62

Super-channels that could provide different conclusions regarding the most adequate demand

ordering and routing algorithms.

Extend the planning tool to support traffic grooming. The scenarios evaluated in this thesis

assume that each client demand is directly mapped to a single optical signal. With grooming,

multiple client signals can be aggregated into a single optical signal, which improves network

utilization.

63

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65

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Appendices

A-1

Appendix A: Results

A.1. Demand Ordering - Uniform Distribution

Complementary graphics to the obtained results elaborated for different demand orderings at uniform

model are presented in present appendix with the only a purpose to help the understanding of the

results. These graphics illustrate mean values of TBT and TRC for different networks (COST, GBN and

PRT) grouped by different routing criteria (1,2,3,4,A,B,C), where each set has 5 bars ordered by different

demand orderings (0,1,2,3,4) accordingly the sequence indicated in the title and subtitles of the figures

(generally from best to worst)40. Thus, each bar represents mean values obtained for some specific

demand order and routing criteria and considers obtained results for 7 traffic distributions and 3

modulation scenarios (21 different combinations, where each value is composed by the mean of 50

results obtained from OPS). These results were compiled in tables presented in Section 4.1.1. Thus,

Table 4.3 is obtained performing the mean of results obtained for 7 traffic distributions, 3 modulation

scenarios and 7 routing criteria (147 combinations).

Relatively to the figures (graphics) it was decided to maintain the same routing ordering sequence

(1,2,3,4,A,B,C) for all combinations. In opposite, the demand ordering sequence was adapted from lower

to higher (or in some cases from higher to lower), to support better the analysis of the results.

Figure 6.1 - Mean values of TBT (Gbps) for COST network at uniform model (yy axes) grouped by different routing criteria (1,2,3,4,A,B,C) and sub ordered by different demand orderings (4,2,3,0,1) (xx axes)

40 Note: colours of different graphics presented in Appendices A.1, A.2 and A.3 were generated automatically by

Excel® spreadsheet and don’t have any meaning.

A-2

Figure 6.2 - Mean values of TBT (Gbps) for GBN network at uniform model (yy axes) grouped by different routing criteria (1,2,3,4,A,B,C) and sub ordered by different demand orderings (2,3,4,1,0) (xx axes)

Figure 6.3 - Mean values of TBT (Gbps) for PRT network at uniform model (yy axes) grouped by different routing criteria (1,2,3,4,A,B,C) and sub ordered by different demand orderings (0,1,4,3,2) (xx axes)

Figure 6.4 - Mean values of TRC for COST network at uniform model (yy axes) grouped by different routing criteria (1,2,3,4,A,B,C) and sub ordered by different demand orderings (3,2,4,0,1) (xx axes)

Figure 6.5 - Mean values of TRC for GBN network at uniform model (yy axes) grouped by different routing criteria (1,2,3,4,A,B,C) and sub ordered by different demand orderings (2,3,4,0,1) (xx axes)

A-3

Figure 6.6 - Mean values of TRC for PRT network at uniform model (yy axes) grouped by different routing criteria (1,2,3,4,A,B,C) and sub ordered by different demand orderings (1,0,3,2,4) (xx axes)

A-4

A.2. Demand Ordering – Gravitational Model

Complementary graphics to the obtained results elaborated for different demand orderings at

gravitational model are presented in present appendix with the only a purpose to help the understanding

of the results. These graphics were performed with the same reasoning of the ones presented in

Appendix A.1. and support results compiled in Appendix A.1 and other results of Section 4.1.2.

Relatively to the figures (graphics) it was decided to maintain the same routing ordering sequence

(1,2,3,4,A,B,C) for all combinations. In opposite, the demand ordering sequence was adapted from lower

to higher (or in some cases from higher to lower), to support better the analysis of the results.

Figure 6.7 - – Mean values of TBT (Gbps) for COST network at gravitational model (yy axes) grouped by different routing criteria (1,2,3,4,A,B,C) and sub ordered by different demand orderings (4,2,3,1,0) (xx axes)

Figure 6.8 - Mean values of TBT (Gbps) for GBN network at gravitational model (yy axes) grouped by different routing criteria (1,2,3,4,A,B,C) and sub ordered by different demand orderings (2,4,1,3,0) (xx axes)

Figure 6.9 - Mean values of TBT (Gbps) for PRT network at gravitational model (yy axes) grouped by different routing criteria (1,2,3,4,A,B,C) and sub ordered by different demand orderings (2,4,1,3,0) (xx axes)

A-5

Figure 6.10 - Mean values of TRC for COST network at gravitational model (yy axes) grouped by different routing criteria (1,2,3,4,A,B,C) and sub ordered by different demand orderings (2,3,4,0,1) (xx axes)

Figure 6.11 - Mean values of TRC for GBN network at gravitational model (yy axes) grouped by different routing criteria (1,2,3,4,A,B,C) and sub ordered by different demand orderings (0,3,2,4,1) (xx axes)

Figure 6.12 - Mean values of TRC for PRT network at gravitational model (yy axes) grouped by different routing criteria (1,2,3,4,A,B,C) and sub ordered by different demand orderings (2,3,0,4,1) (xx axes)

A-6

A.3. Demand Routing - Uniform & Gravitational

Complementary tables and graphics to the obtained results elaborated for different routing criteria

for uniform and gravitational models are presented in present appendix with the only a purpose to help

the understanding of the results. Graphics illustrate mean values of TBT and TRC for different networks

(COST, GBN and PRT) grouped by different demand orderings (0,1,2,3,4), where each set has 7 bars

ordered by different routing criteria (1,2,3,4,A,B,C) accordingly the sequence indicated in the title and

subtitles of the figures (generally from best to worst). Thus, each bar represents mean values obtained

for some specific routing criteria and demand order and considers obtained results for 7 traffic

distributions and 3 modulation scenarios (21 different combinations, where each value is composed by

the mean of 50 results obtained from OPS). Although referring to same results of the ones indicated in

Appendices A.1 and A.2, different angle of observation permits to withdraw additional information. These

results were compiled in tables presented in Sections 4.2.1. and 4.2.2. Thus, Table 4.10 and Table 4.13

are obtained performing the mean of results obtained for 7 traffic distributions, 3 modulation scenarios

and 7 routing criteria (147 combinations).

Relatively to the figures (graphics) it was decided to maintain the same demand ordering sequence

(0,1,2,3,4) for all combinations. In opposite, the routing criteria sequence was adapted from lower to

higher (or in some cases from higher to lower), to support better the analysis of the results.

Figure 6.13 - Mean values of TBT (Gbps) for COST network at uniform model (yy axes) grouped by different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (4,2,1,3,C,A,B) (xx axes).

Figure 6.14 - Mean values of TBT (Gbps) for GBN network at uniform model (yy axes) grouped by different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (4,2,C,1,3,A,B) (xx axes)

A-7

Figure 6.15 - Mean values of TBT (Gbps) for PRT network at uniform model (yy axes) grouped by different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (4,2,3,C,1,A,B) (xx axes)

Figure 6.16 - Mean values of TRC for COST network at uniform model (yy axis) grouped by different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (C,3,1,A,B,4,2) (xx axes)

Figure 6.17 - Mean values of TRC for GBN network at uniform model (yy axis) grouped by different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (C,3,1,A,B,2,4) (xx axes)

Figure 6.18 - Mean values of TRC for PRT network at uniform model (yy axes) grouped by different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (C,3,A,1,B,4,2) (xx axes)

A-8

Figure 6.19 - Mean values of TBT (Gbps) for COST network at gravitational model (yy axes) grouped by different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (4,2,1,3,C,A,B) (xx axes)

Figure 6.20 - Mean values of TBT (Gbps) for GBN network at gravitational model (yy axes) grouped by different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (4,2,C,1,3,A,B) (xx axes)

Figure 6.21 - Mean values of TBT (Gbps) for PRT network at gravitational model (yy axes) grouped by different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (4,2,3,C,1,A,B) (xx axes)

Figure 6.22 - Mean values of TRC for COST network at gravitational model (yy axes) grouped by different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (C,3,1,A,B,4,2) (xx axes)

A-9

Figure 6.23 - Mean values of TRC for GBN network at gravitational model (yy axes) grouped by different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (C,3,1,A,B,2,4) (xx axes)

Figure 6.24 - Mean values of TRC for PRT network at gravitational model (yy axes) grouped by different demand orderings (0,1,2,3,4) and sub ordered by different routing criteria (C,3,A,1,B,4,2) (xx axes)

TBT (from best to worst) Model NTWK MS=0 MS=1 MS=2

UNI

COST

DO: 4-2-3-0-1 (comb) RC: 2-4-1-3-C-A-B (comb) μ = 5325

DO: 4-2-3-0-1 (comb) RC: 4-2-3-1-B-A-C (comb) μ =1248

DO: 4-2-3-0-1 (comb) RC: C-2-4-A-B-1-3 (almost comb) μ =228

GBN

DO: 2-3-4-1-0 (comb) RC: 4-2-1-3-C-A-B (comb; almost comb for DO=0&1) μ =33436

DO: 2-3-4-1-0 (comb) RC: 2-4-1-3-C-A-B (comb; steady-comb at DO=0&1) μ =25973

DO: 2-3-4-1-0 (comb) RC: 2-4-C-A-1-3-B (comb) μ =24943

PRT

DO: 1-0-4-3-2 @RC=1,2,3,4 DO: 3-4-2-0-1 @RC=A,B,C (almost comb) RC: C-2-4-3-1-B-A (almost comb) μ =2285

DO: 0-1-4-3-2 @RC=1,2,3,4 (comb) DO: 3-4-2-0-1 @RC=A,B,C (comb ) RC: C-B-A-3-4-2-1 (steady @DO=0&1; steady-comb @DO=2,3,4) μ =255

DO:0-1-4-3-2 @RC=1,2,3,4 (comb) DO: 0-1-4-2-3 @RC=A,B (comb) DO: 4-3-2-0-1 @RC=C (steady-comb) RC: B-A-C-2-3-4-1 (steady insignificant mean values @RC=B,A,C; steady @RC=2,3,4,1) μ =208

GM COST DO: 2-4-3-1-0 (comb; almost comb @RC=2,4)

DO: 4-2-3-1-0 (comb; almost comb @RC=A,C,2,4)

DO: 4-2-3-1-0 (almost comb)

A-10

RC: 2-4-A-C-B-3-1 (comb; almost comb @DO=0,3,4) μ =40155

RC: 4-2-3-1-C-B-A comb @DO=0,1 RC: 4-2-C-B-A-1-3 comb @DO=2,3,4 μ =29252

RC: 4-2-1-3-C-A-B comb @DO=0 RC: 4-2-A-C-B-1-3 comb @DO=1 RC: 4-2-A-B-C-1-3 comb @DO=2,3,4 μ =27539

GBN

DO: 4-2-1-3-0 (comb) RC: 2-4-C-A-1-B-3 (comb @DO=1) RC: 2-4-C-A-B-1-3 (comb @DO=2,3,4) RC: 2-4-C-1-B-A-3 (comb @DO=0) μ =73265

DO: 2-4-1-3-0 (comb) RC: 4-2-A-C-B-3-1 comb steady μ =68524

DO: 2-4-1-3-0 (comb) RC: 2-4-B-A-C-3-1 (steady; RC=2,4 lower that remain) μ =68486

PRT

DO: 2-4-3-1-0 (comb); RC: 2-4-C-1-3-B-A steady μ =49339

DO: 2-4-1-3-0 (comb) RC: A-B-C-1-2-4-3 steady μ =36386

DO: 2-4-3-1-0 (comb) RC: A-C-3-1-B-2-4 steady μ =36170

Table 6.1 – TBT (µ - mean value of all results under selected criteria)

TRC

Models NTWK MS=0 MS=1 MS=2

UNI

COST

DO: 4-2-3-0-1 (steady outline) RC: C-3-1-B-A-4-2 (steady insignificant @RC=C,3,1,B,A; steady very high steady @RC=4,2) μ =52

DO: 3-4-2-0-1 (steady outline) RC: 3-C-1-A-B-4-2 (~zero @RC=3,C,1,A,B; steady very high steady @RC=4,2) μ =34

DO: 3-2-4-0-1 (steady outline) RC: A-B-3-C-1-4-2 (steady ~zero @RC=A,B,3,C,1; very high steady @RC=4,2) μ =56

GBN

DO: 2-3-4-0-1 (comb outline) RC: C-1-3-B-A-4-2 (steady insignificant @RC=C,1,3,B,A; steady very high @RC=4,2) μ =18

DO: 2-3-4-0-1 (comb outline) RC: 1-3-C-A-B-2-4 (very low steady-comb @RC=1,3,C,A,B; steady very high @RC=2,4) μ =36

DO: 2-3-4-0-1 (comb outline) RC: C-3-1-A-B-2-4 (comb ~zero @RC=C,3,1,A,B; steady very high @RC=2,4) μ =34

PRT

DO: 3-1-2-0-4 (steady @RC=2,4; insignificant @remain RC) RC: C-3-1-A-B-4-2 (~zero @RC=C,3,1,A,B; steady very high @RC=4,2) μ =2.7

DO: 2-0-1-3-4 (almost steady @RC=2,4; insignificant @remain RC) RC: A-B-C-1-3-2-4 (zero @RC=A,B,C,1,3; steady very high @RC=2,4) μ =0.6

DO=1-3-4-0-2 (steady @RC=2,4; insignificant @remain RC) RC: 1-C-3-A-B-4-2 (zero @RC=1,C,3,A,B; very high steady @RC=2,4) μ =3

GM COST

DO: 2-3-4-1-0 @RC=2,4 (comb); DO inverse insignificant @remain RC

DO: 2-3-4-0-1 (comb @RC=2,4) DO inverse insignificant @remain RC

DO: 2-3-4-0-1 (comb @RC=2,4) DO inverse insignificant @remain RC

A-11

RC: 1-3-C-A-B-2-4 (steady very high @RC=2,4; very low comb @remain RC) μ =24.7

RC: C-3-1-A-B-2-4 (steady very high @RC=2,4; very low @remain RC) μ =29.6

RC: C-1-3-A-B-2-4 (very high steady @RC=2,4; ~zero @remain RC) μ =37.3

GBN

DO: 0-2-4-3-1 (comb very high @RC=2,4) DO:2-4-1-3-0 (comb very low @RC=A,B,C,1,3) RC: C-3-1-A-B-4-2 (steady; RC=4,2 very high; remain RC insignificant) μ =21

DO: 0-3-4-2-1 (comb @RC=2,4); DO insignificant inverse @remain RC RC: C-3-1-A-B-4-2 (steady; RC=4,2 very high; remain RC insignificant) μ =48.8

DO: 1-3-4-2-0 (comb @RC=2,4) DO inverse insignificant @remain RC RC: 3-C-1-A-B-4-2 (steady; RC=4,2 very high; remain RC insignificant) μ =47.7

PRT

DO: 2-3-0-4-1 (comb @RC=2,4) DO insignificant @remain RC RC: C-3-1-A-B-2-4 (steady; RC=4,2 very high; remain RC insignificant) μ =1.9

DO: zero @all RC RC: zero @all RC μ =0

DO: 2-3-0-4-1 comb @RC=2,4; DO ~zero @remain RC RC: C-A-B-3-1-4-2 (steady; very high @RC=4,2; zero @remain RC) μ =2.27

Table 6.2 – TRC (µ - mean value of all results under selected criteria)

B-1

Appendix B: General Network Data

B.1. European Optical Network (COST 239)

COST 239 is a European Optical Network41 Ultra-High Capacity Optical Transmission Network and it

is characterized by 11 nodes and 52 links illustrated at Figure 6.25 and subsequent tables.

Figure 6.25 – COST 239 network (11 nodes and 52 links)

Distance (km)

Node ID 0 1 2 3 4 5 6 7 8 9 10

0 0 594 251 525 768 937 871 1237 916 1035 625 1 594 0 529 671 304 615 966 778 493 490 216 2 251 529 0 281 594 712 641 1036 719 884 646 3 525 671 281 0 590 576 361 933 651 877 843 4 768 304 594 590 0 318 783 480 190 294 536 5 937 615 712 576 318 0 622 356 171 430 830 6 871 966 641 361 783 622 0 953 766 1028 1161 7 1237 778 1036 933 480 356 953 0 321 343 960 8 916 493 719 651 190 171 766 321 0 266 697 9 1035 490 884 877 294 430 1028 343 266 0 641

10 625 216 646 843 536 830 1161 960 697 641 0

Table 6.3 - Distances (km) between COST 239 nodes – modelled (approximated values from Google)

41 European Optical Network is generally abbreviated by EON acronym. However, in the present investigation EON refers to Elastic Optical Network.

B-2

Links

Node ID 0 1 2 3 4 5 6 7 8 9 10

0 0 1 1 1 0 0 0 0 0 0 1

1 1 0 1 0 1 0 0 0 0 1 1

2 1 1 0 1 1 0 1 0 0 0 0

3 1 0 1 0 0 1 1 0 0 1 0

4 0 1 1 0 0 1 0 0 1 0 0

5 0 0 0 1 1 0 1 1 1 0 0

6 0 0 1 1 0 1 0 1 0 0 0

7 0 0 0 0 0 1 1 0 1 1 0

8 0 0 0 0 1 1 0 1 0 1 1

9 0 1 0 1 0 0 0 1 1 0 1

10 1 1 0 0 0 0 0 0 1 1 0

Table 6.4 - COST 239 topology and links (equivalent to Figure 6.25) (adjacency matrix)

B-3

B.2. German Backbone Network (GBN)

German Backbone Network (GBN) is characterized by 17 nodes and 26 links, and it is illustrated at

Figure 6.25. In present investigation, nodes 6, 7, 12 and 16 were not considered since it would require

an amount of memory that was not available in the used computers.

Figure 6.26 - German 17-node backbone network (DTAG), l: nodes with numbers, r: node distances to its destinations by (Hinz, 2009) [29]

ID DISTANCES (km) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

1 0 280 160 550 270 280 313 255 313 525 509 583 701 637 709 787 869 2 280 0 124 288 159 372 401 431 344 395 492 570 590 624 654 696 777 3 160 124 0 396 132 262 291 321 234 373 441 519 568 573 632 674 755 4 550 288 396 0 291 531 564 579 492 195 545 623 446 673 632 622 584 5 270 159 132 291 0 251 281 299 183 264 352 428 465 481 512 554 633 6 280 372 262 531 251 0 35 69 37 454 250 306 466 360 432 510 634 7 313 401 291 564 281 35 0 42 71 486 227 282 443 337 409 487 611 8 255 431 321 579 299 69 42 0 95 502 194 248 407 301 374 451 575 9 313 344 234 492 183 37 71 95 0 420 221 298 437 351 424 502 606

10 525 395 373 195 264 454 486 502 420 0 393 471 281 520 479 470 432 11 509 492 441 545 352 250 227 194 221 393 0 79 225 137 204 288 392 12 583 570 519 623 428 306 282 248 298 471 79 0 241 66 139 216 357 13 701 590 568 446 465 466 443 407 437 281 225 241 0 251 208 178 166 14 637 624 573 673 481 360 337 301 351 520 137 66 251 0 80 156 297 15 709 654 632 632 512 432 409 374 424 479 204 139 208 80 0 92 233 16 787 696 674 622 554 510 487 451 502 470 288 216 178 156 92 0 156 17 869 777 755 584 633 634 611 575 606 432 392 357 166 297 233 156 0

Table 6.5 – Distances (km) between GBN nodes

B-4

NODE ID

LINKS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0

2 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0

3 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0

4 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0

5 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0

6 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0

7 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0

8 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0

9 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0

10 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0

11 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 0

12 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0

13 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1

14 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0

15 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0

16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1

17 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0

Table 6.6 – Links of the GBN nodes (adjacency matrix)

B-5

B.3. Portugal Backbone Network (PBN or PRT)

The reference Portuguese backbone network of reference (PBN or PRT) is illustrated in figure

below.

Figure 6.27 – Portuguese Backbone Network (PBN) [30]

Link Source Link ID Designation Destination Link ID Designation Distance [km]

1 1 Alcácer do Sal 10 Évora 68

2 1 Alcácer do Sal 22 Setúbal 50

3 1 Alcácer do Sal 23 Sines 65

4 2 Aveiro 8 Coimbra 58

5 2 Aveiro 14 Leiria 113

6 2 Aveiro 19 Porto 67

7 3 Beja 10 Évora 76

8 3 Beja 11 Faro 140

9 4 Braga 5 Bragança 209

10 4 Braga 19 Porto 53

11 4 Braga 21 São João da Madeira 85

12 4 Braga 24 Viana do Castelo 47

13 5 Bragança 25 Vila Real 118

14 6 Caldas da Rainha 14 Leiria 54

15 6 Caldas da Rainha 15 Lisboa 88

16 7 Castelo Branco 13 Guarda 94

17 7 Castelo Branco 17 Portalegre 80

18 8 Coimbra 20 Santarém 136

19 8 Coimbra 21 São João da Madeira 84

20 8 Coimbra 26 Viseu 84

21 9 Elvas 10 Évora 83

22 9 Elvas 17 Portalegre 56

23 11 Faro 18 Portimão 62

http://www.av.it.pt/anp/on/figuras/portugal.jpg

B-6

24 12 Funchal 15 Lisboa 1050

25 12 Funchal 16 Ponta Delgada 1050

26 12 Funchal 18 Portimão 1010

27 13 Guarda 26 Viseu 73

28 14 Leiria 20 Santarém 70

29 15 Lisboa 16 Ponta Delgada 1500

30 15 Lisboa 20 Santarém 76

31 15 Lisboa 22 Setúbal 44

32 17 Portalegre 20 Santarém 144

33 18 Portimão 23 Sines 139

34 19 Porto 21 São João da Madeira 32

35 19 Porto 24 Viana do Castelo 70

36 25 Vila Real 26 Viseu 97

Table 6.7 - Links (Distances (km)) between PBN nodes – modelled - 26 nodes and 36 links

Information presented in Table 6.7 may also be compiled at adjacency matrix (Table 6.8).

B-7

Figure 6.28 - Links of the PRT nodes (adjacency matrix)

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B-8

Figure 6.29 - Distances (km) between PRT nodes

Alcáce

r do S

alAvei

roBe

jaBra

gaBra

gançaCal

das da

Rainh

aCas

telo B

rancoCo

imbra

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tarémSão

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eloVila R

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eu

12

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Alcáce

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119416

535173

291257

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168977

369196

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122339

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3070

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267166

21658

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113257

1502

235497

67189

47292

374146

156108

Beja

3119

4120

520558

276309

361182

76140

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300199

1540

203142

467226

442165

117541

535473

Braga

4416

125520

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283325

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417570

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252233

366151

5344

60653

29885

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47106

165

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ça5

535267

558209

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265285

431462

690134

6178

353486

1656

361726

206418

226521

603272

118189

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6173

166276

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125233

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9202

350227

57202

131227

254300

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291216

309325

265212

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445115

794

179241

1569

80325

270173

246276

358344

256186

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25758

361171

285125

1530

244246

411112

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74207

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173447

118136

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18084

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9159

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415431

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2440

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281

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204497

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139625

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19363

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227270

118361

371516

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1290

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24632

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226298

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44285

226202

24684

336346

492117

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50292

165401

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276242

176109

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420415

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Sines

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374117

483603

227358

324244

142138

929437

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(km)

C-1

Appendix C: Auxiliary Data Used for Gravitational Model

C.1. COST 239

In the gravitational model applied for COST 239 network, there were applied input data accordingly

Appendix B: and the subsequent tables and calculations. It was considered the municipal population for

the calculations, since it was estimated that for the optical network planning it was the most relevant

available information.

Node ID

City Populational Density ( /km2)

Urban Population

Municipal Population

0 Vienna 4326.1 1.867.960

1 Zurich 4500 396.027

2 Prague 1.280.508

3 Berlin 4100 3.671.000

4 Luxembourg 222.8 576.249

5 Amsterdam 4908 1351587 851.573

6 Copenhagen 7000 1295686 602.481

7 London 5518 9787426 8.673.713

8 Brussels 7025 1.175.173

9 Paris 21000 10601122 2.229.621

10 Milan 7500 1.368.590

Total: 22.692.895

Table 6.8 – Relevant populational data of COST 239 cities – populational density, urban population and municipal

population (data available at Google)

Node 0 1 2 3 4 5 6 7 8 9 10

0 0.0E+00 1.3E+06 2.7E+07 1.6E+07 1.2E+06 1.2E+06 9.0E+05 7.2E+06 1.7E+06 2.7E+06 3.5E+06

1 1.3E+06 0.0E+00 1.1E+06 2.0E+06 1.1E+06 5.0E+05 1.6E+05 3.8E+06 1.1E+06 2.4E+06 6.4E+06

2 2.7E+07 1.1E+06 0.0E+00 3.8E+07 1.3E+06 1.4E+06 1.2E+06 6.6E+06 1.9E+06 2.6E+06 2.3E+06

3 1.6E+07 2.0E+06 3.8E+07 0.0E+00 3.6E+06 7.0E+06 1.1E+07 2.6E+07 7.3E+06 7.1E+06 4.6E+06

4 1.2E+06 1.1E+06 1.3E+06 3.6E+06 0.0E+00 3.0E+06 3.9E+05 1.4E+07 1.4E+07 9.1E+06 1.6E+06

5 1.2E+06 5.0E+05 1.4E+06 7.0E+06 3.0E+06 0.0E+00 8.0E+05 4.0E+07 2.3E+07 6.9E+06 1.0E+06

6 9.0E+05 1.6E+05 1.2E+06 1.1E+07 3.9E+05 8.0E+05 0.0E+00 3.3E+06 8.2E+05 8.9E+05 4.0E+05

7 7.2E+06 3.8E+06 6.6E+06 2.6E+07 1.4E+07 4.0E+07 3.3E+06 0.0E+00 7.4E+07 8.9E+07 7.5E+06

8 1.7E+06 1.1E+06 1.9E+06 7.3E+06 1.4E+07 2.3E+07 8.2E+05 7.4E+07 0.0E+00 2.6E+07 1.9E+06

9 2.7E+06 2.4E+06 2.6E+06 7.1E+06 9.1E+06 6.9E+06 8.9E+05 8.9E+07 2.6E+07 0.0E+00 4.1E+06

10 3.5E+06 6.4E+06 2.3E+06 4.6E+06 1.6E+06 1.0E+06 4.0E+05 7.5E+06 1.9E+06 4.1E+06 0.0E+00

Table 6.9 – Results for Expected Traffic, 𝐸𝑖𝑗 (popi*popj /dij2) for COST and considering available data

(approximated values).

C-2

Node 0 1 2 3 4 5 6 7 8 9 10

0 0.0E+00 1.3E+06 2.8E+07 4.4E+07 4.5E+07 4.7E+07 4.7E+07 5.5E+07 5.6E+07 5.9E+07 6.2E+07

1 1.3E+06 1.3E+06 2.4E+06 4.4E+06 5.5E+06 6.0E+06 6.2E+06 1.0E+07 1.1E+07 1.3E+07 2.0E+07

2 2.7E+07 2.8E+07 2.8E+07 6.6E+07 6.7E+07 6.9E+07 7.0E+07 7.7E+07 7.8E+07 8.1E+07 8.3E+07

3 1.6E+07 1.8E+07 5.7E+07 5.7E+07 6.0E+07 6.7E+07 7.8E+07 1.0E+08 1.1E+08 1.2E+08 1.2E+08

4 1.2E+06 2.3E+06 3.7E+06 7.2E+06 7.2E+06 1.0E+07 1.1E+07 2.5E+07 3.9E+07 4.8E+07 5.0E+07

5 1.2E+06 1.7E+06 3.1E+06 1.0E+07 1.3E+07 1.3E+07 1.4E+07 5.4E+07 7.7E+07 8.3E+07 8.4E+07

6 9.0E+05 1.1E+06 2.3E+06 1.3E+07 1.4E+07 1.4E+07 1.4E+07 1.8E+07 1.9E+07 1.9E+07 2.0E+07

7 7.2E+06 1.1E+07 1.8E+07 4.4E+07 5.8E+07 9.8E+07 1.0E+08 1.0E+08 1.8E+08 2.7E+08 2.7E+08

8 1.7E+06 2.8E+06 4.6E+06 1.2E+07 2.6E+07 4.9E+07 4.9E+07 1.2E+08 1.2E+08 1.5E+08 1.5E+08

9 2.7E+06 5.1E+06 7.7E+06 1.5E+07 2.4E+07 3.1E+07 3.2E+07 1.2E+08 1.5E+08 1.5E+08 1.5E+08

10 3.5E+06 9.9E+06 1.2E+07 1.7E+07 1.8E+07 1.9E+07 2.0E+07 2.7E+07 2.9E+07 3.3E+07 3.3E+07

Table 6.10 – Results of cumulative expected traffic, 𝑐𝑖𝑗 for COST (cumulative sum, at each table row, of results

obtained in Table 6.9) (approximated values).

Node 0 1 2 3 4 5 6 7 8 9 10

0 0.0E+00 2.1E-02 4.3E-01 2.6E-01 1.9E-02 1.9E-02 1.4E-02 1.2E-01 2.7E-02 4.3E-02 5.5E-02

1 6.6E-02 0.0E+00 5.3E-02 1.0E-01 5.7E-02 2.5E-02 8.1E-03 1.9E-01 5.4E-02 1.2E-01 3.2E-01

2 3.2E-01 1.3E-02 0.0E+00 4.6E-01 1.6E-02 1.7E-02 1.5E-02 7.9E-02 2.2E-02 3.1E-02 2.7E-02

3 1.3E-01 1.6E-02 3.1E-01 0.0E+00 2.9E-02 5.6E-02 8.8E-02 2.1E-01 5.9E-02 5.8E-02 3.8E-02

4 2.4E-02 2.3E-02 2.7E-02 7.2E-02 0.0E+00 6.0E-02 7.9E-03 2.9E-01 2.8E-01 1.8E-01 3.2E-02

5 1.4E-02 5.9E-03 1.7E-02 8.3E-02 3.5E-02 0.0E+00 9.5E-03 4.7E-01 2.7E-01 8.2E-02 1.2E-02

6 4.5E-02 8.1E-03 6.2E-02 5.5E-01 2.0E-02 4.0E-02 0.0E+00 1.7E-01 4.1E-02 4.5E-02 2.0E-02

7 2.6E-02 1.4E-02 2.4E-02 9.6E-02 5.3E-02 1.5E-01 1.2E-02 0.0E+00 2.7E-01 3.3E-01 2.7E-02

8 1.1E-02 7.1E-03 1.2E-02 4.8E-02 9.2E-02 1.5E-01 5.4E-03 4.9E-01 0.0E+00 1.7E-01 1.3E-02

9 1.8E-02 1.6E-02 1.7E-02 4.7E-02 6.1E-02 4.6E-02 5.9E-03 5.9E-01 1.7E-01 0.0E+00 2.7E-02

10 1.0E-01 1.9E-01 6.8E-02 1.4E-01 4.8E-02 3.0E-02 1.2E-02 2.2E-01 5.7E-02 1.2E-01 0.0E+00

Table 6.11 – Results of probability of expected traffic, 𝑝𝑖𝑗 ( (popi*popj /dij2) / 𝑐𝑖𝑗) for COST.

Finally, there were obtained cumulative probabilities for the expected traffic accordingly Table 6.12.

Node 0 1 2 3 4 5 6 7 8 9 10

0 0.000 0.021 0.447 0.707 0.726 0.745 0.760 0.875 0.902 0.945 1.000

1 0.066 0.066 0.120 0.221 0.277 0.302 0.310 0.502 0.555 0.676 1.000

2 0.319 0.332 0.332 0.793 0.809 0.826 0.841 0.919 0.942 0.973 1.000

3 0.131 0.148 0.459 0.459 0.487 0.544 0.632 0.846 0.904 0.962 1.000

4 0.024 0.047 0.074 0.146 0.146 0.206 0.214 0.502 0.784 0.968 1.000

5 0.014 0.020 0.037 0.119 0.155 0.155 0.164 0.638 0.907 0.988 1.000

6 0.045 0.053 0.116 0.667 0.687 0.728 0.728 0.894 0.935 0.980 1.000

7 0.026 0.040 0.064 0.161 0.213 0.360 0.372 0.372 0.645 0.973 1.000

8 0.011 0.018 0.030 0.079 0.171 0.321 0.326 0.818 0.818 0.987 1.000

9 0.018 0.034 0.051 0.098 0.159 0.204 0.210 0.803 0.973 0.973 1.000

10 0.104 0.297 0.365 0.504 0.553 0.583 0.595 0.819 0.876 1.000 1.000

Table 6.12 - Cumulative probability of expected traffic obtained accordingly proposed formulation for gravity model for the modelled distances, for COST.

C-3

C.2. GBN

In gravitational model applied for GBN network, there were applied input data accordingly Appendix

C and the subsequent tables and calculations. It was considered the municipal population for the

calculations, since it was estimated that for the optical network planning it was the most relevant

available information.

Node ID City Population

1 Norden 25 117

2 Hamburg 1 787 408

3 Bremen 557 464

4 Berlin 3 520 031

5 Hannover 532 163

6 Essen 582 624

7 Dusseldorf 612 178

8 Koln 1 060 582

9 Dortmund 586 181

10 Leipzig 560 472

11 Frankfurt 732 688

12 Mannheim 305 780

13 Nurnberg 509 975

14 Karlsruhe 307 755

15 Stuttgart 623 738

16 Ulm 122 636

17 Munchen 1 450 381

Total: 13.877.173

C-4

C.3. PRT

Follows relevant data used to perform simulations with PRT network [31].

Node number City (node location) Population

1 Alcácer do Sal 26.479

2 Aveiro 297.233

3 Beja 117.868

4 Braga 403.953

5 Bragança 108.547

6 Caldas da Rainha 357.706

7 Castelo Branco 81.814

8 Coimbra 436.948

9 Elvas 32.336

10 Évora 154.536

11 Faro 237.884

12 Funchal 254.368

13 Guarda 216.188

14 Leiria 286.309

15 Lisboa 2.050.793

16 Ponta Delgada 243.862

17 Portalegre 72.102

18 Portimão 201.733

19 Porto 1.719.702

20 Santarém 238.715

21 São João da Madeira 65.862

22 Setúbal 782.886

23 Sines 67.295

24 Viana do Castelo 232.178

25 Vila Real 192.046

26 Viseu 254.631

Total: 9.133.974

Table 6.13 – Population for gravitational model with PRT network [31]

C-5

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

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23

24

25

26

1

0

30

7

11

9

41

6

53

5

17

3

29

1

25

7

15

9

68

16

8

97

7

36

9

19

6

95

14

8 2

15

7

20

4

36

3

12

2

33

9

50

65

43

7

43

2

36

9

2 30

7 0

41

2

12

5

26

7

16

6

21

6

58

30

6

30

8

46

1

11

4 3

15

8

11

3

25

7

15

0 2

23

5

49

7

67

18

9

47

29

2

37

4

14

6

15

6

10

8

3 11

9

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2 0

52

0

55

8

27

6

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9

36

1

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2

76

14

0

98

8

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41

5

43

1

23

3

18

0

24

4 0

83

27

8

11

0 4

25

8

24

0

20

9

15

9 3

56

22

8

36

1

17

7

33

6

17

6

24

4

43

5

42

1

35

2

10

68

30

8

76

41

7

46

2

20

9

21

1

24

6

83

0

20

2

10

4 1

29

4

20

4

14

2

15

4 2

11

0

23

7

37

1

12

7

34

6

10

9

14

2

44

5

41

4

38

8

11

16

8

46

1

14

0

57

0

69

0

31

4

44

5

41

1

27

8

20

2 0

93

2

52

1

34

9

24

8

15

2 6

29

9

62

51

6

27

5

49

2

21

4

13

8

59

0

58

5

52

2

12

97

7

11

4 3

98

8

12

3 2

13

4 6

10

1 6

11

5 7

11

2 1

11

0 4

10

4 1

93

2 0

12

1 7

10

6 1

10

5 0

10

5 0

11

0 3

10

1 0

11

8 8

10

3 0

11

7 3

96

4

92

9

12

2 3

12

4 8

12

0 7

13

36

9

15

8

38

7

25

2

17

8

29

0

94

15

4

25

8

29

4

52

1

12

1 7

0

15

8

32

0

15

9 6

18

8

56

0

19

7

18

8

17

3

35

5

43

7

27

2

16

7

73

14

19

6

11

3

30

0

23

3

35

3

54

17

9

74

24

0

20

4

34

9

10

6 1

15

8 0

13

2

14

5 8

16

9

37

6

18

0

70

15

6

16

8

25

3

25

5

24

9

18

7

15

95

25

7

19

9

36

6

48

6

88

24

1

20

7

20

9

14

2

24

8

10

5 0

32

0

13

2 0

15

0 0

23

0

28

3

31

3

76

28

8

44

16

0

38

7

38

1

31

9

16

14

8 2

15

0 2

15

4 0

15

1 5

16

5 6

14

2 9

15

6 9

14

9 5

15

9 3

15

4 2

15

2 6

10

5 0

15

9 6

14

5 8

15

0 0

0

15

6 2

14

9 0

14

9 1

14

6 7

14

9 7

14

5 0

14

6 0

14

8 4

15

6 6

15

5 4

17

15

7

23

5

20

3

34

4

36

1

20

2

80

17

3

56

11

0

29

9

11

0 3

18

8

16

9

23

0

15

6 2

0

24

9

29

0

14

4

26

6

17

6

24

5

36

4

35

1

28

1

18

20

4

49

7

14

2

60

6

72

6

35

0

32

5

44

7

22

8

23

7

62

10

1 0

56

0

37

6

28

3

14

9 0

24

9 0

55

1

31

0

52

7

24

9

13

9

62

5

62

0

55

7

19

36

3

67

46

7

53

20

6

22

7

27

0

11

8

36

1

37

1

51

6

11

8 8

19

7

18

0

31

3

14

9 1

29

0

55

1 0

24

6

32

34

9

43

1

70

93

15

1

20

12

2

18

9

22

6

29

8

41

8

57

17

3

13

6

17

7

12

7

27

5

10

3 0

18

8

70

76

14

6 7

14

4

31

0

24

6 0

22

0

11

8

18

9

31

8

31

3

25

0

21

33

9

47

44

2

85

22

6

20

2

24

6

84

33

6

34

6

49

2

11

7 3

17

3

15

6

28

8

14

9 7

26

6

52

7

32

22

0 0

32

2

40

4

11

2

11

3

12

5

22

50

29

2

16

5

40

1

52

1

13

1

27

6

24

2

17

6

10

9

21

4

96

4

35

5

16

8

44

14

5 0

17

6

24

9

34

9

11

8

32

2 0

12

5

42

0

41

5

35

2

23

65

37

4

11

7

48

3

60

3

22

7

35

8

32

4

24

4

14

2

13

8

92

9

43

7

25

3

16

0

14

6 0

24

5

13

9

43

1

18

9

40

4

12

5 0

50

3

49

7

43

5

24

43

7

14

6

54

1

47

27

2

25

4

34

4

19

2

43

5

44

5

59

0

12

2 3

27

2

25

5

38

7

14

8 4

36

4

62

5

70

31

8

11

2

42

0

50

3 0

16

1

22

3

25

43

2

15

6

53

5

10

6

11

8

30

0

25

6

18

0

42

1

41

4

58

5

12

4 8

16

7

24

9

38

1

15

6 6

35

1

62

0

93

31

3

11

3

41

5

49

7

16

1 0

97

26

36

9

10

8

47

3

16

5

18

9

23

8

18

6

84

35

2

38

8

52

2

12

0 7

73

18

7

31

9

15

5 4

28

1

55

7

15

1

25

0

12

5

35

2

43

5

22

3

97

0

Table 6.14 – Distance (km) between cities used in the gravitational model for the PRT network

optical transport networks with flexi-grid planning...canais com elevadas capacidades que poderão...

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