rwa algorithm design and performance analysis for all...

RWA Algorithm Design and PerformanceAnalysis for All-Optical Networks Subject

to Physical Impairments

A Dissertation

Presented to

the faculty of the School of Engineering and Applied Science

University of Virginia

In Partial Fulfillment

of the requirements for the Degree

Doctor of Philosophy

(Electrical Engineering)

by

Jun He

May 2008

c© Copyright by

Jun He

All rights reserved

May 2008

APPROVAL SHEET

The dissertation is submitted in partial fulfillment of the

requirements for the degree of

Doctor of Philosophy

(Electrical Engineering)

JUN HE (author)

This thesis has been read and approved by the examining Committee:

Prof. Maıte Brandt-Pearce (advisor)

Prof. Stephen G. Wilson (chair)

Prof. Malathi Veeraraghavan

Prof. Toby Berger

Prof. Suresh Subramaniam

Accepted for the School of Engineering and Applied Science:

James H. Aylor (Dean)

May 2008

Abstract

Thanks to the rapid development of optical signal processing functions (e.g., am-

plification, filtering, and dispersion compensation) for fiber communication systems,

and novel routing techniques and switching node architectures, highly flexible and

transparent so-called “wavelength routed all-optical network” solutions have emerged.

All-optical networks eliminate the restrictions incurred by periodic electronic regen-

eration, as signals remain in the optical domain from end-to-end through a lightpath.

As an optical signal propagates along a lightpath to its destination in wavelength-

routed optical networks, the signal’s quality of transmission (QoT) is degraded by

physical impairments, such as crosstalk, which is induced by other signals traversing

the same optical crossconnects, demultiplexers, and fiber segments. Consequently,

the signal’s bit error rate at the destination’s receiver might become unacceptably

high. Thus optical fiber components and intermediate switching nodes can be the

dominant reason calls are blocked in wide-area all-optical wavelength division mul-

tiplexed networks. Moreover, estimating the impact of the physical impairments on

the quality of a lightpath before provisioning it can cause a significant delay, which

also affects the performance of networks because the latency worsens the contention

and decreases the network utilization.

In this doctoral dissertation, we first provide a general mathematical formulation

to the optimal routing and wavelength assignment (RWA) in impaired optical net-

works. Several dominant degradations from the physical layer are exemplified and

incorporated in the general formulation. Realizing that routing algorithms and wave-

length assignment algorithms can both be powerful tools used to mitigate the effect

of physical impairments, we study the problem of designing efficiently routing and

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wavelength assignment algorithms in all-optical networks with physical impairments.

We consider dynamic traffic arrival in centralized and distributed networks. Several

adaptive routing policies accounting for the quality of transmission in optical networks

are proposed to efficiently and intelligently find a feasible lightpath. In particular, we

propose using the noise and crosstalk variance along the route as a selection criterion.

In addition, several spectrum allocation techniques are presented to alleviate physi-

cal impairments and also decrease the processing delay due to the QoT estimation.

Our techniques are based on the notion of wavelength ordering, so that wavelengths

less likely to cause degradation are used first. To thoroughly understand the RWAs

and evaluate their performance incorporating multiple physical layer impairments, we

present an analytical technique and compare it to simulation results. We are able to

predict the network behavior correctly on various network topologies.

We then investigate the impact of processing delay induced from QoT estimation.

Simulations presented show that our design successfully remove not only part of the

physical degradation but also decrease the delay due to QoT estimation. The results

show that RWA algorithms should be chosen depending on the traffic load and the

requirements of the application in order to achieve the best performance.

Acknowledgements

I want to show my deepest gratitude to my advisor, Maıte Brandt-Pearce, who

has guided me throughout my graduate studies. Her insights into research have

enlightened me through many problems and illuminated my way in my research. She

has helped me improve my research skills, has always encouraged me, and has given

me good ideas when I have had problems. Thanks to her help, I have found many

interests in the research process. She has assisted me not only in the academic arena,

but also in the improvement of my English writing skills and speaking abilities. I

would like to thank her for her generous contribution of time and her commitment to

the success of my dissertation; I really appreciate all she has done on my behalf.

I also want to gratefully thank Prof. Wilson, Prof. Subramaniam, Prof. Veer-

araghavan, and Prof. Berger for being my dissertation committee members and for

their generous help in my studies and research.

I want to thank my former colleague, Dr. Yvan Pointurier, who has given me much

help in my research and on my dissertation; he has given me much useful information

and suggestions that have benefited me a great deal.

I want to acknowledge my colleagues, Tao Li, Qianling Cao, and Kirtan Modi; I

also want to thank the other colleagues on my team. The weekly meetings have in-

spired me and given me many new ideas in my studies. I know exactly how important

a good environment is to foster one’s academic growth.

My thanks also go to the department of Electrical and Computer Engineering,

University of Virginia, for giving me the opportunity to study in a place where I have

met many great professors. The academic quality of life here is one of the greatest

treasures of my entire life. I also appreciate the financial support of the research from

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the National Science Foundation.

Finally, I would like to thank my wife Si. She always supports me with her care

and encouragement, staying by my side in my life and in my studies. I also thank

to my parents and my brother. Although we have a long distance relationship, they

have always supported me. I feel very lucky to have them as my family. Their love

helps me focus on my research.

To all these people whom I respect, I dedicate this paper.

Contents

1 Introduction 1

1.1 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Mathematical Formulation of the RWA Problem with QoT Con-

straints 9

2.1 Model of Physical Impairments . . . . . . . . . . . . . . . . . . . . . 10

2.1.1 Origins of Physical Impairments . . . . . . . . . . . . . . . . . 11

2.1.2 Estimation of Impact of Physical Impairments . . . . . . . . . 13

2.2 Problem Formulation to RWA with QoT Constraints . . . . . . . . . 17

2.2.1 General Mathematical Formulation . . . . . . . . . . . . . . . 18

2.2.2 QoT Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2.3 QCQP Approximation . . . . . . . . . . . . . . . . . . . . . . 21

2.3 Simulation Results and Discussion . . . . . . . . . . . . . . . . . . . . 22

2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3 Suboptimal RWA Considering Physical Impairments 27

3.1 Routing with QoT Constraints . . . . . . . . . . . . . . . . . . . . . . 28

3.1.1 Distributed Network Architecture . . . . . . . . . . . . . . . . 30

3.1.2 QoT-Aware Routing Algorithms . . . . . . . . . . . . . . . . . 32

3.1.2.1 Routing Based on QoT Cost Criterion . . . . . . . . 32

3.1.2.2 Other Routing Algorithms with QoT Constraints . . 35

3.1.3 Simulation Results and Discussion . . . . . . . . . . . . . . . . 36

3.1.3.1 Blocking Probability vs. Network Load . . . . . . . . 37

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3.1.3.2 Blocking Probability vs. Node Crosstalk . . . . . . . 39

3.1.3.3 Number of Wavelengths Needed vs. Traffic Load . . 41

3.1.3.4 Maximum Traffic Loads for Different Crosstalk Levels 43

3.2 WA Algorithms Considering Physical Impairments . . . . . . . . . . . 44

3.2.1 Static Wavelength Ordering . . . . . . . . . . . . . . . . . . . 45

3.2.2 Wavelength Spectrum Separation . . . . . . . . . . . . . . . . 49

3.2.3 Adaptive Wavelength Ordering . . . . . . . . . . . . . . . . . 51

3.2.4 Simulation Results and Discussion . . . . . . . . . . . . . . . . 55

3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4 Analytical Model for RWA with QoT Constraints 61

4.1 Proposed Analytical Framework for FF WA with QoT Constraints . . 63

4.2 Wavelength Decomposition Approach for Computing Wavelength Block-

ing Probabilities in All-Optical Networks . . . . . . . . . . . . . . . . 67

4.2.1 Wavelength Blocking Probability in a Single Wavelength . . . 67

4.2.2 Computing the Overall Wavelength Blocking Probability by Us-

ing the Overflow Model . . . . . . . . . . . . . . . . . . . . . . 68

4.3 RWA Analytical Model with QoT Constraints . . . . . . . . . . . . . 70

4.3.1 Counting QoT Blocking Events . . . . . . . . . . . . . . . . . 72

4.3.2 Approximation to Compute QoT Blocking . . . . . . . . . . . 76

4.3.3 Total Blocking Probability for QoT-Aware RWA . . . . . . . . 77

4.3.4 Total Blocking Probability for QoT-Guaranteed RWA . . . . . 79

4.3.5 Impact of Static Wavelength Ordering . . . . . . . . . . . . . 79

4.4 Numerical Examples and Validation by Simulations . . . . . . . . . . 81

4.4.1 4-Node Tandem Network . . . . . . . . . . . . . . . . . . . . . 81

4.4.1.1 Performance of FF and FFwO WAs . . . . . . . . . 82

4.4.1.2 Results of the Approximation Method . . . . . . . . 84

4.4.2 Validation Via Simulation in Other Networks . . . . . . . . . 85

4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

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5 Impact of Complexity of QoT Estimation on RWA 90

5.1 Impact of QoT Complexity . . . . . . . . . . . . . . . . . . . . . . . . 92

5.1.1 Centralized Network Architecture . . . . . . . . . . . . . . . . 92

5.1.2 Setup Latency . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.1.3 RWA with QoT and Latency Constraints . . . . . . . . . . . . 96

5.2 Simulations and Results . . . . . . . . . . . . . . . . . . . . . . . . . 98

5.2.1 Blocking vs. Processing Time . . . . . . . . . . . . . . . . . . 101

5.2.2 Blocking vs. Network Traffic Load . . . . . . . . . . . . . . . 108

5.2.3 Blocking vs. Crosstalk Level . . . . . . . . . . . . . . . . . . . 116

5.2.4 Blocking vs. Path Length . . . . . . . . . . . . . . . . . . . . 123

5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

6 Conclusions and Future Work 129

6.1 Main Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6.2 Summary of Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . 130

6.3 Conclusions and Recommendations . . . . . . . . . . . . . . . . . . . 132

6.4 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

List of Figures

1.1 Example illustrating sources of adjacent-port crosstalk and switching

crosstalk in a single switching node. A WRS is an optical component

called a wavelength-routed switch (WRS); CH refers to a channel; LP

refers to a lightpath. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 A generic lightpath structure with n + 1 nodes and n links. . . . . . . 11

2.2 A generic all-optical switching node. optical add-drop multiplexers

(OADMs) are omitted here. . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Another possible adjacent port crosstalk. A WRS is a wavelength-

routed switch; CH refers to a channel. . . . . . . . . . . . . . . . . . . 13

2.4 Network topologies used in simulation. (a) 6-node mesh network, (b)

10-node ring network, and (c) 8-node tandem network. . . . . . . . . 23

2.5 Number of consecutive wavelengths needed for the six schemes with 12

random requests in 6-node mesh network, 10-node ring network, and

8-node tandem network. . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.6 Average number of consecutive wavelengths needed for the six schemes

with different number of random requests in 10-node ring network. . . 25

2.7 Outage rate for the six schemes with different number of random re-

quests in 10-node ring network with a limited of 4 wavelengths. . . . 26

3.1 Structure for distributed network models, WRS refers to a wavelength

routed switch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2 Flow chart of adaptive routing algorithms in the source-RWA scheme. 33

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3.3 Topology of a downsized version of the NSF network with 14 nodes

and 21 bidirectional links, using link lengths 1/10 of their original size.

The numbers on the links represent number of spans along the link.

Each span is around 75 km long. . . . . . . . . . . . . . . . . . . . . 36

3.4 Blocking probability with QoT constraints for the various routing al-

gorithms in different traffic loads using FF WA; Xadj = −20 dB and

Xsw = −40 dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38


gorithms in different traffic loads using RP WA; Xadj = −20 dB and

Xsw = −40 dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.6 Blocking probability with QoT constraints for the various routing algo-

rithms for different levels of crosstalk using FF WA; the network load

is fixed at 156 Erlangs. . . . . . . . . . . . . . . . . . . . . . . . . . . 40


gorithms for different levels of crosstalk using RP WA; the network

load is fixed at 156 Erlangs. . . . . . . . . . . . . . . . . . . . . . . . 41

3.8 Flow chart of AFFwSS algorithm in the hop-by-hop-RWA scheme. . . 52

3.9 An illustrative example with only one node. LP1 from source node 1

and LP3 from source node 2 are directed to destination node 1 and

LP2 from source node 1 and LP4 from source node 2 are directed to

destination node 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.10 Topology of network used for simulation . . . . . . . . . . . . . . . . 56

3.11 Blocking probability for Xadj = −25 dB and a load of 22.5 Erlangs.

Hth = 122, 43, 24, 12, 0, 0, 0 for Xsw = −55,−50,−45,−40,−35,−30,−25dB, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.12 Blocking probability of FF, RP, FFwO, FFwSS, and AFFwSS for

Xsw = −30 dB and Xadj = −20 dB. Hth = 0. . . . . . . . . . . . . . . 58

3.13 Blocking probability of FF, RP, FFwO, FFwSS, and AFFwSS for

Xsw = −40 dB and Xadj = −25 dB. Hth = 12. . . . . . . . . . . . . . 58

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4.1 Layered network model for wavelength-routed all-optical networks (WRONs). 64

4.2 First layer in layered network model for QoT-aware RWA algorithms. 66

4.3 Topology of 4-node tandem network . . . . . . . . . . . . . . . . . . . 74

4.4 Topology of 7-node ring network used for analysis and simulation . . 82

4.5 FF WA blocking probability computed using the exact analysis and

simulation for the 4-node tandem network, 5 wavelengths, Xadj = −20

dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.6 FFwO WA blocking probability computed using the exact analysis

and simulation for the 4-node tandem network, 5 wavelengths with

wavelength ordering 1, 5, 2, 4, 3, Xadj = −20 dB. . . . . . . . . . . 84

4.7 FF WA blocking probability computed using the approximate method

and simulation for the 4-node tandem network, 5 wavelengths, Xadj =

−20 dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.8 FFwO WA blocking probability computed using the approximate method

and simulation for the 4-node tandem network, 5 wavelengths with

wavelength ordering 1, 5, 2, 4, 3, Xadj = −20 dB. . . . . . . . . . . 86


and simulation for the 7-node ring network, 5 wavelengths, Xadj = −20

dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87


and simulation for the 7-node ring network, 5 wavelengths with wave-

length ordering 1, 5, 2, 4, 3, Xadj = −20 dB. . . . . . . . . . . . . . 87


and simulation for the NSF network, 6 wavelengths, Xadj = −20 dB. . 88


and simulation for the NSF network, 6 wavelengths with wavelength

ordering 1, 6, 3, 5, 2, 4, Xadj = −20 dB. . . . . . . . . . . . . . . . 88

5.1 All-optical network node architecture including control plane and data

plane. λi represents the ith wavelength. . . . . . . . . . . . . . . . . . 93

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5.2 The timeline of a call admission procedure for request k in centralized

WDM networks if Da(k) < Tmax. . . . . . . . . . . . . . . . . . . . . 96

5.3 Flowchart of QoS-aware WA algorithms using SP or ALT routing in-

corporating both QoT and latency thresholds. . . . . . . . . . . . . . 97

5.4 Network topologies used in simulation. (a) 16-node mesh toroid net-

work (MESHnet) with identical link length of 100 kilometers and (b)

Topology of a downsized version of the NSF network (NSFnet), using

link lengths 1/10 of their original size, with 14 nodes and 21 bidirec-

tional links. The number on the links represents the length of the links

in kilometers. Each link is considered as a single span. . . . . . . . . 100

5.5 Simulation of Ptotal with QoT and latency constraints for the six WA

algorithms when SP routing is applied; (a) 16-node mesh toroid net-

work with Xadj = −20 dB, Xsw = −40 dB, and total traffic load of 160

Erlangs; (b) NSF network with Xadj = −25 dB, Xsw = −45 dB, and

total traffic load of 100 Erlangs. . . . . . . . . . . . . . . . . . . . . . 103

5.6 Simulation of PT with QoT and latency constraints for the six WA




total traffic load of 100 Erlangs. Missing points or lines indicate that

the data fall below the ordinate values plotted. . . . . . . . . . . . . . 104

5.7 Simulation of PQoT with QoT and latency constraints for the six WA




total traffic load of 100 Erlangs. . . . . . . . . . . . . . . . . . . . . . 105

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algorithms when ALT routing is applied; (a) 16-node mesh toroid net-


















algorithms when SP routing is applied, using τ = 7×10−6; (a) 16-node

mesh toroid network with Xadj = −20 dB and Xsw = −40 dB; (b) NSF

network with Xadj = −25 dB and Xsw = −45 dB. Missing points or

lines indicate that the data fall below the ordinate values plotted. . . 112







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algorithms when ALT routing is applied, using τ = 7 × 10−6; (a) 16-

node mesh toroid network with Xadj = −20 dB and Xsw = −40 dB; (b)

NSF network with Xadj = −25 dB and Xsw = −45 dB. Missing points

or lines indicate that the data fall below the ordinate values plotted. . 115














algorithms when SP routing is applied, using τ = 7 × 10−6; (a) 16-

node mesh toroid network with Xadj = −20 dB and traffic load of 160

Erlangs; (b) NSF network with Xadj = −25 dB and traffic load of 100

Erlangs. Missing points or lines indicate that the data fall below the

ordinate values plotted. . . . . . . . . . . . . . . . . . . . . . . . . . . 120

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5.23 Total blocking probability with QoT and latency constraints for dif-

ferent routing path length for the six WA algorithms when SP routing

is applied, using τ = 7 × 10−6; (a) 16-node mesh toroid network with

Xadj = −20 dB, Xsw = −40 dB, and traffic load of 160 Erlangs; (b)

NSF network with Xadj = −25 dB, Xsw = −45 dB, and traffic load of

100 Erlangs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

List of Tables

2.1 Parameter Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1 Network Simulation Parameters . . . . . . . . . . . . . . . . . . . . . 36

3.2 Number of wavelengths needed (W ) for Ptotal ≤ 10−3, Xsw = −40 dB,

Xadj = −20 dB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.3 Maximum traffic load for different levels of crosstalk when W = 32 and

Ptotal ≈ 10−3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.4 Channel status, Xsw = −27 dB and Xadj = −30 dB. Hth = 0.1 . . . . 54

4.1 Routing table including Nadjmax for Fig. 4.3 . . . . . . . . . . . . . . . 74

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List of Acronyms

AFFwSS adaptive FF with spectrum separation

AGC automatic gain controlled

ALT fixed alternate

ASE amplified spontaneous emission

BER bit-error-rate

BPP Bernoulli-Poisson-Pascal

CAC connection admission control

DC dispersion compensator

EDFA Erbium-doped fiber amplifier

FCFS first-come, first-served

FF first fit

FFwO FF with ordering

FFwSS FF with wavelength spectrum separation

FH fewest number of hops

FR fixed routing based on fewest number of hops

FWM four-wave mixing

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ILP integer linear programming

LP lightpath

LV least variance

MEMS micro-electro-mechanical systems

NP nondeterministic polynomial-time

NSF National Science Foundation

OADM optical add-drop multiplexer

OEO optical-electro-optical

Opt-RWA optimal routing and wavelength assignment

Opt-WA optimal wavelength assignment

OXC optical crossconnect

PMD polarization mode dispersion

QCQP quadratically constrained quadratic program

QM Q-maximizing

QoS quality of service

QoT quality of transmission

RP random pick

RWA routing and wavelength assignment

SD shortest distance

SP fixed shortest path

s-d source-destination

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WA wavelength assignment

WDM wavelength division multiplexed

WRON wavelength-routed all-optical network

WRS wavelength-routed switch

XPM cross-phase modulation

Chapter 1

Introduction

Wavelength-routed all-optical wavelength division multiplexed (WDM) networks

have been proposed as a promising solution to satisfy society’s dramatically increas-

ing network throughput demand. In today’s transport networks, which operate at

several tens of Gigabits per second, electronic switches requiring optical-electro-

optical (OEO) conversion have become complex and costly [1]. These electronic

switches are becoming a bottleneck when a network must sustain a system-wide ca-

pacity of several tens of terabits per second, making it necessary to replace them with

all-optical switches where no electric conversion is used [1]. As discussed in [1–4], it

is possible to introduce highly flexible and transparent optical network solutions that

eliminate the restrictions incurred by periodic OEO regenerators. Deploying networks

utilizing all-optical switches is promising yet also quite challenging as many novel

problems must be anticipated [2, 5]. One of the major issues in designing all-optical

networks is to determine how to best assign lightpaths to call requests such that the

impact of physical-layer impairments and delay is limited. In this dissertation, we

study how to mitigate crosstalk as well as other physical impairments using routing

and wavelength assignment (RWA) algorithms that consider the impact of physical

degradations. We design and evaluate adaptive routing and wavelength assignment

1

2

techniques through simulations and analytical modeling.

In a wavelength-routed all-optical network (WRON), a signal is transmitted by

first establishing a call or lightpath (LP), i.e., a route from the source to the destination

consisting of one or more fiber links. In this dissertation, no wavelength conversion

is assumed as these devices are still in experimental phases of development. Thus,

the data signal is carried by a single chosen wavelength in the optical domain over

the entire lightpath, often traveling through a number of intermediate nodes. This

transparency greatly simplifies the way that heterogeneous users share network re-

sources [6]. For example, analog and digital signals can be carried simultaneously in

the networks by different wavelengths. Moreover, different signal modulation formats

and transmission bit rates can be supported simultaneously in all-optical networks.

The costs of maintenance at the intermediate nodes decrease greatly because no net-

work reconfiguration is needed when the source and destination are upgraded. Thus,

the users decide upon their hardware and the network provides bandwidth on de-

mand. Last but not least, the price of optical devices is decreasing and is expected

to become cheaper than the cost of their electrical counterparts at similarly high bit

rates.

Another key feature of WRONs is the ability to send data with good quality

of transmission (QoT) over hundreds of kilometers (QoT is measured by bit-error-

rate (BER) in this dissertation). However, the data signal propagating through

a large network encounters many physical impairments such as amplified sponta-

neous emission (ASE) noise from Erbium-doped fiber amplifiers (EDFAs) and node

crosstalk. These interferences limit the QoT as networks expand, wavelength den-

sity increases, and load increases [7, 8]. Physical impairments may cause the quality

of the optical signal to degrade and become so poor that its QoT is unacceptably

poor. The lessons learned from experiments at MIT Lincoln Laboratory show that

crosstalk from wavelength-selective elements is a major concern [6]. Moreover, the

3

switchingfabriccrosstalk

WRS

WRS

crosstakadjacent−port

LP3

λ4λ2 λ3λ1

CH1 CH2 (crosstalk)CH2(λ2)

CH2 CH1 (crosstalk)

CH1

CH2

CH1 CH2 CH3 CH4

CH1 (λ1)

CH2

CH1

crosstalk from LP3

CH1 (λ1)

LP2

LP1

Figure 1.1: Example illustrating sources of adjacent-port crosstalk and switchingcrosstalk in a single switching node. A WRS is an optical component called a WRS;CH refers to a channel; LP refers to a lightpath.

inappropriate assignment of new lightpaths may cause unacceptable degradation on

existing communications. The highly intense computation from the QoT (BER) es-

timation induces a high processing delay to further degrade the system performance

and decrease the link’s utilization. More details of the QoT model are presented in [9]

and reviewed in Chapter 2.

Fig. 1.1 presents an example showing the two main sources of node crosstalk.

In the switching fabric, a small fraction of one signal is sent to the wrong output

port at the same wavelength, producing switching crosstalk. In Fig 1.1, a part of the

LP3’s signal becomes switching crosstalk when LP2 and LP3 meet during wavelength

switching.

The other source of crosstalk, adjacent-port crosstalk, occurs when a portion of

the power from adjacent wavelengths cannot be entirely filtered out. In Fig. 1.1,

this happens when a proportion of LP1 injects crosstalk on LP2 as LP1 and LP2

are multiplexed together in the output. The crosstalk power level is wavelength

dependent, with crosstalk from immediately adjacent wavelengths more powerful than

crosstalk from those separated by one or more wavelengths. Thus, we only consider

4

the first two channels adjacent to the channel of interest as sources of adjacent-port

crosstalk.

Once the network infrastructure is built and buried, it is difficult to reduce phys-

ical impairments via hardware solutions, at the physical layer. Rather, RWA has

emerged as a best method to reduce physical impairments in WRON at the network

layer. The function of RWA algorithms is to find and assign a lightpath to the incom-

ing requests in order to maximize the network performance [10]. Suppose for instance

that, in Fig. 1.1, LP1 is already established, but not LP2 and LP3. Routing algo-

rithms can avoid the depicted node, which experiences high crosstalk, and re-route

the other requests LP2 and LP3 through paths with better QoT. Alternately, the

WA algorithm could intelligently select another wavelengths when assigning an wave-

length to LP2, such as wavelength 4 (λ4), which is unused and far from wavelength 2

in the wavelength spectrum.

Conventional studies on RWA have proposed many algorithms for establishing

lightpaths without considering any physical impairments [10–14]. The RWA algo-

rithms find available routes and wavelengths and assign them to the requests. These

techniques normally are evaluated by using the blocking probability. A blocking event,

called wavelength blocking, occurs when a lightpath cannot be set up due to the short-

age of a free route or a jointly free wavelength along the route.

Because of the impact of physical impairments, a call/request can also be blocked

in WRONs if the lightpath picked by the RWA has unsatisfactory poor QoT (or,

equivalently, worse BER). Such an event is called a QoT blocking. The impact of the

QoT can affect the choice of RWA algorithms. It is well known that wavelength block-

ing when using the random pick (RP) WA algorithm (choosing randomly amongst

the available wavelengths) is worse than that when the first fit (FF) WA algorithm

(choosing the free wavelength with the lowest index) is selected [10]. However, RP

WA is a QoT-friendly algorithm because it tends to geographically spread wavelength

5

use across the network such that crosstalk effects are not likely to be as severe [8].

Therefore, the overall blocking probability of RP WA may be less than that of FF

WA in some scenarios [9, 15,16].

If the latency incurred in processing the call exceeds a given constraint, yet another

blocking event, called latency blocking or timeout, happens. In this dissertation, the

term quality of service (QoS) blocking denotes QoT blocking and latency blocking

combined.

In this dissertation, the two main problems considered are how to efficiently design

RWA algorithms with QoT constraints and how the latency induced from quality es-

timation computations affects the network performance. In case of slow traffic arrival

or long inter-arrival time, QoT blocking and wavelength blocking have a dominating

impact on the performance of the networks since the effect of timeout is negligible. In

the case of fast traffic arrival or delay-sensitive lightpath set-up, the three components

of QoS blocking (wavelength blocking, QoT blocking, timeout) should be considered

together and a delay bound should be enforced.

In the recent years, new RWA techniques that incorporate both QoT blocking and

wavelength blocking have been the subject of intense research [8,9,17–28]. In [8,22],

a technique called QoT-guaranteed enforces the acceptability of QoT by allowing

lightpaths to be established only if the QoT requirement is met, thereby inducing

a much higher blocking rate than the conventional techniques. More sophisticated

techniques are truly QoT-aware and select routes and/or wavelengths based on some

criterion of performance. In the QoT-aware WA algorithm proposed in [9], available

lightpaths are tested until one with a sufficiently poor BER is found, and if none exists

the call is blocked. In [27], QoT-aware adaptive RWA algorithms are proposed that

incorporate QoT information to yield better performance in terms of average BER

and fairness among network users. In [17, 19], the authors propose several methods

to combat four-wave mixing (FWM) impairment.

6

In [18, 21, 26], variations on a type of routing algorithm with impairment con-

straints are explored, such as best Q factor1 and best optical signal to noise ratio.

The routes are computed by a shortest-path or k-shortest path algorithm in terms of

the physical distance or the number of hops along the route. Then QoT is estimated

for the computed routes. This type of technique may not efficiently find a route since

the physical impairments are not considered as a cost metric in the RWA itself; they

are only used as a final gate.

In [20], the authors provide a set of linear link cost functions for computing the

route considering QoT. However, it can only handle one type of physical impairment.

In [23], the authors use the measured average Q factors of current lightpaths in a link

as the link cost function to compute a shortest path for each coming call. However,

the Q factors of existing lightpaths only partly reflect the physical impairments in

the paths because the performance of the proposed lightpath is ignored. As men-

tioned in [29], different policies of wavelength choices bring different levels of physical

impairments. But the average Q factors of the current lightpaths ignore the true ef-

fect of the chosen candidate wavelengths. Thus the standard shortest path algorithm

used in [23] cannot effectively find a route with the least degradation to the chosen

lightpath and it is not an effective way to build a feasible lightpath.

Although there has been recently a vast amount of research activity aimed at de-

signing powerful RWA algorithms that auto-adapt to the instantaneous network state

and minimize the effects of the physical layer impairments, including our own work,

these QoT-aware algorithms are ad-hoc designs whose performances are compared

via simulation to other suboptimal solutions for specific network topologies. There

has been no attempt to quantify how close these algorithms are to being optimal,

except [20], which considers only one effect.

1Q is a measure for QoT via the BER, defined in (2.2).

7

1.1 Thesis Organization

In Chapter 2, we present a mathematical formulation to obtain the performance

of optimal RWA algorithms that satisfy a QoT constraint given by a threshold on

the Q factor in a static lightpath provisioning environment. The static RWA prob-

lem without consideration for physical degradations can be expressed using different

integer linear programming (ILP) formulations, such as flow formulation and route

formulation [30]. However, an essential assumption in those formulations (linearity)

no longer holds when the QoT constraints are enforced. We formulate the optimal

RWA as a nonlinear problem, obtain the lower bound for all QoT-aware RWA, thereby

helping researchers identify the relative importance of various physical effects.

In Chapter 3, new QoT-aware routing algorithms are explored. Instead of using

the measured average Q factors of current lightpaths in a link as the link cost function

[23], we propose a new cost function which uses variance (power) of the noise along

the candidate lightpath to determine link weights. All physical impairments, such as

linear and nonlinear fiber effects, are modeled as noise terms whose variance can be

predicted. Moreover, noise variances are additive on a per-hop basis. Thus, the total

noise variance is a better choice than the Q factor to represent the cost in a shortest

path algorithm (such as Dijkstra): it includes the impairments of the proposed path

and can be computed in a distributed way. In addition to the routing algorithms, we

propose a new WA technique, called wavelength ordering, which can be applied to

both QoT-guaranteed and QoT-aware cases. Wavelength ordering techniques remove

a part of the crosstalk without adding any complexity or sacrificing bandwidth. They

only require local traffic information and QoT conditions and are therefore suitable

for networks relying on distributed controllers. Furthermore, the simplicity of the

idea of wavelength ordering makes it applicable as a practical solution to the real

current implementations.

Evaluating RWA via simulations is a time-consuming process and an alternate

8

analytical method is needed. Although many models [11, 31, 32] in the literature

have solved the problem of analytically computing blocking probability in WRONs,

the physical layer has rarely been considered in any analytical work. To our knowl-

edge, the only analytical model considering QoT constraints is from our colleague’s

work [33]. However, that model is only applicable to QoT-aware RP WA algorithms.

In [12,34], a layered graph model is proposed to obtain the wavelength blocking prob-

ability for the FF WA algorithm ignoring physical impairments. In Chapter 4, we

extend this analytical method to compute blocking probability in WRON for QoT-

guaranteed and QoT-aware FF WA algorithm, including the blocking due to QoT.

The QoT in our analytical model includes both topology dependent noise (ASE) and

load-dependent degradation (node crosstalk). This model is the first of its kind to

include QoT blocking

Another impact of QoT-awareness on RWA algorithms is the computational com-

plexity of the QoT estimation procedure. Estimating the impact of the physical

impairments on the quality of a lightpath before provisioning it can cause a signifi-

cant delay. In Chapter 5 we include QoT computations time into a QoS requirement,

and study the impact of latency in several scenarios. Conclusions are drawn and

future work is outlined in Chapter 6.

Chapter 2

Mathematical Formulation of the

RWA Problem with QoT

Constraints

WRONs are becoming core components of metro and regional information in-

frastructures. However, linear and nonlinear distortion and crosstalk can accumulate

causing so much physical layer degradation as to make lightpaths unusable. Powerful

RWA algorithms are needed to minimize the effects of the physical-layer degradations

— a major challenge facing the optical network research community.

This chapter first presents the physical model used through this dissertation. The

impact of several dominant physical degradations are estimated in terms of the con-

tribution to the BER of the signal. Then, we present an optimal RWA algorithm

that satisfies a QoT constraint given by a threshold on the QoT in a static lightpath

provisioning environment. The optimality criterion used is the number of consecutive

wavelengths needed to support all or fraction of the call requests. The goal in de-

scribing the optimal solution is not to present a viable algorithm (this is impractical

for larger networks given the nondeterministic polynomial-time (NP)-hardness of the

9

10

problem), but rather to provide a framework by which the relative importance of

various effects can be quantified. Optimal algorithms have been previously proposed

for networks suffering no physical impairments [10, 30, 35] and for systems affected

only by a single physical degradation [20]. None has included a mathematical model

to show the combined impact of physical interferences. With our technique the total

effect of the physical layer on the routing and the wavelength assignment problem

can be isolated since artifacts based on the choice of RWA have been removed. Re-

sults for three different networks comparing the optimal technique to a standard

first-fit/shortest path technique show the maximum gain that can be obtained by

QoT-aware design.

In this chapter, we assume that the whole network knows the static traffic. The

network can also be dynamic, in which the traffic arrives randomly. The dynamic

case is studied in Chapter 3.

The chapter begins with the system model (Section 2.1), which is used in the

rest of the dissertation, followed by a formulation to the optimal RWA algorithm

(Section 2.2). The optimal solution is compared to classic suboptimal algorithms for

three different networks under various physical impairment scenarios and results are

shown in Section 2.3. Then the chapter is summarized in Section 2.4.

2.1 Model of Physical Impairments

In this chapter, we consider that the dominating impairments from the physical

layer are ASE noise and in-band node crosstalk from the intermediate nodes [8,9,36,

37]. Other impairments considered here include shot noise and thermal noise. Fiber

nonlinearities are considered in the next chapter. Other degradations, such as fiber

dispersion, can also be integrated by using models in the literature.

11

DC A G

Hop1

1Link

0 1 m n

Destination

Linkm

Other spansOne spanSource

ASE noise Thermal noiseShot noise

Node crosstalk

m−1 A lightpath

1

2

Sm

12

. . .. . .

. . .. . .

Sm

λ1, λ2, . . . , λW

Figure 2.1: A generic lightpath structure with n + 1 nodes and n links.

Switch fabric

Input link

Amplifier

Amplifier Amplifier

Amplifier

Demultiplexer Multiplexer......

......

......

......

Output link

Output link

Input link λ1

λn

λ1

λn

λ1

λn

λ1

λn

Figure 2.2: A generic all-optical switching node. optical add-drop multiplexers(OADMs) are omitted here.

2.1.1 Origins of Physical Impairments

The origins of impairments are highlighted in Fig. 2.1, which shows a typi-

cal lightpath comprising n + 1 nodes and n links (n hops). Each node or optical

crossconnect (OXC) is composed of a bank of input and output EDFAs, multiplexers

and demultiplexers, and a switch, as shown in Fig. 2.2. Each link can have more

than one span. A span contains a long fiber, a dispersion compensator (DC) and

an amplifier with gain AG. ASE noise accumulates as a signal traverses the spans.

In this chapter, the power compensation from the EDFAs is assumed to be perfect,

which means that the signal power is constant along the lightpath and ASE noise

only depends on the length of the lightpath (number of spans). A more complex case

is studied in Chapter 5.

As shown in Fig. 1.1, when a signal remains in the optical domain along the

12

lightpath and travels through a possibly large number of intermediate nodes, it en-

counters node crosstalk at OXC switches. Crosstalk in general can be classified in

two categories, one is nonlinear crosstalk which depends on the nonlinear effects in

optical fibers, another is linear crosstalk which occurs in linear WDM components

such as demultiplexers and optical switches. Linear crosstalk can be divided into two

kinds, out-of-band crosstalk and in-band crosstalk, depending on the wavelength of

the crosstalk term [37]. Out-of-band crosstalk is incoherent and is less of a problem

since it can be filtered out by optical devices. On the other hand, compared to out-

of-band crosstalk, in-band crosstalk cannot be separated from the desired signal with

any optical filter. Thus, in-band node crosstalk is much more influential in terms of

channel performance than out-of-band crosstalk. In this dissertation, only in-band

node crosstalk is considered.

There are two main origins for in-band node crosstalk, as introduced in Chap-

ter 1. The switching fabric crosstalk comes from power leaking in OXCs, the level

of which depends on the device type. In guided-wave switches, such as electro-optic,

thermo-optic, acousto-optic, and liquid crystal, switching fabric crosstalk ranges from

15 to 35 dB below the valid signal [9, 38, 39]. In micro-electro-mechanical systems

(MEMS)-based switching fabrics, crosstalk is highly attenuated, sometimes as much

as 60 dB [9]. But MEMS-based switching has a high switching response time and

cannot yet fulfill the requirement of next generation all-optical networks.

The other kind of in-band crosstalk, adjacent-port crosstalk, is due to the non-ideal

channel isolation in WDM demultiplexers. Adjacent-port crosstalk is more significant

as the density of wavelengths in the network increases. When a demultiplexer sep-

arates wavelengths, each individual output port not only contains the signal on the

desired wavelength, but also some unwanted signals on other wavelengths. This power

leaking effect mostly occurs on channels that are adjacent to the considered channel

(one wavelength channel slot apart). In addition to the case of adjacent-port crosstalk

13



WRS

WRS

crosstakadjacent−port

CH1

crosstalk from LP2

λ4λ2 λ3λ1

CH1 CH2 CH3 CH4

CH2(λ2)

CH1

CH2

CH1 (λ1)

CH1 (λ1)

LP2

LP1

LP3

CH2 CH1 (crosstalk) CH2

CH1

Figure 2.3: Another possible adjacent port crosstalk. A WRS is a wavelength-routedswitch; CH refers to a channel.

demonstrated in Fig. 1.1, adjacent-port crosstalk can happen when two wavelengths

are multiplexed together as shown in Fig. 2.3. If LP1 is switched to the same output

as LP3, a proportion of LP2’s signal brought by LP1 becomes crosstalk to LP3. To dis-

tinguish between two different adjacent port crosstalk terms, we name self-crosstalk

the one shown in Fig. 1.1 because the crosstalk power originates from the considered

channel itself, and we name neighbor-crosstalk the kind shown in Fig. 2.3. The exact

value of adjacent-port crosstalk depends on channel separations, modulation types,

and device specifications. For a channel spacing of 50GHz, crosstalk can be as high

as −20 dB, becoming the most important source of physical layer impairment [9]. A

detailed description of crosstalk sources in optical networks can be found in [9,37]. In

this dissertation, Xsw and Xadj denote the switching fabric crosstalk and adjacent-port

crosstalk power level attenuations with respect to the main signal, respectively.

2.1.2 Estimation of Impact of Physical Impairments

The QoT can be measured by using line monitoring. However, it is hard to obtain

a value for BER in a short testing time. Moreover, it is hard to monitor the QoT

of the lightpath before it is lit. Thus, we employ a model to estimate the impact

14

of the degradation. Our algorithms can also be applied to other QoT estimation

techniques. The model we use to estimate the impact of physical impairments is

derived in [8, 36, 37]. We repeat the model briefly for the sake of completeness and

to make explicit how our technique uses this model to estimate the crosstalk impact;

however our algorithms could be adapted to other physical degradation computation

techniques.

Assuming binary on-off keying (OOK) modulation, the BER of the signal can be

approximated using the statistics of the received signal after photodetection, filtering,

and sampling for both the “0” and “1” bits. Denote by µ0 and σ0 the mean value

and the standard deviation of the received samples for a “0” bit, and by µ1 and σ1

the mean value and the standard deviation of the received samples for a “1” bit,

respectively. Under a Gaussian noise assumption, the BER can be approximated by

BER ≈ 0.5erfc(Q/√

2), (2.1)

where the Q factor is given by [37]

Q =µ1 − µ0

σ1 + σ0

. (2.2)

Typically, both µ0 and σ0 are small; σ21 dominates since it includes beat terms as well

as noise.

Because of perfect power compensation, the accumulated noises can be estimated

in each hop and summed together to obtain the total degradation at destination.

Then the overall noise variance can be written as the sum of variances from noise and

crosstalk components, which are assumed to be independent [40,41],

σ21 = σ2

XT + σ2ASE + σ2

th + σ2sh,1, (2.3)

σ20 = σ2

th + σ2sh,0, (2.4)

15

where σ2XT and σ2

ASE are variance due to crosstalk and ASE noise, respectively. σ2th

is the noise variance due to thermal noise, which is the same for bit “1” and bit “0”.

σ2sh is the noise variance from shot noise, where the “0” or “1” subscripts represent

which bit is sent. σ2ASE, σ2

th, and σ2sh are as derived in (6.1.17), (4.4.5), and (4.4.8)

of [37] and for a path of J spans can be written as

σ2ASE = 4ρ2Po

J∑j=1

nsp(Gj − 1)hfBe (2.5)

σ2th = η2

thBe, (2.6)

σ2sh,1 = 2ρq[Po + PXT +

J∑j=1

nsp(Gj − 1)hfBo]Be, (2.7)

σ2sh,0 = 2ρq[

J∑j=1

nsp(Gj − 1)hfBo]Be, (2.8)

where ρ is the receiver responsivity; Po is the received signal power for bit “1”; j is

a span of the chosen path; Gj is the gain of the EDFA in span j; Be is the electrical

bandwidth; h is Planck’s constant; f is the optical frequency; ηth is the thermal noise

current; q is the electronic charge; PXT is the sum of all crosstalk terms’ powers at

the receiver; nsp is the ASE factor; and Bo is the receiver’s optical bandwidth.

The crosstalk variance, σ2XT , is due to the beating between the signal and crosstalk

power, computed by [8]

σ2XT = ρ2PoPXT . (2.9)

The calculation of PXT is derived as follows. In Fig. 2.1, assuming that the mth

node has Sm input/output fiber links, if a lightpath is assigned wavelength i (λi) and

enters through the kth port, the induced switching crosstalk power to this lightpath

16

is computed by

Psw(m) =Sm∑

u=1,u6=k

Im,u(i)XswPo. (2.10)

where Im,u(i) is an indicator function equaling unity if λi is currently used in input u

of node m. The adjacent-port crosstalk power induced by other existing connections

on a new candidate wavelength λi of input k and output l to node m is estimated by

Padj(m) = (I ′m,k,l(i− 1) + I ′m,k,l(i + 1))XadjPo (2.11)

+

Sm∑x=1,x6=k

Sm∑y=1,y 6=l

I ′m,x,y(i)(I′m,x,l(i− 1) + I ′m,x,l(i + 1))

XadjPo

Where I ′m,x,y(i) is an indicator function equaling unity if λi is switched from input x to

output y at node m. The first term in the above equation is the power of self-crosstalk,

the second term is the power of neighbor-crosstalk. Note that we ignore the subscripts

of (i, k) in Psw(m) and Padj(m) for the sake of clarity. In this dissertation, we consider

only adjacent-port crosstalk that originates from the adjacent wavelengths λi−1 and

λi+1. Consequently,

PXT (m) = Psw(m) + Padj(m) (2.12)

is the sum of all crosstalk terms’ powers at node m if the assigned wavelength is λi

and the input port is k. The total PXT at the destination passing through n hops is

PXT =n∑

m=0

(Psw(m) + Padj(m)). (2.13)

Note that Padj(0) = 0, but Psw(0) can be greater than 0.

When a lightpath is established, the QoT for lightpaths that share one or more

OXCs must be re-estimated to account for crosstalk components that are injected or

17

Table 2.1: Parameter Settings

Parameter Value

Wavelength spacing 50GHz

Data rate per channel 10Gps

ASE factor (nsp) 1.5

Laser source power Po 0 dBm

Receiver responsivity ρ 0.95A/W

BER threshold 10−12

Q factor threshold 7

Optical bandwidth Bo =wavelength spacing

Electrical bandwidth Be =data rate

Input EDFA gain 22 dB

Ouput EDFA gain 16 dB

Center wavelength 1550 nm

Thermal noise current ηth 3.8× 10−12 A

removed, changing the value of σ1 directly through σ2XT .

In the dissertation, unless otherwise noted, parameters are set to the default values

in Table 2.1.

2.2 Problem Formulation to RWA with QoT Con-

straints

In this section, we consider the problem of establishing a given set of requests in

a given optical network with non-negligible physical impairments. The objective is to

find a lightpath for each request satisfying the QoT threshold and using the minimum

bandwidth needed. This is called the static RWA problem and can be formulated as

18

an integer linear programming (ILP) problem if the physical degradations are ignored,

which has been studied in previous research [30, 35]. Usually, the ILP is formulated

using either a flow or route model. In the flow formulation, the decision variables in

the ILP are the flows on the links generated through each source-destination (s-d)

pair [30,35]. The route formulation starts with an enumeration of all routes between

all s-d pairs and determines how many wavelengths have to be used in each route.

Based on the discussion in [30, 35], the route formulation has a better performance

than the flow model. Thus, the route formulation is employed here.

When we consider the additional constraints resulting from a threshold on the

QoT, the previous ILP formulation has to be extended and the constraint set is no

longer linear. With physical distortion, such as fiber nonlinearity and switch crosstalk,

wavelengths cannot be treated identically. Furthermore, part of the wavelength band-

width in the assigned wavelength spectrum may not be occupied because the quality

of those wavelengths is so bad that the requests cannot use them. Consequently, the

objective function is nonlinear; we must minimize the number of consecutive wave-

lengths used instead of the total number of wavelengths occupied. This leads to

optimal network design.

2.2.1 General Mathematical Formulation

Here, a new nonlinear formulation is proposed to solve the optimal problem of

RWA considering physical impairments by extending the models in [30, 35]. The

same notations as in [30,35] are used for the sake of consistency.

Let G(N , V ) be the network graph consisting of N nodes, N = 1, 2, · · · , N and

L vectors (links), V = 1, 2, · · · , L. Assume that each link is a bi-directional single

fiber (the model can be easily extended to the multi-fiber case). A path p ⊆ V is a

connected sequence of links excluding any cycle. Define I(j ∈ p) = 1 if j is a link

of path p and I(j ∈ p) = 0 otherwise. Z is the set of all possible s-d pairs and Φ is

19

the static deterministic traffic matrix, in which Φz denotes the number of connections

needed between s-d pair z ∈ Z. Let R = |Φ|. Define Az = p : s → d to be set of

routes for s-d pair z.

A lightpath is identified by the path p and its wavelength i. Wavelengths in each

fiber are numbered sequentially. Define δzp,i = 1 if (p, i) is selected as an active good-

quality lightpath for z and δzp,i = 0 otherwise. Define a variable Λi which is set to 1

if wavelength i is used by at least one lightpath within the network, and 0 otherwise.

The objective of the problem is to minimize the number of the consecutive wave-

lengths needed, subject to the presence of a good active lightpath for each request.

Thus, the problem can be formulated as follows:

min arg maxi

(Λi = 1)− arg mini

(Λi = 1) (2.14)

subject to

R∑i=1

∑p∈Az

δzp,i = Φz, ∀z ∈ Z (2.15)

Λi ≥ δzp,i, ∀z ∈ Z, ∀p ∈ Az,∀i (2.16)

∑z∈Z

∑p∈Az

δzp,iI(j ∈ p) ≤ 1, ∀j ∈ V, ∀i (2.17)

C(p, i, z) ≥ Cth, ∀z ∈ Z, ∀p ∈ Az,∀i, (2.18)

where (2.18) represents the QoT constraints. C(p, i, z) is a function of the impact to

QoT of the physical impairments, and Cth is the threshold.

2.2.2 QoT Constraint

Above, we provide a general mathematical model to solve the optimal RWA prob-

lem with any physical impairments. The constraint in (2.18) depends on the types of

20

physical degradations considered. We derive the constraint given the optical impair-

ments in Section 2.1.2 as follows including only ASE noise and crosstalk. ASE noise

is computed using (2.5).

We define Kswp,p1

as the number of switching fabric crosstalk terms induced by path

p1 on p (same wavelength) and define Kself−adjp,p1

as the number of adjacent-port self-

crosstalk in path p induced from adjacent channels in p1. Both can be easily counted

by using the way in Section 2.1.2. For example, the number of terms of switching

fabric crosstalk Kswp,p1

is equal to the node number shared by p and p1. If p and p1 share

n′ hops, n′ − 1 units of self-crosstalk Kself−adjp,p1

are induced. The neighbor-crosstalk

depends on the usage of other paths and cannot be counted this way. Then the total

number of crosstalk terms in lightpath (p, i) for a s-d pair z except neighbor-crosstalk

is computed by:

N swz,p,i =

∑z1∈Z,z16=z

∑p1∈Az1

δzp,iδ

z1p1,iK

swp,p1

(2.19)

N self−adjz,p,i =

∑z1∈Z

∑p1∈Az1

δzp,i(δ

z1p1,i−1 + δz1

p1,i+1)Kself−adjp,p1

. (2.20)

N swz,p,i and N self−adj

z,p,i are state dependent and represent the total number of switching

fabric crosstalk and adjacent-port self-crosstalk terms in lightpath (p, i) for s-d pair

z, respectively. The neighbor-crosstalk has to be computed by hop by hop. Assume

that p and p1 share a set of hops, 1, . . . , n′. Then the neighbor-crosstalk term at hop

m is

Nneighbor−adjz,p,i (m) = δz

p,i

∑z1∈Z

∑p1∈Az1

∑z2∈Z,z2 6=z

∑p2∈Az2 ,

p2 6=p

(Iz1,z2(m)δz2p2,iδ

z1p1,i−1) (2.21)

where Iz1,z2(m) = 1 if z1 and z2 share the same input demultiplexer. The total

number of adjacent port crosstalk terms is the sum of the neighbor-crosstalk from

21

each hop and self-crosstalk, given by

Nadjz,p,i = N self−adj

z,p,i +n′∑

m=1

Nneighbor−adjz,p,i (m). (2.22)

Consequently, the crosstalk power in lightpath (p, i) for s-d pair z can be derived

as

PXT = Po(XswN swz,p,i + XadjN

adjz,p,i). (2.23)

Note that this expression is equivalent to (2.13). The dependence of PXT on (z, p, i)

is hidden from the notation.

Then, using (2.2), (2.18) is re-written as:

C(p, i, z) = Q =µ1 − µ0

σ1(p, i, z) + σ0(p, i, z)≥ Cth,∀z ∈ Z, ∀p ∈ Az,∀i. (2.24)

Ignoring intersymbol interference and a non-zero extinction ratio, we set µ1 = Po and

µ0 = 0.

2.2.3 QCQP Approximation

The objective function (2.14) can be approximated by a quadratic form,

min∑

i

∑

j 6=i

ΛiΛj(i− j)v, (2.25)

where v is a large even number. The problem in (2.14)-(2.18) can then be formulated

as a quadratically constrained quadratic program (QCQP) if C(p, i, z) is a quadratic

constraint, which is true in many practical cases. Then approximation methods can

be used to solve this in a reduced time for large networks.

To formulate C(p, i, z) in a quadratic form, we ignore the neighbor-crosstalk

22

(which is cubic) and use the standard deviation directly instead of the Q factor

given the direct relation between them in (2.24). Usually QoT is measured using the

Q-factor which depends on Po and σ20 and σ2

1. Since only σ21 and σ2

0 depend on the

state, we write constraint (2.18) simply as

C(p, i, z) = σ21(p, i, z) + σ2

0(p, i, z) ≤ Cth, ∀z ∈ Z, ∀p ∈ Az,∀i, (2.26)

where σ21(p, i, z) and σ2

0(p, i, z), which are quadratic in the state variables, can be

computed as in (2.3) and (2.4). Cth is now the threshold on the noise standard

deviation.

The binary integer constraint on variables can be re-written as two quadratic

constraints by

x(x− 1) ≤ 0, (2.27)

x(x− 1) ≥ 0, (2.28)

where x denotes any binary variable in the constraints above.

Even though as a non-convex QCQP this is still an NP-hard problem, approxima-

tion methods and commercial software can be used to solve this problem in a shorter

time on average for large networks.

2.3 Simulation Results and Discussion

To compare the performance and the impact of physical impairments, three dif-

ferent networks are considered as shown in Fig. 2.4. The algorithms we simulate are

the proposed optimal RWA, shortest path routing (SP) with an optimal wavelength

assignment (WA), and shortest path routing with first-fit WA. They are referred to as

Opt-RWA, Opt-WA, and SP-FF, respectively. For comparison, we present results for

23

(a)

1 2

3 4

5

1 102 ......

81 2 ......

(b)

(c)

6

Figure 2.4: Network topologies used in simulation. (a) 6-node mesh network, (b)10-node ring network, and (c) 8-node tandem network.

networks subject to physical impairments, labeled PHY, and for networks immune to

physical impairments (no labeling).

Simulation parameters are: µ1 = Po = 0 dBm and µ0 = 0, Xsw = −30 dB, and

Xadj = −20 dB.

Given R requests, the size of the set of possible requests generated is (N × (N −1))R. It is impossible for us to solve the RWA problem for every point from the set

because the RWA problem is NP-hard [30,35]. Thus, one thousand sample points are

randomly chosen from the set of possible requests and results are shown in Figs. 2.5

and 2.6.

We plot the mean and 90th percentile for the case R = 12 in Fig. 2.5. The

performance of Opt-RWA-PHY is on the order of one wavelength improvement over

that of Opt-WA-PHY and SP-FF-PHY except in the tandem network. The gap

between Opt-RWA and Opt-WA shows the improvement of using optimal routing on

the network performance. Note that the performance of Opt-RWA is the same as

that of OPT-WA in the tandem network, because there is only one route for each s-d

pair. Opt-WA-PHY is somewhat better than SP-FF-PHY in all networks, showing

that the benefit of optimizing the WA is not as large as that from optimizing routing.

The impact of physical degradation is shown by comparing the solid lines to the

adjacent dashed lines in Fig. 2.5 (labeled PHY and their unlabeled counterparts). We

observe that the smallest impact occurs for Opt-RWA, followed by Opt-WA, and then

24

Mesh network Ring network Tandem network

3

4

5

6

7

8

9

Num

ber

of c

onse

cutiv

e w

avel

engt

hs n

eede

d

Opt−RWA−PHYOpt−WA−PHYSP−FF−PHYOpt−RWAOpt−WASP−FF

90%

mean

mean 90%mean

mean

90%

90%

mean mean

90% 90%

Figure 2.5: Number of consecutive wavelengths needed for the six schemes with 12random requests in 6-node mesh network, 10-node ring network, and 8-node tandemnetwork.

SP-FF. Consequently, we conclude that optimal RWA algorithms can help reduce (yet

not remove) the impact of physical degradations.

Fig. 2.6 shows the performance of the 3 algorithms for different traffic loads (num-

ber of requests), for the 10-node ring network. As the traffic load increases, the gaps

between the schemes without physical impairments and those with impairments in-

crease. Their slopes show that optimal routing and optimal WA algorithms help more

in high traffic cases.

We now limit the number of wavelength in the links to 4. Then if R static

requests arrive and require more than 4 wavelengths, they are blocked and counted

as 1 outage event. Then, for one thousand randomly generated requests, the outage

rate for the six RWA algorithms when R = 6, 8, 10, 12 in 10-node ring network are

shown in Fig. 2.7. The outage rate of the optimal RWA is lowest by a factor of 10

in R = 6, 8, 10 and in factor of 5 in R = 12 over other two algorithms. The optimal

25

6 7 8 9 10 11 122

2.5

3

3.5

4

4.5

5

5.5

R, number of requests

Num

ber

of c

onse

cutiv

e w

avel

engt

hs n

eede

d


Figure 2.6: Average number of consecutive wavelengths needed for the six schemeswith different number of random requests in 10-node ring network.

WA outperforms the FF WA by a factor of 1.5. All RWA algorithms with physical

impairment constraints cannot reach the same outage rates as RWA without physical

impairments. The results in Fig. 2.7 show that optimal RWA and optimal WA reduce

the impact of physical degradations significantly in terms of the outage rate.

2.4 Summary

In this chapter, the physical models used in this dissertation are described. Be-

cause of the difficulty of online monitoring the BER, an estimation model is necessary

for the RWA algorithms subject to QoT constraints. The model we employed can be

extended to include more complicate degradations, such as fiber nonlinearity, which

is shown in the next chapter.

It is well known that optimal RWA problems are computationally expensive, given

the large number of variables and constraints generated [30, 35]. However, formula-

26

6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

R, number of requests

Out

age

rate


Figure 2.7: Outage rate for the six schemes with different number of random requestsin 10-node ring network with a limited of 4 wavelengths.

tions are necessary to provide a formal description of the problem, and to propose

effective methods of approximation. In this chapter, we propose a mathematical for-

mulation for the problem of optimal RWA for systems with several state-dependent

physical impairments. The proposed formulation provides a lower bound on the

performance for other QoT-aware RWA algorithms. Simulation results show that an

optimal routing policy can effectively decrease the number of consecutive wavelengths

needed and its impact is more powerful than optimizing the WA if multiple paths are

available. Improving the WA can further reduce the physical degradation, especially

in tandem and other sparsely connected networks.

Chapter 3

Suboptimal RWA Considering

Physical Impairments

Replacing electrical switches with all-optical switches promises a more cost effec-

tive and flexible optical network design solution. Avoiding OEO conversion in WRON

brings one potential problem: lightpaths in the networks can be many hundreds of

kilometers long with no regeneration other than optical amplification and dispersion

compensation. The data signal propagating through a large network encounters phys-

ical impairments that limit system performance as networks expand and wavelength

density increases [7,8]. Linear and nonlinear distortion and crosstalk can accumulate

causing so much physical layer degradation as to make the lightpath unusable. In

this chapter, we show how to mitigate the impact of physical-layer degradation at the

network layer by the proper design of low-complexity RWA algorithms.

As a practical alternative to the optimal but complex algorithm presented in Sec-

tion 2.2, we consider computationally efficient RWA here. We split the RWA problem

into a routing sub-problem and a WA sub-problem. The algorithms in this chapter

are not optimal because the optimal combined routing algorithm and optimal wave-

length assignment algorithm are impossible to obtain in practical scenarios because

27

28

the problem is NP-hard. Several new adaptive routing algorithms and adaptive wave-

length assignment algorithms are presented that account for physical impairments in

their design and improve the QoT without sacrificing the network throughput. Fur-

thermore, these RWA algorithms perform well both in centralized and de-centralized

networks. The performance of all algorithms is computed via simulation in sev-

eral realistic scenarios. Simulation results show that the proposed RWA techniques

successfully mitigate physical layer effects and perform better than traditional algo-

rithms.

3.1 Routing with QoT Constraints

In this section, we focus on the routing component of RWA to incorporate QoT: we

propose a novel routing algorithm that finds a route based on both the network uti-

lization and the physical impairments experienced over the tentative route. As men-

tioned in [42], there are two types of routing approaches to provide QoT-awareness.

The first is called route admission control with impairment constraints, which is a

two-step routing procedure. First a lightpath is computed using a certain RWA pol-

icy that does not incorporate any effect of physical impairments. The QoT of the

lightpath is estimated in the second step. In [8, 18, 26, 27], variations on this routing

algorithm with impairment constraints are explored, such as best Q factor and best

optical signal to noise ratio. The route is computed by a shortest-path algorithm

where costs are defined in terms of physical distance or number of hops along the

route. This type of technique may not efficiently account for physical impairments,

since the physical impairments are not considered as a cost metric in the RWA itself;

they are only used as a final gate. In [21], the authors exhaustively search k-shortest

paths found by a conventional routing algorithm, such as Dijkstra. Then the path

with the least impact to all flows in the networks is assigned to the request. Since

29

the routing is done by conventional routing algorithms, it belongs to the same class

of algorithms as in [8, 18, 26,27] except that it searches k-shortest paths.

The second routing scheme incorporates impairments into the cost function of

the routing policy. How to choose the cost function to include linear and nonlinear

impairments is challenging. In [20], the authors provide a linear cost function that can

only handle one type of physical impairments. In [23], the authors use the measured

average Q factors of current lightpaths in a link as the link cost function. The Q

factors of existing lightpaths partly reflect the physical impairments in the paths, but

the average Q factors of the current lightpaths ignore the QoT of the chosen candidate

wavelengths.

The adaptive QoT-aware routing technique proposed in this chapter utilize a new

cost function to account for the level of physical impairments. All linear physical im-

pairments, such as node crosstalk and ASE noise, are modeled according to Section 2.1

as noises whose variance can be predicted. Nonlinear effects including FWM and

cross-phase modulation (XPM) are estimated using the technique described in [27].

Any other noises can be integrated in our model if they can be expressed by their

noise variance. With the assumption of perfect power amplification, noise variances

are additive hop by hop. Thus the total noise variance is simpler than the Q fac-

tor to represent the cost in a shortest path algorithm (such as Dijkstra): the total

noise variance includes the impairments of the proposed path and can be computed

in a distributed fashion. Using this new cost function, our adaptive routing algo-

rithm effectively finds a better route based on physical impairments and significantly

outperforms other routing algorithms as measured by blocking probability and other

performance metrics, such as the number of wavelengths needed and maximum traffic

load to remain below a given blocking rate. Our adaptive QoT-aware routing algo-

rithm can be implemented in both centralized and distributed networks, because the

cost function only uses local information (the state of the links between a node and

30

Destination node

......

......

Tx Rx

Quality of TransmissionMonitoring

......

......

......

Tx Rx


......

......

......

Tx Rx


Distributed signaling, routing andwavelength reservation protocols

BERestimator

RWA

Routing table

Physical info.

Wavelength usage

BERestimator

RWA

Routing table

Physical info.

Wavelength usage

Management plane

Data plane

Control plane

......

WRS WRS WRS

Source node Intermediate nodes

Figure 3.1: Structure for distributed network models, WRS refers to a wavelengthrouted switch.

its neighbors).

3.1.1 Distributed Network Architecture

In this chapter, an all-optical network is modeled as a distributed circuit-switched

network, a type of connection-oriented network with a data-plane, a management

plane, and a control plane [4]. A simplified structure for our distributed network

model is illustrated by Fig. 3.1.

So that data transmission can occur, an end-to-end lightpath must be established

between a source and a destination by a distributed signaling, routing and wavelength

reservation protocol. The management plane initiates, at any node, the connection

establishment process. The initiating node can be the source of the call, but not

necessarily, since it can simply have received a request from another node to be part of

a lightpath. The purpose of the management plane is to determine the instantaneous

local quality of transmission, that is, for a given node, the QoT of a LP between its

source node and itself, for every lightpath already established in the network.

The management plane provides information that is used by the control plane to

complete the QoT-aware lightpath establishment. The control plane collects wave-

31

length usage and physical layer information at each node, and estimates the QoT by

calculating the BER of the signal.

In distributed networks, QoT must be computed by the nodes themselves as

lightpaths are established, contrary to centralized networks where QoT can be pre-

computed by the centralized controller which has complete knowledge of the whole

system [29]. This makes distributed optical networks more difficult to implement

but removes this single point of failure and heavy processing requirements on the

centralized management system.

Borrowing the idea from telecommunication [43], the RWA comes in two flavors

in distributed networks: hop by hop and source only. We call these hop-by-hop-RWA

and source-RWA, respectively.

In hop-by-hop RWA, a node determines the next hop on the demanded route by

consulting the local routing table. Each network node on the route used by the light-

path reserves the network resources (i.e., a wavelength over the next hop), constructs

a new signaling message that includes local physical impairment information, and

sends that message to the next node on the lightpath. Upon its arrival at a node,

the signaling message is parsed to extract the QoT information from the previous

node on the route, and a decision is made regarding the lightpath establishment: if

available network resources are not sufficient to meet the required QoT requirement

of a connection request in the allotted time, the connection request is rejected and

a failure message is sent back towards the source to release any resource reserved

between the source and the considered node.

On the other hand, in source-RWA, all nodes in the network communicate with

each other to exchange information including the wavelength usage and the QoT of

all wavelengths. The source of a request finds a route and assigns a wavelength to it

based on the information stored at the source node. The actual QoT of the selected

lightpath has to be estimated again from source to destination along the chosen

32

lightpath before the communication connection is established. In this chapter, we

consider both schemes: source-RWA is assumed in QoT-aware routing and hop-by-

hop-RWA is assumed in WA with QoT constraints.

Control plane signaling can be in-band, in which case the control messages share

the same network as the transmitted user data, or out-of-band, in which case another

network (possibly physically separate, or simply though a dedicated wavelength) is

maintained for management and control messages [44]. To avoid interfering with the

data plane, we assume the control messages are carried out-of-band. Our work can

be applied to both cases.

3.1.2 QoT-Aware Routing Algorithms

Here, we focus on path routing, and hence we employ conventional wavelength

assignment (WA) techniques: first fit (FF) WA, which picks the shared free wave-

length along the path with the lowest index, or random pick (RP) WA, which picks a

random wavelength amongst the available wavelengths on the route. The flow chart

of the resulting routing and wavelength assignment algorithms is shown in Fig. 3.2.

Note that BER estimation of the considered lightpath and other involved lightpaths

is done by all nodes along the selected path. In the following sections, we consider a

new QoT-aware routing algorithm and compare it to others found in the literature.

3.1.2.1 Routing Based on QoT Cost Criterion

In the proposed algorithm, called least variance (LV), we use the variance of the

crosstalk interference and noise instead of the Q factor in the cost function. The

variance of the noise is well-defined and is easily obtained from the existing physical

models described in Section 2.1. An added benefit is that our routing algorithm is well

suited to distributed network management since the cost function is cumulative and

can be calculated hop by hop. Here we use the source-RWA scheme to demonstrate

33

No

Block the request

threshold BER <

the requestAccept

A request arrives

Find the available path with theshortest distance, fewest hops,

the chosen wavelength

minimized measured Q factors, or lowest variance of noises for

BER estimation of the lightpathand other involved lightpaths

Choose a new wavelength based on wavelengthassignment algorithm, such as FF or RP

No free wavelength

Yes

Figure 3.2: Flow chart of adaptive routing algorithms in the source-RWA scheme.

the procedure.

The Dijkstra shortest path algorithm [12] is used to adaptively obtain the least

cost path, i.e, the path with the least total weight. The weight of a hop is defined by

the variance of the noises plus a stabilizing factor αi. The weight of hop i when λj is

selected is:

W (i, j) = σ2XT (i, j) + σ2

NL(i, j) + σ2ASE(i, j) + αi, (3.1)

where σ2XT and σ2

ASE(i, j) are defined in (2.9) and (2.5), respectively.

The variance of FWM/XPM crosstalk from link i, σ2NL(i, j), is estimated using

the technique described in [27] by creating a table of crosstalk contributions based

on the spectral positions of active wavelengths. We consider channel λj in hop i

and, without loss of generality, reassign to it index “0”; other channels are then

indexed with respect to channel 0 in ascending frequency order. Each entry of the

table is identified by a triplet (l, m, n) and contains the XPM or FWM variances

σ2nl(l, m, n) created on channel 0 by signals present on channels l, m, and n. For non-

zero nonlinear interference, valid choices of l, m, n are such that m = l + n and l, m,

n cannot simultaneously all be equal to 0; if l = 0 or n = 0, then σ2nl(l,m, n) results

from XPM between channels 0 and m; otherwise, σ2nl(l,m, n) results from FWM

34

between channels 0, l, m, and n. The terms σ2nl(l, m, n) are precomputed assuming

transmission through a single fiber span using the method presented in [45], for all

valid combinations of indices (l, m, n). Computing the overall XPM/FWM variance

σ2NL(i, j) on link i simply consists in adding for all spans the variances σ2

nl(l,m, n)

found in the table for entries in which wavelengths l, m, n are in use on the link

considered.

Instead of using only the variances to define the hop weight, we apply a stabilizing

factor αi in the cost function for two purposes. One is to avoid the case of negligible

physical impairments, which can occur when the network is idle or lightly loaded, in

which case the routing algorithm cannot make a wise decision. The second reason

for adding a constant αi is to reduce wavelength blocking if physical impairments are

not the dominating source of blocking. In these cases, when physical impairments

are small, the cost function reduces to the number of hops and our new LV routing

becomes identical to shortest-path routing (in terms of the number of hops).

To make the algorithm more dynamic and implementable in distributed networks,

we use an adaptive αi that can respond to the instantaneous load on the network

and is set as a per-node variable instead of a network-wide variable. For stability, we

bound the value of αi by defining αmin ≤ αi ≤ αmax. When nodes in the network

detect wavelength blocking through an acknowledgment or other control message, αi

is updated as

αi ⇐= maxαi + ∆α, αmax (3.2)

whereas when nodes detect QoT blocking, αi is updated as

αi ⇐= minαi −∆α, αmin (3.3)

where ∆α is the incremental step in adjusting αi for the instantaneous network state.

35

∆α, αmax, and αmin are preset based on previous training, such as a preliminary

calibration via short simulations.

3.1.2.2 Other Routing Algorithms with QoT Constraints

We choose three adaptive routing algorithms initially proposed in [12,23] based on

different cost metrics to compare with our new algorithm. The first is based on the

shortest distance (SD), which chooses the path with the shortest physical distance.

The second is based on the fewest number of hops (FH), which chooses the path

traversing the fewest number of nodes. Here, hop i refers to link i and node i on the

route used by the lightpath, as shown in Fig. 2.1. The idea behind SD routing is that

the algorithm chooses a lightpath with the least link impairments (fiber nonlinearity

and noise); the idea behind FH routing is that the algorithm chooses a lightpath with

the least node impairments (crosstalk) [20]. FH routing is expected to bring a lower

level of wavelength blocking than SD routing since SD uses more link resources than

FH routing.

The third technique is proposed in [23]. The route is selected by the shortest

path algorithm in which the hop cost is weighted with a value that is equivalent

to the average measured Q factor of the current lightpaths on this hop. The Q-

maximizing (QM) algorithm finds the shortest path for each wavelength based on

the measured Q factors collected from other nodes. We emulate its performance by

assuming that the estimated Q factors is equal to the measured Q factors. Note that

neither the Q factor of the lightpath that is being established nor the effect that

establishing the lightpath would have on the other lightpath’s Q factors is considered

in the routing cost metric.

36

NY

CA1CO

MD

4

21

2

2

4

1

11

4

1

1 2

2

2

12

1

2

1

TX

1

MI

NJ

GA

CA2

UT

WA

NE

IL

PA

Figure 3.3: Topology of a downsized version of the NSF network with 14 nodes and21 bidirectional links, using link lengths 1/10 of their original size. The numbers onthe links represent number of spans along the link. Each span is around 75 km long.

Table 3.1: Network Simulation Parameters

Parameters Value

Number of wavelengths 32

Nonlinearity constant 2.2 (W.m)−1

αmax 3× 10−10 A2

αmin 1× 10−10 A2

∆α 1× 10−11 A2

3.1.3 Simulation Results and Discussion

We consider a downsized version of the National Science Foundation (NSF) net-

work depicted in Fig. 3.3 as a practical example to compare the routing algorithms.

The parameter values used in the simulations are listed in Tables 2.1 and 3.1. The

number of calls generated is more than 106 for each simulation. We model the arrival

process as Poisson and the service time as exponentially distributed. In the plots, the

vertical dashed line is used to indicate a common point in the simulations.

A signal must utilize the same wavelength on the route from its source to its

37

destination as wavelength conversion is assumed to be absent. If the signal’s QoT

is below the QoT threshold or it causes other signals’ QoT to drop below the QoT

threshold, the call is rejected and network resources are not allocated. The blocking

probability measured includes wavelength blocking and QoT blocking. We assume

that the time for computing QoT is negligible in this chapter.

The adaptive routing algorithms described in Section 3.1.2 are compared in terms

of blocking probability. First-fit and random-pick wavelength assignment algorithms

are compared. We call FF WA with SD routing “FFwSD”, FF WA with FH routing

“FFwFH”, FF WA with QM routing “FFwQM”, FF WA with LV routing “FFwLV”,

RP WA with SD routing “RPwSD”, RP WA with FH routing “RPwFH”, RP WA with

QM routing “RPwQM”, and RP WA with LV routing “RPwLV”. For comparison, we

also plot FF WA with fixed routing based on fewest number of hops (FR) (FFwFR)

and RP WA with FR (RPwFR), which try all possible free wavelengths in a fixed

shortest hop path and are not adaptive: they do not select a path for each available

wavelength call by call.

3.1.3.1 Blocking Probability vs. Network Load

To show how the routing algorithms perform in different network conditions, we

examine in Fig. 3.4 and Fig. 3.5 the various blocking probabilities for total network

loads ranging from 117 Erlangs to 255 Erlangs. The results clearly indicate that the

FFwLV algorithm yields the lowest average blocking probability in all traffic load

cases.

First, consider the various routing algorithms using FF WA in Fig. 3.4. For the pa-

rameters we assume, FFwLV is best followed by FFwQM, FFwFH, and then FFwSD.

FFwFR has the worst performance — as expected, since for fixed routing there are

fewer available candidate free wavelengths than for adaptive routing, especially in

dynamic traffic cases. FFwQM is slightly better than FFwFH and FFwSD in all

38

120 140 160 180 200 220 24010

−5

10−4

10−3

10−2

10−1

100

Load, erlangs

Blo

ckin

g pr

obab

ility

FFwFRFFwSDFFwFHFFwQMFFwLV

Figure 3.4: Blocking probability with QoT constraints for the various routing al-gorithms in different traffic loads using FF WA; Xadj = −20 dB and Xsw = −40dB.

traffic cases. FFwFH is better than FFwSD except at low loads because FFwFH has

lower wavelength blocking. FFwFH can be worse than FFwSD if the link physical

impairments dominate the blocking, as discussed below. The blocking probability

of the new routing algorithm is lower by a factor of two over the other techniques

tested when the network load is less than 160 Erlangs. The gap is larger in the lower

traffic cases, giving a full order of magnitude advantage at 120 Erlangs. In high traffic

cases, the four lines converge because of large wavelength blocking and severe physical

impairments from high traffic.

When RP WA is used, shown in Fig. 3.5, the same trend can be observed as for FF

WA. RPwLV is the best routing technique, followed by RPwQM, RPwFH, RPwSD,

and RPwFR. The blocking probability for RP WA for each routing algorithm is higher

than for the corresponding FF WA algorithm because RP WA has a higher level of

wavelength blocking, as discussed in [10].

39

120 140 160 180 200 220 24010

−5

10−4

10−3

10−2

10−1

100

Load, erlangs

Blo

ckin

g pr

obab

ility

RPwFRRPwSDRPwFHRPwQMRPwLV

Figure 3.5: Blocking probability with QoT constraints for the various routing al-gorithms in different traffic loads using RP WA; Xadj = −20 dB and Xsw = −40dB.

3.1.3.2 Blocking Probability vs. Node Crosstalk

As crosstalk is considered one of the dominant physical impairments in this dis-

sertation, it is important to determine how each algorithm performs under different

crosstalk power levels. The blocking probabilities for the various routing algorithms

are plotted in Fig. 3.6 and Fig. 3.7 for several values of (Xsw, Xadj), which represent

the crosstalk levels in the network.

Considering the FF WA case in Fig. 3.6, we observe that FFwLV always outper-

forms the other routing algorithms because of the QoT adaptive cost function. For

the parameter values we tested, FFwFR results in the worst performance. FFwQM is

slightly better than FFwSD and FFwFH. FFwSD and FFwFH are close, alternatively

performing third best at different crosstalk levels. Fig. 3.7 shows that when RP WA is

applied to each routing algorithm, the same performance behavior is observed. Again,

RPwLV is the best routing policy among all routing policies, followed by RPwQM,

40

(−30, −15) (−35, −20) (−40, −20) (−45, −25) (−50, −30)10

−4

10−3

10−2

10−1

100

(Xsw

dB, Xadj

dB)

Blo

ckin

g pr

obab

ility

FFwFRFFwSDFFwFHFFwQMFFwLV

Figure 3.6: Blocking probability with QoT constraints for the various routing algo-rithms for different levels of crosstalk using FF WA; the network load is fixed at 156Erlangs.

RPwFH and RPwSD.

At higher crosstalk levels, FH results in fewer blocked calls because degradations

originating at the nodes (both node and adjacent crosstalk) dominate degradations

originating in the fibers (FWM/XPM and ASE noise). In low crosstalk cases, the

performance of SD is better than that of FH since the noise from the links dominate.

Network designers do not need to predict the level of crosstalk and load the network

might experience if they us the LV or QM routing since it dynamically finds a suitable

route. The results show that in all cases QM routing is not as effective as LV routing.

In summary, FFwLV is significantly superior to the other algorithms we evaluated for

all levels of crosstalk power.

41

(−30, −15) (−35, −20) (−40, −20) (−45, −25) (−50, −30)10

−4

10−3

10−2

10−1

100

(Xsw

dB, Xadj

dB)

Blo

ckin

g pr

obab

ility

RPwFRRPwSDRPwFHRPwQMRPwLV

Figure 3.7: Blocking probability with QoT constraints for the various routing algo-rithms for different levels of crosstalk using RP WA; the network load is fixed at 156Erlangs.

3.1.3.3 Number of Wavelengths Needed vs. Traffic Load

Instead of only evaluating RWA performance in terms of blocking probability,

we select another performance metric when evaluating the QoT-aware algorithms.

Considering that wavelengths are the rare commodity in all-optical networks, we use

the number of wavelengths needed to reach a level of blocking rate for a fixed input

traffic load.

We increase the number of wavelengths until the blocking probability reaches a

given constraint for different, fixed, network traffic loads. The results are shown in Ta-

ble 3.2. Including the nonlinear effects requires building a large table of FWM/XPM

interaction for each bandwidth considered. Therefore, for simplicity we ignore non-

linear effects in this set of simulations. The total blocking probability Ptotal has to

be used as a secondary metric to differentiate the various algorithms in Table 3.2

42

Table 3.2: Number of wavelengths needed (W ) for Ptotal ≤ 10−3, Xsw = −40 dB,

Xadj = −20 dB

Load 255 Erlangs 200 Erlangs 156 Erlangs 100 Erlangs

RWA W Ptotal W Ptotal W Ptotal W Ptotal

FFwSD 43 0.000839 36 0.000853 30 0.000828 23 0.000439

FFwFH 42 0.000501 35 0.000501 29 0.000578 21 0.000811

FFwQM 41 0.000994 34 0.000993 29 0.000478 21 0.000711

FFwLV 41 0.000927 34 0.000979 29 0.000471 21 0.000689

RPwSD 47 0.000730 39 0.000856 33 0.000645 24 0.000874

RPwFH 45 0.000756 37 0.000936 31 0.000688 23 0.000566

RPwQM 45 0.000722 37 0.000864 31 0.000685 23 0.000511

RPwLV 44 0.001000 37 0.000797 31 0.000685 23 0.000498

because the granularity of the wavelength is coarse.

Results show that FFwLV needs the smallest number of wavelengths to keep

the blocking probability less than 10−3. As expected, RWA using the FF algorithm

needs fewer wavelengths than its counterpart using RP WA. FFwQM, FFwFH, and

RPwFH sometimes need the same number of wavelengths as FFwLV and RPwLV,

respectively. However, their blocking probabilities are different. LV routing results in

a lower blocking rate than other routing algorithms.

For these results, since we ignore FWM/XPM effects, the dominant impairments

come from the nodes, thus the route with the fewest hops is possibly the best route

with the least noise variance. This also explains why RPwSD is the worst RWA

algorithm since the shortest physical distance does not mean the least physical layer

degradation.

Using the number of wavelengths to represent the performance of algorithms gives

43

us a direct perspective on the network building cost. However, we still need the

blocking probability as a secondary performance metric to compare the results.

3.1.3.4 Maximum Traffic Loads for Different Crosstalk Levels

Another performance metric evaluated is the maximum traffic load allowed in

the network when the blocking rate is constrained and the number of wavelengths

is fixed. This amounts to determining the amount of traffic acceptable in a network

when the network hardware is determined and the blocking probability requirement

is enforced. In some sense, this represents the real capacity of an all-optical network

for different RWA policies.

Here, since W is fixed, we incorporate the FWM/XPM effects in the simulation.

Performance is evaluated for different levels of physical impairments; we run simu-

lations for three different levels of crosstalk by changing the pair (Xsw, Xadj). The

results are shown in Table 3.3.

It is clear that the network can support larger traffic when using FF WA than

when using RP WA. At higher crosstalk levels, FH allows more calls than SD because

degradations originating at the nodes (both fabric and adjacent-port crosstalk) dom-

inate over degradations originating in the fibers (FWM/XPM and ASE noise). In

low crosstalk cases, the performance of SD is nearly the same as that of FH or even

better than FH (such as with Xadj = −25 dB and Xsw = −45 dB) since the noise

from the links goes up and has the same level of impact as crosstalk. QM algorithm

performs slightly better than FH and SD for all crosstalk levels. But LV beats QM,

SD, and FH since LV dynamically finds a suitable route based on the candidate light-

path noise variance and the traffic load. Thus, FFwLV is significantly superior to the

other algorithms for every level of crosstalk tested.

However, most published papers use blocking probability as the performance met-

ric. The blocking probability model is applicable over different holding times and is

44

Table 3.3: Maximum traffic load for different levels of crosstalk when W = 32 and

Ptotal ≈ 10−3

(Xsw, Xadj) (−15 dB,−35 dB) (−20 dB,−40 dB) (−25 dB,−45 dB)

RWA Load (Erlangs) Load (Erlangs) Load (Erlangs)

FFwSD 120 135 146

FFwFH 124 135 145

FFwQM 126 137 146

FFwLV 133 146 156

RPwSD 105 122 133

RPwFH 112 126 136

RPwQM 115 127 135

RPwLV 123 134 148

easily studied analytically. Moreover, blocking probability can be used as a metric

to dimension networks and link capacity. Therefore, in the remainder of this disser-

tation, only blocking probability is considered as the performance metric to compare

results.

3.2 WA Algorithms Considering Physical Impair-

ments

In this section, we tackle the problem of wavelength assignment with QoT con-

straints. The results of Chapter 2 indicate that appropriate wavelength choices can

significantly reduce the impact of impairments that depend on the spectrum us-

age, such as crosstalk. There are two ways of addressing the WA problem in the

presence of physical impairments, which we call QoT-guaranteed and QoT-aware.

45

QoT-guaranteed WA algorithms only allow lightpaths to be established if the QoT

requirement is met and never try other wavelengths if blocking is due to QoT, thereby

inducing a much higher blocking rate than conventional techniques, but enforcing ac-

ceptable QoT for the lightpath [8]. Conversely, QoT-aware WA algorithms iteratively

try every idle wavelengths. In this section, we use QoT-guaranteed WA algorithms

instead of QoT-aware WA in order to determine the probability that the chosen wave-

length is feasible in the first trial. We discuss the QoT-aware WA in the next chapter.

The new WA algorithms proposed in this section work well in centralized and

de-centralized networks, by avoiding the need to collect accurate information on all

assigned lightpaths and physical impairments required to estimate of QoT.

3.2.1 Static Wavelength Ordering

We seek WA algorithms that are able to reduce crosstalk effects, a dominating

state dependent physical impairment in large dense WDM networks. To do this,

the algorithm must attempt to use wavelengths that are as spectrally separated as

possible to avoid adjacent-port crosstalk. Simultaneously, the WA should use as small

a number of wavelengths as possible to minimize subsequent wavelength blocking,

which the FF WA algorithm excels at. We propose to use a conventional FF WA

technique except that the wavelengths are pre-ordered so as to minimize the adjacent

wavelength crosstalk effect. In this section we refer to as a channel the sequential

order of resources to be accessed. We reserve the term wavelength to refer to the actual

spectral band utilized. The WA module then picks the first channel available from the

list of unused channels, and this channel corresponds to a particular wavelength that

depends on the ordering. This idea is similar to the algorithm developed in [19] where

WA using ordering is used to reduce four-wave mixing crosstalk in WDM systems.

Wavelength ordering can be done off-line (static pre-ordering) or on-line (adap-

tive ordering). First, we explore the use of a static off-line technique. Then on-line

46

ordering techniques are proposed, which attempt to minimize the crosstalk impair-

ments for the current network state by finding all available wavelengths on a route

and picking the one that is spectrally furthest away from all used wavelengths.

The off-line ordering algorithm is run once, before the network is put in operation,

leading to a non-adaptive (fixed), low-complexity algorithm. Ideally the algorithm

uses the wavelength order that results in the least amount of crosstalk. Even though

the search for a satisfactory priority-list is performed off-line, it must still be done effi-

ciently. The ordering problem addressed in [19] was shown to be NP-hard because the

search space grows as the factorial of the number of wavelengths per fiber link. This

exhaustive search becomes intractable as the number of wavelengths becomes large.

Let us consider the complexity of our optimal ordering problem before proposing a

low-complexity alternative heuristic.

The optimization objective we consider is to find the wavelength order that mini-

mizes the average crosstalk in the network for given traffic statistics when using a FF

wavelength assignment algorithm. Call arrivals are assumed to be Poisson and service

times are assumed to be exponential. Then the network is Markovian and we can

consider the steady-state distribution of network states. The states identify which

channels are utilized on each link in the network. The crosstalk at each network state

is determined by the wavelength ordering (mapping from wavelengths to channels).

Different orderings may have a different crosstalk impact for the same network state.

Let the network use W wavelengths. Denoting the vector of network states by S

(of size |S|) and the wavelength ordering W -vector by C ∈ C, the objective can be

written as

minC∈C

|S|∑i=1

P(i)× PXT (i, C), (3.4)

where P(i) is the probability of network state i and PXT (i, C) is the crosstalk power

47

level if the network state is i and wavelengths are ordered as C. Solving (3.4) directly

involves an exhaustive search of C, which has cardinality W !.

An alternative and equivalent way of writing this objective is to consider PXT (i)

dependent only on the network state, and let P(i, C) be determined by both the

network state and the ordering C. The states now describe an actual wavelength

usage and not a channel usage. The crosstalk of network wavelength state i, PXT (i),

is equal to the value of PXT (i′, C) for another channel state i′ for a FF algorithm

using ordering C. The objective can now be written as an optimization over the state

probabilities,

minC∈C

|S|∑i=1

P(i, C)× PXT (i). (3.5)

The optimal ordering must assign the largest probability to the lowest crosstalk

PXT (i). A solution to this problem can be obtained by sorting the PXT (i) and assign-

ing probabilities to each PXT (i). The complexity of sorting PXT (i) is |S|(|S| − 1)/2.

The number of network states increases exponentially in the number of wavelengths

and the number of network links L, |S| = 2LW .

In either case the complexity of finding an optimal solution for the wavelength

ordering problem increases at least exponentially in the number of wavelengths in the

network. A heuristic low-complexity alternative is therefore proposed and described

in Algorithm 3.1. The idea is that at any point the next wavelength to be used

should be as far as possible spectrally from any already assigned wavelengths, since

the crosstalk is modeled as exponentially decreasing with spectral separation. The

first two wavelengths on the ordered list are the extreme points, i.e, wavelength slots

labeled 1 and W . Once ordered, these are removed from the unordered wavelength

list. The algorithm creates the ordered list by successively placing a wavelength

from the remaining unordered wavelength set that has the largest separation from all

48

Algorithm 3.1 Heuristic wavelength ordering algorithm.

1: Define two wavelength arrays, Co and Cs, corresponding to ordered and suc-

cessive wavelength sequences, where successive wavelengths are labeled λj, j =

1, . . . ,W. Initially set Co to λ1 and Cs contains other wavelengths

2: Estimate the crosstalk power level PXT (j, l) for wavelength λj in Cs to every λl

in Co by PXT (j, l) = exp(−α |l − j|) for some constant α > 0

3: Create a set Ck consisting of all candidate wavelengths with the same minimum

worst-case crosstalk level minλj∈Cs maxλl∈Co PXT (j, l)

4: Identify the next wavelength to add to the ordered list, λj =

arg minλk∈Ck

∑λl∈Co

PXT (k, l). Append λj to Co and remove it from Cs

5: Repeat from step 2 until Cs is empty

6: return ordered wavelength sequence Co ∈ C

the wavelengths in the ordered set. If there are several wavelengths with the same

crosstalk impact, the wavelength whose sum of crosstalk contributions to all already-

sorted wavelengths is minimum is chosen, as stated on line 4 in Algorithm 3.1. For

example, if there are 8 wavelengths then the resulting ordering is (1, 8, 4, 6, 2, 7, 3, 5).

Again the term channel is used here to refer to the place in the ordered list, and is not

the same as the wavelength number; in our example channel 2 represents wavelength

8.

To estimate the complexity of this algorithm, we must find the complexity of each

cycle through the loop; note that there is one loop performed W − 1 times. For

the xth cycle, the size of Co is x and the size of Cs is W − x (variables defined in

Algorithm 3.1). The array PXT is of size x(W −x) and the number of steps needed to

compute minλj∈Cs maxλl∈Co is x(W − x− 1) + (x− 1). The size of Ck is bounded by

W −x, so performing step 4 in Algorithm 3.1 is of order (W −x)(x−1)+(W −x−1).

49

The total complexity is then

W∑x=2

x(W − x) + xW − x2 − 1 + xW − x2 − 1 =1

2W 3 − 11

2W + 5, (3.6)

which is O(W 3), only polynomial in W .

The conventional FF wavelength assignment algorithm becomes the FF with

ordering (FFwO) algorithm by picking the next candidate wavelength from the or-

dered array Co instead of sequentially, as is typically done. For a QoT-guaranteed

WA algorithm, it is hoped that wavelength ordering increases the chance that the one

wavelength considered has a small number of adjacent-port crosstalk terms. In the

example in Fig. 1.1, if the system contains 4 wavelengths, the adjacent-port crosstalk

disappears if the ordering algorithm is applied, which yields a numbering 1, 4, 2, 3.

3.2.2 Wavelength Spectrum Separation

The static wavelength ordering scheme can only combat adjacent channel crosstalk.

Dynamic network state-dependent on-line wavelength ordering algorithms helps re-

duce the impact of physical impairments when the switching fabric crosstalk is not

negligibly small. Here, a dynamic wavelength ordering technique called wavelength

spectrum separation is proposed based on defined performance penalty factors.

All free channels are sorted during the lightpath setup procedure to find a chan-

nel which has the smallest performance penalty factor that represents the level of

impairment normalized to fabric crosstalk. This measure is partly related to QoT.

Consider a typical lightpath traversing n nodes as shown in Fig. 2.1. The penalty

factor on candidate wavelength λs given wavelength λl is currently used in node i is

50

denoted Di(λs, λl) and defined as

Di(λs, λl) =

Xadj

Xswif λs & λl adjacent;

1 if λs = λl;

0 else,

(3.7)

where Di(λs, λl) represents the relative crosstalk power levels normalized to the

switching crosstalk power level. We define XTmax(λs) as the maximum node crosstalk

effect experienced by wavelength λs along the lightpath, which can be calculated as

XTmax(λs) = maxi=1,...,n

Si∑j=1

W∑

l=1

Di(λs, λl(i, j)), (3.8)

where λl(i, j) denotes wavelength l of link j at node i. XTtotal(λs), the total penalty

factor on λs, is the summation of all crosstalk components along the lightpath, which

can be calculated as

XTtotal(λs) =n∑

i=1

Si∑j=1

W∑

l=1

Di(λs, λl(i, j)). (3.9)

The total penalty factor is a simple measure of the dominant node crosstalk effect,

which is the major physical impairment considered here.

Combined with FF WA, a new dynamic WA algorithm is proposed, called FF

with wavelength spectrum separation (FFwSS). FFwSS only adds a small amount of

calculation compared to the FFwO scheme. The penalty factor is a simple count of

the relative effects of node crosstalk, instead of estimating the actual QoT for each

candidate channel and other affected channels in the entire network. To assign a

wavelength to a call, a set of wavelengths (which we denote by Λ) with minimum

XTmax are first found, and from that set the one wavelength with minimum XTtotal

51

is selected. The algorithm’s goal is to find

arg minλi∈Λ

XTtotal(λi), (3.10)

where the set of wavelengths Λ is defined by

Λ = λi : XTmax(λi) = minj=1,...,r

XTmax(λj). (3.11)

The idea behind FFwSS is that the channels with the smallest total penalty factor

are the least likely to be blocked because of an unsatisfactory QoT of lightpaths.

However this type of WA algorithm only works well when the physical-layer blocking

dominates over the wavelength blocking, because its wavelength blocking rate is higher

than for other techniques that cluster wavelength usage, such as FF [15].

3.2.3 Adaptive Wavelength Ordering

To exploit the benefits of both algorithms proposed above, we introduce an adap-

tive wavelength ordering technique, called adaptive FF with spectrum separation

(AFFwSS). There is a switch function in the AFFwSS algorithm to choose between

two different schemes based on the instantaneous network physical impairment sever-

ity. One is the FFwO algorithm left intact, and the other is similar to the FFwSS. We

have added the effect of nonlinear fiber crosstalk (FWM and XPM), and redefined

the performance penalty factor.

The adaptive algorithm’s flow chart is shown in Fig. 3.8. When a call arrives,

the source node finds a route by checking its routing table generated by a standard

shortest path routing algorithm. Each node i on the route then calculates its own

52

XT

XT i

i

Shortest PathFixed Routing

Switch functionAre physical impairments

"small"?

other nodes. When source node receives it,lightpath is built using assigned wavelength

The destination sends response back to inform

) for each freemaximum crosstalk penalty (

) to the chosen routeminimum (

Call Arrival

No FFwSS

Yes

FFwO

Along the chosen route, each node counts

Assign the wavelength that has the

wavelength in the whole route. The destination

Assign the wavelength

makes decision as the signaling message arrives.

such as 1,8,4,6,3,7,2,5

based on thewavelength order,

Figure 3.8: Flow chart of AFFwSS algorithm in the hop-by-hop-RWA scheme.

penalty factor XTi(λs) for every free wavelength as

XTi(λs) = γσ2NL(i, s) +

Si∑j=1

W∑

l=1

Di(λs, λl(i, j)), (3.12)

where Di(λs, λl) is defined in (3.7). The term γσ2NL(i, s) represents the relative non-

linear fiber crosstalk power level normalized to the fabric crosstalk power level, where

the coefficient γ is defined as the strength of the nonlinear crosstalk relative to the

switching crosstalk, i.e.,

γ =1

P 2o Xsw

. (3.13)

We calculate σ2NL(i, s) using the same technique as for (3.1).

53

Once the node penalty is computed, the total penalty factor for the link is obtained

as

XTmin = mins=1,...,Wf

maxi=1,...,n

XTi(λs), (3.14)

where Wf is the number of wavelengths free over the entire route.

In Fig. 3.8, after calculating the penalty factor, the algorithm chooses between

two WA options. This choice is based on a threshold, called the impairment severity

threshold (Hth) that is set using preliminary calibration simulations. During network

operation, the switch compares XTmin with Hth, opting for FFwO if XTmin is less

than Hth and using wavelength λc, where c is the argument of the minimum in (3.14),

otherwise.

To illustrate the algorithm, consider Fig. 3.9. Assume there are four channels

in each fiber link. The first two lightpaths, LP1 and LP2, occupy channel 1 (CH1)

and channel 2 (CH2) of Link 1, respectively; LP3 occupies CH3 of Link 2. The WA

algorithm needs to assign a wavelength for LP4 of Link 2. Here, only two wavelengths

are used, so there is no FWM effect. Based on [45], the channels’ XPM variances can

be estimated as γσ2NL(l,m, n) = 0.3 if (l, m, n) = (0, 2, 2), and γσ2

NL(l, m, n) = 0.1 if

(l,m, n) = (0,−1,−1) or (0, 1, 1) for Po = 0 dBm.

Using FFwO and assuming the four wavelengths to be ordered as 1, 4, 2, 3 (CH1

uses λ1, CH2 uses λ4, CH3 uses λ2, and CH4 uses λ3), in this scenario, LP4 is

assigned CH1, which is not the optimal choice since LP4 adds fabric crosstalk to LP1.

Moreover, an additional adjacent-port crosstalk affects LP1 because part of LP4’s (λ1)

power leaks to adjacent LP3 (λ2) when LP1 and LP3 are multiplexed together at the

output [9].

Let us consider what happens if we employ our new adaptive algorithm. Based

on (3.14), the node assigns CH4 (λ4) to LP4, which is the optimal assignment since

54

WRS CH 1

WRS

WRS

CH

CH

3

2

LP 1 using CH 1

LP 2 using CH 2

LP 3 using CH 3

LP 4 using ?

Source

Source node 1

node 2 Destination

Destination

node 2

node 1 Link1

Link2

Figure 3.9: An illustrative example with only one node. LP1 from source node 1 andLP3 from source node 2 are directed to destination node 1 and LP2 from source node1 and LP4 from source node 2 are directed to destination node 2.

Table 3.4: Channel status, Xsw = −27 dB and Xadj = −30 dB. Hth = 0.1

Channel Status XTi(λs) γσ2(λs)

CH1 free 1.6 0.1

CH2 occupied - -

CH3 occupied - -

CH4 free 0.3 0.3

no crosstalk is introduced. The values of XTi(λs) and γσ2(λs) for this example are

listed in Table 3.4.

In a distributed architecture network, the new AFFwSS algorithm chooses a wave-

length according to the following rules. When a call comes in the source node, the

node finds its link’s available wavelengths, calculates XTsource(λs) for each free chan-

nel λs, saves those values in a signaling message, and sends the message to the next

hop. The next node finds its available wavelengths and finds the intersection with

the source node’s free wavelengths. Then it calculates a new XT2(λs) for each free

channel λs of the intersection of the free wavelengths. For every λs, XT2(λs) is

compared with XTsource(λs). The maximum value is saved to the signaling message

55

and sent to the next hop, and so on. After the destination node finishes calculating

XTdestination(λs), it makes a decision in two steps. First, it inspects the severity of

physical impairments to decide if physical impairments are small, which is done by

comparing XTmin to Hth. The threshold Hth is preset based on previous training,

such as a preliminary calibration via short simulations. If XTmin is bigger than the

threshold, AFFwSS assigns the wavelength λc that has the minimum penalty factor to

the route. If not, AFFwSS reverts to FFwO and assigns the wavelength by a first fit

algorithm according to the pre-set order. After this decision is made, the destination

sends the response back to inform the other nodes on the route. When the source

node receives the response, the lightpath is built using the assigned wavelength.

3.2.4 Simulation Results and Discussion

The WA techniques are evaluated by a simulation of a random 15-node network

illustrated in Fig. 3.10, with a physical layer described by link parameters listed in

Tables 2.1 and 3.1 except for the wavelength capacity in each link, which is set to

8. All WA algorithms are QoT-guaranteed. The number of calls generated is more

than 9 × 105 for each WA scheme. We model the arrival process as Poisson and the

holding time as exponentially distributed. Shortest-path routing is assumed. The

measured blocking probability includes calls blocked due to a shortage of continuous

wavelength paths and the failure of the chosen path to satisfy the QoT threshold.

We evaluate the performance of three ordering algorithms by comparing them

to FF and RP. First, the adjacent-port crosstalk power attenuation ratio is set to

Xadj = −25 dB and the network load is fixed at 22.5 Erlangs. The blocking probability

versus fabric crosstalk ratio Xsw for this network is given in Fig. 3.11 for these WA

algorithms. Plots of blocking rates of FF and RP without physical impairments

give the lower bound for the performance since they only count the network layer

blocking and ignore physical layer blocking. The plots show that FFwSS should

56

7

11

1

2

3

13

5

6

4

15

14

9

10

8

12

Figure 3.10: Topology of network used for simulation

switch to FFwO when Xsw ≤ −40 dB to get a better performance since FFwO

has a smaller blocking rate than FFwSS. The blocking rate is further decreased by

applying the AFFwSS technique. The idea behind AFFwSS is that a technique

similar to FFwSS is used if the candidate lightpath meets many physical impairments

because FFwSS can handle more physical impairments than FFwO. If the physical

impairments in the candidate lightpath are minor, FFwO can mitigate them and

satisfy the QoT requirement. Furthermore, FFwO packs the communicating channels

in as few wavelengths as possible, which decreases the wavelength blocking. FFwO

cannot remove all of the physical impairments and thus its blocking probability cannot

converge to that of the ideal physical layer FF WA as the crosstalk Xsw decreases;

rather, the blocking probability of FFwO converges to a value larger than that of

FF with the ideal physical layer. The same is true for AFFwSS. There is still a

performance gap between AFFwSS and its lower bound, the ideal physical layer case,

originating from a residual physical impairment limiting the network performance as

expected from the results of the optimal WA algorithm shown in Section 2.2. Yet the

benefit of using AFFwSS is more than one order of magnitude in blocking probability

compared to FF when physical impairments are severe, for instance when Xadj = −25

dB and Xsw > −35 dB.

57

−55 −50 −45 −40 −35 −30 −25

10−2

10−1

100

Xsw

(dB)

Blo

ckin

g P

roba

bilit

y

FF wavelength assignment(FFWA)

RP wavelength assignment(RPWA)

FFwO wavelength assignment

FFwSS wavelength assignment

AFFwSS wavelength assignment

FFWA without physical impairments

RPWA without physical impairments

Figure 3.11: Blocking probability for Xadj = −25 dB and a load of 22.5 Erlangs.Hth = 122, 43, 24, 12, 0, 0, 0 for Xsw = −55,−50,−45,−40,−35,−30,−25 dB,respectively.

Fig. 3.12 shows the blocking probability as the network load varies for Xadj = −20

dB and Xsw = −30 dB. In this case, AFFwSS has the best performance, which is

basically the same as FFwSS since the physical impairments are severe. No WA

schemes performs close to the blocking probability for networks with ideal physical

layer.

Fig. 3.13 shows the blocking probability as the network load varies for Xadj = −25

dB and Xsw = −40 dB. For this case AFFwSS has the best performance, followed

by FFwO since the physical impairments are light. AFFwSS performs close to the

blocking probability for an ideal network. The difference between FFwO and FFwSS

fluctuates as the traffic load changes, which indicates that the AFFwSS switch thresh-

old could be affected by the network traffic load. Unfortunately, the network traffic

load is dynamically changing and hard to measure in a realistic network. Therefore,

our algorithm AFFwSS assumes that Hth is independent of the traffic load.

58

10 15 20 25 30 35 40 45 5010

−5

10−4

10−3

10−2

10−1

100

Network load (Erlang)

Blo

ckin

g P

roba

bilit

y








Figure 3.12: Blocking probability of FF, RP, FFwO, FFwSS, and AFFwSS for Xsw =−30 dB and Xadj = −20 dB. Hth = 0.

10 15 20 25 30 35 40 45 5010

−5

10−4

10−3

10−2

10−1

Network load (Erlang)

Blo

ckin

g P

roba

bilit

y








Figure 3.13: Blocking probability of FF, RP, FFwO, FFwSS, and AFFwSS for Xsw =−40 dB and Xadj = −25 dB. Hth = 12.

59

We can conclude that AFFwSS improves the network performance and decreases

crosstalk to achieve an excellent performance. Although AFFwSS cannot successfully

remove all physical impairments, it exhibits great improvements compared to FF, RP,

FFwO, and FFwSS.

Moreover, AFFwSS has the same complexity as FFwSS. Call S the maximum

number of input/output fibers at any node in the network, n the maximum number

of nodes along a lightpath, and W the number of wavelengths in each fiber link. Ig-

noring nonlinear fiber crosstalk computations, it can be seen that the computational

complexity for FFwSS is O(W (nWS + nWS + nWS)) = O(nW 2S), while the com-

plexity for AFFwSS is O((WS + WS)nW ) = O(nW 2S). Each of FF, RP and FFwO

is less complex: O(nW ). Including nonlinear crosstalk computations impacts the

complexity for all algorithms identically, and thus AFFwSS is as complex as FFwSS,

while performing better in terms of blocking probability.

3.3 Summary

In this chapter, we study the impact of incorporating QoT constraints into routing

algorithms and WA algorithms for all-optical networks. Performance is evaluated via

simulations.

For the routing problem, the proposed new cost function helps the QoT-aware

routing algorithm wisely select the route with least physical impairments. The simu-

lation results show that the new LV routing policy can effectively improve the network

performance in terms of several performance metrics for all the scenarios tested. In-

stead of solely using blocking probability, the number of wavelengths needed and

the maximum traffic load conveyed are considered as evaluation metrics. However,

the coarse granularity of counting wavelengths hinder the fine difference between the

performances of the RWA algorithms.

60

For the WA problem, three ordering techniques are proposed to decrease the effect

of physical impairments. Among them, AFFwSS has a particularly strong advantage

in terms of blocking probability over other schemes at all levels of physical impair-

ments and at all network loads. The wavelength ordering techniques can alleviate the

physical impairments caused by power leaking in the network nodes and nonlinear

effects in the fibers. They can be applied along with any routing algorithm to create

a better RWA function.

The techniques proposed in this section only use the state of the links between a

node and its neighbors when they estimate the physical degradation, thus are practical

for both centralized and distributed networks.

Chapter 4

Analytical Model for RWA with

QoT Constraints

In Chapter 2, we provide an analytical model to compute the number of consec-

utive wavelengths needed to minimize blocking probability in the static traffic case.

In this chapter, we present an analytical model to compute blocking probabilities

for RWA with QoT constraints in WRONs in the dynamic traffic case. Computing

the blocking probability by simulation, as we did in Chapter 3, is a time-consuming

process. An analytical model is desirable because it is faster and helps us understand

and design RWA algorithms with QoT constraints.

Several analytical models for RP WA with no QoT constraint are proposed in the

literature [11, 31, 32, 46–49]. The work in [11] assumes that the wavelengths used on

a link depend only on the wavelengths used on the previous link along the selected

route. In [46,47], a path decomposition technique is proposed, in which a long paths

are divided into small segments (of two or three links). Then an approximate Markov

process is obtained to study each segment separately and the blocking probability of

the long path is computed by appropriately combining the blocking probabilities of

the segments. In [32], the blocking probability of a multiple hop path is recursively

61

62

solved; first, two-hop segments are dealt with, then the first segment is treated as

one hop and combined with the next hop as a new two-hop segment. The process is

repeated iteratively.

Blocking probabilities in WRONs for FF WA are harder to analyze [46, 47]. The

utilization of a layered graph approach, or “wavelength decomposition”, is proposed

in several works [34, 50–54]. In [50, 52, 53], link independence is assumed, thereby

overestimating blocking probabilities, especially in tandem networks [34,51]. In [51],

an object independence assumption is made, where the object is a free link or path.

In [54], the traffic is modeled as flowing from one layer to the other, and the overflow

traffic is modeled as a Bernoulli-Poisson-Pascal (BPP) process. In [34], the author

derives an iterative model to calculate the blocking probability for fixed routing in

networks with any topology. It assumes wavelength independence and divides the

network into layers as shown in Fig. 4.1. The moment matching and equivalent path

methods are used to characterize the overflow traffic.

None of these techniques account for QoT. In more recent research [33], an analyt-

ical framework for a class of QoT-aware RWA algorithms is proposed by extending the

techniques published in [48,49]. In that work, the self-crosstalk, as shown in Fig. 1.1,

is considered for RP WA algorithms with fixed routing. However, this model can-

not be adapted to computing blocking probabilities in cases when different crosstalk

attenuations are present in the network. If adjacent channel crosstalk is significant,

even for RP WA, the wavelength equivalence assumption is no longer valid because

each wavelength may have different degradation as shown in previous chapters.

Here, we propose an analytical model to compute the blocking probabilities for FF

and FFwO wavelength assignments (WAs) with QoT constraints. Each path is treated

individually and the path wavelength blocking probability is calculated by using the

model in [34]. The technique can be applied to QoT-aware and QoT-guaranteed WA

algorithms.

63

This chapter begins with our model framework and assumptions in Section 4.1

and gives an overview of the model presented in [34] in Section 4.2. We extend this

technique to compute the QoT blocking in Section 4.3. Numerical examples are shown

in Section 4.4 and simulation is used to validate the model. A summary is given in

Section 4.5.

4.1 Proposed Analytical Framework for FF WA

with QoT Constraints

We extend the method from [34] and decompose the WRON with physical im-

pairments by wavelengths as a layered system, shown in Fig. 4.1. A WRON with W

wavelengths in each link is decomposed to W layered networks, each of which has the

same topology but one wavelength capacity in each link. The offered network traffic

first goes into layer 1, then blocked traffic (overflow traffic) flows down to layer 2 and

so on. At layer W , the overflow traffic becomes the overall network blocked traffic

and the blocking probability can be computed. The wavelength continuity constraint,

which forces a call to remain on the same wavelength along the path, is automatically

enforced in this approach. Wavelength independence is also assumed, which means

that each wavelength is considered separately and the probability is only conditional

to the arrival rates.

Because this model deals with each wavelength separately and the traffic overflows

from one wavelength with large index to the next wavelength with the small index,

it is natural to use this method to analyze FF WA [34].

First, we present our assumptions concerning the model used throughout this

chapter. The same notation is used as in Chapters 2 and 3, as well as in [34] for

the sake of consistency. We assume that each link between nodes is unidirectional

consisting of a single fiber; routing is fixed without alternate paths and wavelength

64

Wavelength W

Wavelength 1

Wavelength 2WRON

Overall blocked traffic

Offered network traffic

Original WRON systemwith W wavelengths ineach link

......

Overflow traffic

Overflow traffic

Offered network traffic

Overflow traffic

Figure 4.1: Layered network model for WRONs.

assignment is FF. Z is the set of all s-d pairs in the networks. In general, a path

from source node to destination node is denoted by r(s, d) or r(z) for z ∈ Z. r(z) is

decided by the fixed shortest path routing algorithm. Define a segment r(i, j) as a

subset of path r(s, d) as in Fig. 2.1. An n-hop path r(0, n) is shown in Fig. 2.1; it

consists of a set of n links. In particular, r(i, j) ∩ r(l, m) = ∅ means that there are

no shared links between r(i, j) and r(l,m). Let Φs,d be the Poisson arrival rate for

a s-d pair ((s, d) or z). Call durations follow an exponential distribution with mean

value of E[X]. Without loss of generality, E[X] = 1. Denote by Awz the equivalent

Poisson offered load to wavelength (layer) w for r(z). Then clearly A1s,d = Φs,d. aw

i,j is

the total equivalent Poisson offered load to wavelength (layer) w from node i to node

j. Note that Awi,j is the traffic originating from node i to node j and aw

i,j is the total

traffic passing through the segment of r(i, j). βwi,j ∈ 0, 1 is the number of currently

active calls in r(i, j) at wavelength (layer) w. Ws,d is the path capacity or number

of wavelengths for r(s, d). We assume that each link has the same number of wave-

lengths, then Ws,d is denoted as W for all (s, d) ∈ Z. Pws,d represents the wavelength

blocking probability and Pws,d represents the QoT blocking probability for r(s, d) on

wavelength w. Similarly, P represents the overall network wavelength blocking prob-

65

ability and Ps,d represents the overall path wavelength blocking probability. Denote

by P the overall network blocking probability and by Ps,d the overall path blocking

probability.

We extend the model in [34] to consider QoT blocking. In Fig. 4.2, we show

the first layer of a new system if QoT-aware RWA algorithms are applied. The

computation of the blocking probabilities is derived in the Section 4.3. Each layer

is divided into two sublayers. The offered traffic is first checked for QoT compliance

for each path on which the requests might be assigned in the QoT blocking sublayer.

Then it enters a second sublayer to check whether the path and wavelength (i.e.

lightpath) is available. Then the total blocked traffic from the two sublayers overflows

down to the next layer. The QoT blocking depends on the usage of other layers and

is computed by using the stationary state probabilities in other layers. Thus we have

to iterate this process until a steady-state is reached. Fig. 4.2 only shows the flow

after the system is stable.

In QoT-guaranteed RWA, a part of QoT blocked traffic flows out of the system

instead of going to the next layer. Thus, if a call finds an idle path with the unac-

ceptable QoT, the call is instantly blocked and does not try other wavelengths. We

use the probability that an idle path exists for a s-d pair in the wavelength blocking

sublayer to approximate the s-d pair idle probability in the QoT blocking sublayer.

Then a proportion of the flow is directly blocked in each layer and removed from the

system so it does not flow into the next layer.

Using this framework, we can also evaluate the FFwO WA algorithm. In FFwO,

the layer index is not equal to the wavelength index. Thus in the QoT blocking

sublayer for FFwO, we have to choose different layer state probabilities to obtain the

QoT blocking, depending on the wavelength ordering. The calculation for wavelength

blocking is same as with FF WA.

66

Wavelength 1

Layer 2

Wavelength blocking sublayerQoT blocking sublayer

Layer 1

System checks the QoT ofthe traffic at wavelength 1.The QoT blocking probability

based on the traffic in otherwavelengths.

Traffic flows whose candidatepaths have good quality

Overflow traffic due towavelength blocking

Overflow trafficdue to QoT blocking

Φs,d(1− P1s,d), ∀(s, d) ∈ Z

P1s,d is computed

Φs,dP1s,d, ∀(s, d) ∈ Z

Φs,d, ∀(s, d) ∈ Z

Figure 4.2: First layer in layered network model for QoT-aware RWA algorithms.

67

4.2 Wavelength Decomposition Approach for Com-

puting Wavelength Blocking Probabilities in

All-Optical Networks

In this section, we briefly review how the wavelength blocking probability is com-

puted in the wavelength blocking sublayer. The technique presented here was pub-

lished in [34] without considering QoT constraints. We repeat it for the sake of

completeness and to show how to compute the QoT blocking and the wavelength

blocking iteratively. Our method to compute the QoT blocking can also be applied

to other models of calculating wavelength blocking. Note that the QoT blocked traffic

is not considered in this section.

4.2.1 Wavelength Blocking Probability in a Single Wavelength

Considering an n hop path (see Fig. 2.1), the state of a wavelength w at time t

can be expressed by the n(n + 1)/2 dimensional process:

(βw0,1(t), β

w0,2(t), . . . , β

wn−1,n(t)), (4.1)

where

βwi,j + βw

l,m ≤ 1, ∀r(i, j) ∩ r(l, m) 6= ∅, 0 ≤ l < m ≤ n

According to [55], the above process is a time-reversible Markov process and the

stationary probability vector πw is given by

πw(βw0,1 · βw

0,2, · · · , βwn−1,n) =

1

Gwr (0, n)

[((aw

0,1)βw0,1 · (aw

0,2)βw0,2 , . . . , (aw

n−1,n)βwn−1,n)

],

(4.2)

68

where Gwr (0, n) are normalization constants computed recursively by [34]

Gwr (0, n) = Gw

r (0, n− 1) +n−1∑i=0

Gwr (0, i)aw

i,n, w = 1, . . . , W, (4.3)

with Gwr (0, 0) = 1. aw

i,j is the sum of all equivalent Poisson traffic from all s-d pairs

on segment r(i, j) at wavelength w, given by [56]:

awi,j =

∑

r(i,j)⊆r(s,d)r(i,j)⇐Aw

s,d, then r(m,l):Aws,d

∀r(l,m)⊆r(0,n)

Aws,d · (1− Pw

s,d)

1− Pwi,j

, (4.4)

where “r(i, j) ⇐ Aws,d, then r(m, l) : Aw

s,d, ∀r(l, m) ⊆ r(0, n)” means that the traffic

that belongs to segment r(i, j) is unique [34]. The wavelength blocking probability

for r(0, n) at wavelength w is computed as:

Pw0,n = 1− πw(0, 0, . . . , 0) = 1− 1

Gwr(0,n)

. (4.5)

4.2.2 Computing the Overall Wavelength Blocking Probabil-

ity by Using the Overflow Model

The traffic blocked at wavelength w flows down to the next wavelength (layer).

However, the overflow is not Poisson distributed and its variance is larger than the

mean, which indicates that the traffic is bursty [56]. Many studies have analyzed

the overflow traffic in conventional circuit switching network [56]. The mean of the

overflow traffic to the next layer is

Aw+1s,d = Aw

s,d · Pws,d. (4.6)

69

The variance of the overflow traffic V w+1s,d is computed by using Riordan’s formula [56]

as

V w+1s,d = Aw+1

s,d

(1− Aw+1

s,d +Φs,d

Ωws,d + 1 + Aw+1

s,d − Φs,d

), (4.7)

where Ωws,d is the capacity of an equivalent single-link system for layer 1 to w, which

can be obtained from:

Φs,d · Er(Φs,d, Ωws,d) = Aw+1

s,d . (4.8)

Er(Φs,d, Ωws,d) is the generalized Erlang-B formula for non-integral capacity, given

by [57]

Er(x, y) =xye−x

Γ(y + 1)[1− Γ(x, y + 1)], (4.9)

where Γ(x, y + 1) is the incomplete Gamma function.

Then the burstiness is defined as the ratio between the variance and the mean

value,

Zw+1s,d =

V w+1s,d

Aw+1s,d

. (4.10)

Fredericks and Hayward’s approximation is used to account for the non-Poisson

overflow traffic as [56]

Aw+1s,d · Pw+1

s,d ≈ Aw+1s,d · Er

(Aw+1

s,d

Zw+1s,d

,Ωw+1

s,d

Zw+1s,d

,

), (4.11)

70

where the value of Ωw+1s,d is obtained by

Pw+1s,d = Er(Aw+1

s,d , Ωw+1s,d ), (4.12)

and can be treated as the capacity of another equivalent single-link system for only

layer w + 1 with a mean arrival rate of Aw+1s,d .

Using (4.5), (4.11), and (4.12), we can approximate the wavelength blocking prob-

ability and path arrival rate for each layer. Then the overall path wavelength blocking

probability is computed as

Ps,d =AW

s,d · PWs,d

Φs,d

=AW+1

s,d

Φs,d

. (4.13)

The overall network wavelength blocking probability in the network is given by

P =

∑(s,d)∈Z AW+1

s,d∑(s,d)∈Z Φs,d

. (4.14)

Algorithm 4.1 shows the main steps used to compute the overall path and network

wavelength blocking probabilities for FF WA if w0 = 1, A1s,d = Φs,d, V 1

s,d = Φs,d,

and Z1s,d = 1 for all (s, d) ∈ Z. If the relative difference between for the blocking

probabilities between two successive iterations differ by less than ε for each path, the

current layer is seen stable and start the iteration for the next layer.

4.3 RWA Analytical Model with QoT Constraints

In Section 4.1, we show our general analytical framework to calculate the total

blocking probability for FF WA algorithms. In this section, we give a detailed analyt-

ical model considering QoT blocking due to self-crosstalk, ASE noise, thermal noise

and shot noise. The switching crosstalk and neighbor-crosstalk are ignored here. The

71

Algorithm 4.1 Algorithm to compute the wavelength blocking from wavelength

w = w0 to W given Aws,d, V w

s,d, and Zws,d for all (s, d) ∈ Z.

1: Assume initial values for Aws,d = Aw

s,d, and initial path wavelength blocking prob-

ability as P ′s,d = 0 for all (s, d) ∈ Z

2: Compute Pws,d with (4.4), (4.3), and (4.5).

3: Obtain Ωws,d with (4.12) for all (s, d) ∈ Z

4: Calculate the equivalent Poisson traffic Aws,d for layer w with (4.11) and (4.12) for

all (s, d) ∈ Z

5: if|P w

s,d−P ′s,d|P ′s,d

> ε ∀(s, d) ∈ Z then

6: P ′s,d = Pw

s,d

7: go back to Step 2

8: else

9: w = w + 1

10: Compute Aws,d, V w

s,d, and Zws,d with (4.6), (4.7), (4.8), and (4.10)

11: if w ≤ W then

12: go back to Step 1

13: else

14: Calculate the overall path and network wavelength blocking probabilities

with (4.13) and (4.14)

15: return P and Ps,d for all (s, d) ∈ Z

16: end if

17: end if

72

wavelength blocking probabilities are based on Section 4.2 and [34]. Our model can

be combined with other algorithms that compute the wavelength blocking for each

route and each layer.

4.3.1 Counting QoT Blocking Events

To compute the QoT blocking, we need to enumerate all possible ways that a

QoT event can happen when a call z reaches wavelength w. Here a call z is a call

for s-d pair (s, d). The QoT blocking is based on the physical model in Chapter 2.

Given the network topology, the ASE noise, thermal noise, and shot noise are all

decided by the path r(z) ∀z ∈ Z. Assuming that the noises alone are not enough to

bring QoT below the acceptable threshold, then the QoT blocking depends on only

the strength of self-crosstalk and the number of terms of self-crosstalk. The number

of crosstalk terms Nadj(z) is decided by the state of the network. Nadjmax(z) represents

the maximum number of crosstalk terms allowed in r(z) before the QoT constraint

is violated. Using the model in Chapter 2, Nadjmax(z) can be computed for each route

r(z), ∀z ∈ Z.

We list all the paths in Z as z1, . . . , z|Z|. Define a 1×|Z| vector Iw =[Iwz1

, . . . , Iwz|Z|

]

for wavelength w, where Iwz = 1 if r(z) is active at wavelength w and Iw

z = 0 otherwise.

Thus Iw represents the utilizations of paths at layer w. We use the notation Iw(z′) =[Iwz1

, . . . , Iwz′ = 1, . . . , Iw

z|Z|

]to represent all states such that path r(z′) is known to be

used at wavelength w. All used paths at wavelength w form a subset of Z, called

Zwu = z : Iw

z = 1. Note that two paths cannot be used simultaneously if they share

a common link in the same layer.

Self-crosstalk happens if and only if two paths share two or more consecutive hops

on adjacent wavelengths. One unit of self-crosstalk is introduced to each call for each

set of two consecutive hops. Given the routing table, we can count how many units

of self-crosstalk, say Xzz′ ∈ Z, are induced by z, ∀z ∈ Z to a chosen z′. Define a

73

|Z| × 1 vector Xz′ =[Xz1

z′ , . . . , Xz|Z|z′

]T. Xz′ gives the possible crosstalk interference

at a chosen z′ from other s-d pairs.

Because we consider crosstalk from the nearest adjacent wavelengths only, only

lighpaths in wavelength λ−1 = w − 1 and wavelength λ+1 = w + 1 can produce

crosstalk to r(z) ∀z ∈ Z in layer λ0 = w. Then for a call arriving on z′, a QoT

blocking event occurs at wavelength w if the current network state at λ−1 and λ+1

satisfies

(Iλ−1 + Iλ+1) · Xzc > Nadjmax(zc). (4.15)

Furthermore, the new assigned path at wavelength w cannot make the QoT of

other existing lightpaths fall below the QoT requirement. Thus, wavelengths λi for

i = −2,−1, 0, +1, +2 have to be considered, i.e., w−2, w−1, w, w+1, w+2. Because

of this, an arriving call zc has to be blocked if either (4.15) holds or

∃ze ∈ Zλ+1u s.t. (Iλ0(z′) + Iλ+2) · Xze > Nadj

max(ze); (4.16)

or

∃ze ∈ Zλ−1u s.t. (Iλ0(z′) + Iλ−2) · Xze > Nadj

max(ze). (4.17)

Define a 5 × |Z| vector Iw =[Iλ−2 ; Iλ−1 ; Iλ0 ; Iλ−1 ; Iλ−2

], which represents the

states in five layers λi for i = −2,−1, 0, +1, +2 centered at layer λ0 = w. Given an

arriving request, z′, we can obtain all possible ways that the QoT blocking happens by

this vector. Define a set Iw(z′) consisting of all Iw that satisfy (4.15), (4.16), or (4.17)

for call z′. Then Iw(z′) includes all possible QoT blocking events. Let K = |Iw(z′)|.Each QoT blocking event, named ξw,z′

k , k = 1, . . . , K, ξw,z′k ∈ Iw(z′). We now rewrite

ξw,z′k =

[Iλ−2

k (z′); Iλ−1

k (z′); Iλ0k (z′); Iλ−1

k (z′); Iλ−2

k (z′)].

74

41 32

Figure 4.3: Topology of 4-node tandem network

Table 4.1: Routing table including Nadjmax for Fig. 4.3

Z z1 z2 z3 z4 z5 z6

s-d pair (1,2) (1,3) (1,4) (2,3) (2,4) (3,4)

r(s,d) 1 → 2 1 → 2 → 3 1 → 2 → 3 → 4 2 → 3 2 → 3 → 4 3 → 4

Nadjmax 2 1 1 2 1 2

Note that we only show equations valid for w > 2 and w < W − 2. For w =

1, 2,W − 1,W , QoT blocking events that refer to wavelengths outside the spectrum

band have to be excluded.

For example, consider a 4-node unidirectional tandem network as shown in Fig. 4.3.

Assume that each node is equipped with an input EDFA with a gain of 22 dB and an

output EDFA with a gain of 16 dB; no other EDFAs exists between the nodes; each

link has 5 wavelengths; Xadj = −20 dB; the routing table including Nadjmax is shown as

Table 4.1. Note that one-hop traffic is not impaired by the self-crosstalk degradation.

We illustrate how the QoT blocked events are counted using the 2-hop path z2

at wavelength 1 using a FF WA. Let λ0 = w = 1, λ+1 = 2, and λ+2 = 3. Based on

(4.15), (4.16), and (4.17), the QoT blocking events ξλ0,z2

k , k = 1, . . . , 10 are listed as

ξλ0,z2

1 =

− − − − − −− − − − − −∗ ∗ ∗ ∗ ∗ ∗0 1 0 0 0 0

0 1 0 0 0 0

︸︷︷︸

z1 z2 z3 z4 z5 z6

λ−2

λ−1

λ0

λ+1

λ+2

, ξλ0,z2

2 =

− − − − − −− − − − − −∗ ∗ ∗ ∗ ∗ ∗0 1 0 0 0 0

0 1 0 0 0 1

,

75

ξλ0,z2

3 =

− − − − − −− − − − − −∗ ∗ ∗ ∗ ∗ ∗0 1 0 0 0 1

0 1 0 0 0 0

, ξλ0,z2

4 =

− − − − − −− − − − − −∗ ∗ ∗ ∗ ∗ ∗0 1 0 0 0 1

0 1 0 0 0 1

,

ξλ0,z2

5 =

− − − − − −− − − − − −∗ ∗ ∗ ∗ ∗ ∗0 0 1 0 0 0

0 1 0 0 0 0

, ξλ0,z2

6 =

− − − − − −− − − − − −∗ ∗ ∗ ∗ ∗ ∗0 0 1 0 0 0

0 1 0 0 0 1

,

ξλ0,z2

7 =

− − − − − −− − − − − −∗ ∗ ∗ ∗ ∗ ∗0 0 1 0 0 0

0 0 0 0 1 0

, ξλ0,z2

8 =

− − − − − −− − − − − −∗ ∗ ∗ ∗ ∗ ∗0 0 1 0 0 0

1 0 0 0 1 0

,

ξλ0,z2

9 =

− − − − − −− − − − − −∗ ∗ ∗ ∗ ∗ ∗0 1 0 0 0 0

0 0 1 0 0 0

, ξλ0,z2

10 =

− − − − − −− − − − − −∗ ∗ ∗ ∗ ∗ ∗0 1 0 0 0 1

0 0 1 0 0 0

,

where “-” means inapplicable because there are no wavelength less than λ0 = w = 1,

“*” means unknown and can be zero or one. Note that λ0 has not been assigned

to the arriving call; it is just being evaluated for QoT compliance. Because of the

wavelength independence assumption, the probability of each event, can be directly

76

computed. For example, for ξλ0,z2

1 ,

Pr(ξλ0,z′1 ) = (1−Pλ+1

z2)πλ+1(0, 1, 0, 0, 0, 0) · (1−Pλ+2

z2)πλ+2(0, 1, 0, 0, 0, 0).

πw is the stationary probability as computed by (4.2), where βws,d is set to the value

of Iwz for each z. More generally, we can compute the probability of ξλ0,z′

i by

Pr(ξλ0,z′i ) =

−1∏j=−2

∏

ze∈z:Iwjz =1

(1− Pλjze

)πwj(Iwj

i (z′))1− Pr(r(z′) is idle in wj)

(4.18)

·2∏

j=0

∏

ze∈z:Iwjz =1

(1− Pλjze

)πwj(Iwj

i (z′))

, 2 < λ0 < W − 1.

Note that, for layers not less than w (j = 0, 1, and 2), the network can be any state,

but for layer less than w, (j = −1 and − 2), r(z′) cannot be idle because z′ has to

have flowed down to w from the upper layer.

The QoT blocking probability is the sum of the probabilities of the K blocking

events, given by

Pws,d =

K∑i=1

Pr(ξw,z′i ). (4.19)

Generally K is a large number. We can decrease the computation of complexity of

the algorithm by lumping the states together, as more general blocking events. The

QoT blocking can then be calculated as the probability of the union of these (not

disjoint) events.

4.3.2 Approximation to Compute QoT Blocking

The complexity of computing all QoT events is only reasonable for small networks

and is prohibitive in large networks. We propose an approximation to estimate the

77

QoT blocking for large networks with any topology. Instead of looking at the whole

network, we isolate the path considered to a tandem network with five or less layers,

which are independent of each others. In the above example, when we compute the

QoT blocking probability for z2, the isolated network is a two-hop tandem network

consisting of nodes 1, 2, 3. Note that, the impact of other traffic flows is still con-

sidered by using (4.4) to compute the arrival rates for this two-hop network. Because

the major part of the crosstalk comes from the links shared with the path being con-

sidered, this approximation can include most of the impact of crosstalk with a lower

complexity. In the next section, we compare the approximate solution with the exact

solution for the 4-node tandem network shown in Fig. 4.3.

4.3.3 Total Blocking Probability for QoT-Aware RWA

The total path and network blocking probabilities for QoT-aware RWA are com-

puted using (4.13) and (4.14), where AW+1s,d now includes the QoT blocking traffic.

The detailed steps are shown in Algorithm 4.2, where A1s,d = Φs,d, V 1

s,d = Φs,d, and

Z1s,d = 1 for all (s, d) ∈ Z. We obtain the arrival rates and state probabilities in Step

2 in the network without physical impairments, which are used as the initial values

in the QoT estimation. Then, the flow proceeds to the QoT blocking sublayer, after

which part of the flow with rate of Aws,d = Aw

s,d · (1 − Pws,d) arrives at the wavelength

blocking sublayer. We obtain the blocking probability and equivalent Poisson arrival

rate for this sublayer in Step 4. Then the overflow traffic for layer 2 is equal to

the sum of the flow due to QoT blocked calls and wavelength blocked calls, which

is computed in Step 5 as Aw+1s,d = Aw

s,d · (1 − Pws,d) + Aw

s,dPws,d. Then, we update the

probabilities and arrival rates for layer 2 to layer W without considering QoT using

Algorithm 4.1. Those are used as initial values in the next layer. After passing the

last layer, if the overall blocking has converged, the results are returned; otherwise,

we go back to Step 1 and iterate again from the first layer.

78

Algorithm 4.2 Algorithm to compute the total blocking for QoT-aware RWA from

wavelength w = 1 to W given Aws,d, V w


1: Set w = 1 .

2: Use Algorithm 4.1 to compute the wavelength blocking probabilities Pws,d and

arrival rates Aws,d for each path from w to W . They are used as the initial values

in the QoT estimation. Set P ′s,d = Ps,d.

3: Compute QoT blocking probability Pws,d by (4.19) and (4.19), ∀z = (s, d) ∈ Z.

4: Re-calculate the arrival rate for the wavelength sublayer as Aws,d = Aw

s,d · (1−Pws,d)

for all paths. Obtain V ws,d, and Zw

s,d for all (s, d) ∈ Z by (4.7), (4.8), and (4.10).

Re-calculate the wavelength blocking probability Pws,d using (4.5). Use (4.11) to

obtain the sublayer equivalent Poisson traffic rate Aws,d for all paths.

5: Calculate the overflow traffic rate Aw+1s,d = Aw

s,d · (1− Pws,d) + Aw

s,dPws,d for each s-d

pair. Update V w+1s,d , and Zw+1

s,d for all (s, d) ∈ Z by (4.7), (4.8), and (4.10). Set

w = w + 1.

6: if w ≤ W then

7: Go back to Step 2.

8: else

9: Calculate the total path blocking probabilities Ps,d by (4.14).

10: if|Ps,d−P ′s,d|

P ′s,d> ε, ∀(s, d) ∈ Z then


12: else

13: Calculate the total path blocking probabilities P by (4.14).

14: return P and Ps,d for all (s, d) ∈ Z.

15: end if

16: end if

79

4.3.4 Total Blocking Probability for QoT-Guaranteed RWA

The only difference between QoT-aware and QoT-guaranteed algorithms is that

for QoT-guaranteed a part of the traffic is blocked out of the flow in each layer. The

rate of the exiting flow is estimated by

Aws,d = As,dPw

s,d(1− Pws,d).

Thus, the total path blocking probability Ps,d can be computed using

Ps,d =AW+1

s,d +∑W

w=1Aws,d

Φs,d

. (4.20)

The total network blocking probability in the network is given by

P =

∑(s,d)∈Z Φs,dPs,d∑

(s,d)∈Z Φs,d

. (4.21)

The algorithm to compute the total blocking probability for QoT-guaranteed RWA

is shown in Algorithm 4.3, where A1s,d = Φs,d, V 1

s,d = Φs,d, and Z1s,d = 1 for all

(s, d) ∈ Z. We can see it is similar to Algorithm 4.2 except Step 5, where the

overflow traffic rate is computed by Aw+1s,d = Aw

s,d · (1 − Pws,d)P

ws,d + Aw

s,dPws,d and Aw

s,d

has to be deducted from the overflow traffic to the next layer.

4.3.5 Impact of Static Wavelength Ordering

The blocking probability for the FFwO WA can be easily solved in the same way

as for FF WA. Using the static ordering technique from Section 3.2, we can build a

wavelength-channel index mapping table. When the channel index is given, we have

to find the correct wavelength index w for this channel. Then self-crosstalk is induced

not by the adjacent channels, but by the adjacent wavelengths. By checking the table,

we can find the channel index for the adjacent wavelengths and set λ−2, λ−1, λ0, λ+1,

80

Algorithm 4.3 Algorithm to compute the total blocking for QoT-guaranteed RWA

from wavelength w = 1 to W given Aws,d, V w


1: Set w = 1 .

2: Use Algorithm 4.1 to compute the wavelength blocking probabilities Pws,d and

arrival rates Aws,d for each path from w to W . They are used as the initial values

in the QoT estimation. Set P ′s,d = Ps,d.

3: Compute QoT blocking probability Pws,d by (4.19), where ∀z = (s, d) ∈ Z.

4: Re-calculate the arrival rate for the wavelength sublayer as Aws,d = Aw

s,d · (1−Pws,d)

for all paths. Obtain V ws,d, and Zw


Re-calculate the wavelength blocking probability Pws,d using (4.5). Use (4.11) to

obtain the sublayer equivalent Poisson traffic rate Aws,d for all paths.

5: Calculate the overflow traffic rate Aw+1s,d = Aw

s,d · (1− Pws,d)P

ws,d + Aw

s,dPws,d for each

s-d pair. Update V w+1s,d , and Zw+1


Set w = w + 1.

6: if w ≤ W then


8: else

9: Calculate the total path blocking probabilities Ps,d by (4.20).

10: if|Ps,d−P ′s,d|

P ′s,d> ε, ∀(s, d) ∈ Z then


12: else

13: Calculate the total path blocking probabilities P by (4.21).

14: return P and Ps,d for all (s, d) ∈ Z.

15: end if

16: end if

81

and λ+2 correctly. Then using the analytical model proposed, FFwO can be solved

similarly to FF WA. The overflow rates are the same as for FF WA, only the mapping

w → λi changes.

4.4 Numerical Examples and Validation by Simu-

lations

In this section, simulations are used to validate and compare the results. We first

compare the results of the exact analysis to the approximation given in Section 4.3.2

for the 4-node tandem network shown in Fig. 4.3. Then, evaluation is performed using

the approximate method for two other topologies: a 7-node ring network shown in

Fig. 4.4 and the downsized NSF network shown in Fig. 3.3. Unless otherwise stated,

the physical parameters are given in Table 2.1. Simulation results are obtained by

running more than 106 calls. In all analysis results, ε = 10−2. Assume that the

switching crosstalk has no impact as for a MEMS switch network. Uniform load is

assumed. In all plots, the lines marked with circle are the results from simulation.

The lines marked with crosses are the results from analysis. We also plot the results

without considering any physical impairments, marked with dotted line, where only

the wavelength blocking is counted. Results for QoT-aware WA algorithms are plotted

using solid lines and results for QoT-guaranteed WA algorithms are plotted using

dash-dot lines. We analyze networks using a small number of wavelengths, w = 5 in

the tandem network and the ring network and w = 6 in the NSF network, because the

wavelength blocking model we use from [34] is only accurate for the first few layers.

4.4.1 4-Node Tandem Network

Because the 4-node tandem network is a symmetric network, we only consider

unidirectional traffic, which has the same performance as the bi-directional case. The

82

6

1 32 4

7 5

Figure 4.4: Topology of 7-node ring network used for analysis and simulation

physical parameters are as described in the example in Section 4.3.1. The routing

table including Nadjmax is shown as Table 4.1 in Section 4.3.1.

4.4.1.1 Performance of FF and FFwO WAs

By using Algorithm 4.2 and 4.3, we obtain estimates of the blocking probability

for QoS-aware FF WA and QoT-guaranteed FF WA, shown in Fig 4.5. In medium

and large traffic cases, the analytical results for the QoT-aware FF WA and QoT-

guaranteed FF WA are close to the simulation results. When the traffic decreases, the

original model in [34] loses accuracy. Fredericks and Hayward’s approximation [56]

shown in (4.11) used to account for the non-Poisson overflow underestimates the flow

in each layer and leads to inaccuracy. Our algorithms remain accurate because our

calculation of QoT blocking is accurate and the flows are blocked first by the QoT

constraint. In low traffic cases, the QoT blocking is dominant, thus the flow rate still

is still close the the actual traffic. For QoT-guaranteed cases, more calls are blocked

than QoT-aware cases; that analysis is therefore more accurate. The analytical model

correctly gives the improvement from QoT-guaranteed to QoT-aware and gives a good

approximation to the performance considering QoT and wavelength blocking.

For FFwO WA, the static ordering technique proposed in Section 3.2.1 is em-

ployed. The ordering table for 5 wavelength is 1, 5, 2, 4, 3. The performance is

shown in Fig 4.6. The analytical model correctly shows the improvement gained by

using FFwO instead of FF in QoT-guaranteed cases. It also predicts that the QoT-

aware FFwO actually performs slightly worse than QoT-aware FF in some traffic

83

1 2 3 4 5 610

−4

10−3

10−2

10−1

Total network traffic load (Erlangs)

Tot

al b

lock

ing

prob

abili

ty

FF without QoT (simulation)QoT−aware FF (simulation)QoT−guaranteed FF (simulation)FF without QoT (analysis)QoT−aware FF (analysis)QoT−guaranteed FF (analysis)

Figure 4.5: FF WA blocking probability computed using the exact analysis and sim-ulation for the 4-node tandem network, 5 wavelengths, Xadj = −20 dB.

levels if self-crosstalk is dominant. The reason is that QoT-aware FFwO uses all

low crosstalk channels early leaving no good quality channels for future calls. QoT-

aware FF picks the channels following the index of wavelength. It turns out that,

with the QoT constraint we used, the next channel has a quality just over the Q

threshold. Then the other good quality channels can be reserved for future requests.

QoT-guaranteed algorithms do not iterate through all wavelengths, thus the ordering

technique helps. If we add other physical layer impacts, such as neighbor-crosstalk,

and consider the added complexity, the FFwO outperforms FF, which is shown in

the next chapter. Again, we see that the results from the analysis are close to the

simulation for various traffic loads and algorithms, which shows that our model is

accurate. Note that the analytical method is not as accurate for FFwO as for FF; the

algorithm for FFwO must use wavelength blocking estimates for lower layers, which

are themselves not as accurate [34].

84

1 2 3 4 5 610

−4

10−3

10−2

10−1


Tot

al b

lock

ing

prob

abili

ty

FFwO without PHY (simulation)QoT−aware FFwO (simulation)QoT−guaranteed FFwO (simulation)FFwO without PHY (analysis)QoT−aware FFwO (analysis)QoT−guaranteed FFwO (analysis)

Figure 4.6: FFwO WA blocking probability computed using the exact analysis andsimulation for the 4-node tandem network, 5 wavelengths with wavelength ordering1, 5, 2, 4, 3, Xadj = −20 dB.

4.4.1.2 Results of the Approximation Method

Because of the complexity of counting QoT blocking, an approximation is proposed

in Section 4.3.2 to estimate the QoT blocking using a fast and simplified way. Because

only QoT blocking events that happen in the spans that the chosen route traverses

are counted, the QoT blocking rate is underestimated. However, it causes (4.19)

to increase, so the approximation gives an accurate estimate to the overall blocking

probabilities nonetheless.

The results are shown in Figs. 4.7 and 4.8. By comparing the approximation

to simulation in various situations, we conclude that it gives a close estimation to

the real blocking probability and makes it possible to analyze the performance of

large networks. The impact of QoT-aware and QoT-guaranteed RWA is correctly

approximated and the effect of ordering the wavelength is correctly estimated. Thus,

in the following sections, we employ the approximation to obtain analysis results for

85

1 2 3 4 5 610

−4

10−3

10−2

10−1


Tot

al b

lock

ing

prob

abili

ty

FF without QoT (simulation)QoT−aware FF (simulation)QoT−guaranteed FF (simulation)FF without QoT (analysis)QoT−aware FF (approximation)QoT−guaranteed FF (approximation)

Figure 4.7: FF WA blocking probability computed using the approximate methodand simulation for the 4-node tandem network, 5 wavelengths, Xadj = −20 dB.

larger networks than would be possible with the xact analysis.

4.4.2 Validation Via Simulation in Other Networks

In the 7-node ring network, we model 5 wavelengths in each link and assume each

link is bi-directional consisting of two unidirectional fiber links. In the NSF network,

we increase the number of wavelengths to 6 in each link and each link is also bi-

directional. Each link is divided into several spans as noted in Fig. 3.3. Each span

is equipped with a 20 dB gain EDFA to compensate for the fiber attenuation in the

span. Because of the high level of noise, we have to limit the length of the all-optical

lightpaths to three hops in the NSF network. Other parameters used in these two

network are the same those used in the 4-node tandem network.

The results for ring network using FF WA and FFwO WA are shown in Figs. 4.9

and 4.10, respectively. The results for FF WA and FFwO WA in the NSF network are

shown in Figs. 4.11 and 4.12, respectively. In low traffic loads, the underestimation

86

1 2 3 4 5 610

−4

10−3

10−2

10−1


Tot

al b

lock

ing

prob

abili

ty

FFwO without QoT (simulation)QoT−aware FFwO (simulation)QoT−guaranteed FFwO (simulation)FFwO without QoT (analysis)QoT−aware FF (approximation)QoT−guaranteed FF (approximation)

Figure 4.8: FFwO WA blocking probability computed using the approximate methodand simulation for the 4-node tandem network, 5 wavelengths with wavelength or-dering 1, 5, 2, 4, 3, Xadj = −20 dB.

of wavelength blocking causes the blocking probabilities in the analysis to be lower

than the simulation result for both algorithms. In medium and high traffic loads, the

performance difference decreases. In both networks, our analytical results predict the

behavior of QoT-aware and QoT-guaranteed algorithms accurately for both FF WA

and FFwO WA.

4.5 Summary

In this chapter, we present an analytical technique to compute the total blocking

probability in WRONs impaired by self-crosstalk, ASE noise, thermal noise, and shot

noise. Starting with a known method to compute wavelength blocking probability

using a layered approach, we are able to compute the QoT blocking rate for FF

and FFwO WA algorithms. Our method could also use other models to compute

wavelength blocking and obtain the networks state probabilities. The performance is

87

5 10 15 2010

−6

10−5

10−4

10−3

10−2

10−1

100


Tot

al b

lock

ing

prob

abili

ty


Figure 4.9: FF WA blocking probability computed using the approximate methodand simulation for the 7-node ring network, 5 wavelengths, Xadj = −20 dB.

5 10 15 2010

−6

10−5

10−4

10−3

10−2

10−1

100


Tot

al b

lock

ing

prob

abili

ty

FFwO without QoT (simulation)QoT−aware FFwO (simulation)QoT−guaranteed FFwO (simulation)FFwO without QoT (analysis)QoT−aware FFwO (approximation)QoT−guaranteed FFwO (approximation)

Figure 4.10: FFwO WA blocking probability computed using the approximate methodand simulation for the 7-node ring network, 5 wavelengths with wavelength ordering1, 5, 2, 4, 3, Xadj = −20 dB.

88

10 20 30 40 50 6010

−7

10−6

10−5

10−4

10−3

10−2

10−1

100


Tot

al b

lock

ing

prob

abili

ty


Figure 4.11: FF WA blocking probability computed using the approximate methodand simulation for the NSF network, 6 wavelengths, Xadj = −20 dB.

10 20 30 40 50 6010

−7

10−6

10−5

10−4

10−3

10−2

10−1

100


Tot

al b

lock

ing

prob

abili

ty

FFwO without QoT (simulation)QoT−aware FFwO (simulation)QoT−guaranteed FFwO (simulation)FFwO without QoT (analysis)QoT−aware FFwO (approximation)QoT−guaranteed FFwO (approximation)

Figure 4.12: FFwO WA blocking probability computed using the approximate methodand simulation for the NSF network, 6 wavelengths with wavelength ordering 1, 6,3, 5, 2, 4, Xadj = −20 dB.

89

evaluated in three networks with different topologies, where the analysis results are

shown to match the simulation.

Chapter 5

Impact of Complexity of QoT

Estimation on RWA

RWA algorithms that include QoT are inevitably more complex than their conven-

tional counterparts due to exhaustive search and the QoT estimation. The estimation

of QoT is typically not only performed for each incoming request, but also for each

lightpath that the proposed connection might disrupt. It is possible that a new light-

path has an acceptable QoT but provokes so much crosstalk in the network that

the QoT for other lightpaths (interacting lightpaths) drops below threshold [9, 27].

Moreover, the algorithm has to compute the QoT on candidate lightpaths in real-time

before accepting a call because the physical impairments are network state dependent.

The presence or absence of other co-propagating lightpaths, i.e., the instantaneous

network state, affects the number of crosstalk terms, the saturation of the amplifier

gains, and the ASE noise in EDFAs. Therefore, these techniques can be compu-

tationally intensive [58], inducing delays that increase the blocking rate by causing

contentions [59]. Consequently, algorithms that are too complex and add unaccept-

able delays in call setup time are not suitable for application in wide-area networks.

We define latency as the time spent to set up a request. Latency is an important

90

91

performance measure to service providers because a long set-up delay increases the

time cost and decreases network utilization. In future networks, latency-constrained

applications requiring on-demand fast set-up of circuits such as large file transfers

are anticipated. For architectures that include an all-optical network as a high-speed

parallel alternative to a conventional network, a fixed time-out on the call set-up for

the WDM network is needed to determine when the service must be contented to use

the slower connection. Another example of a call that must be handled especially

rapidly is dynamic restoration after a failure, wherein backup paths are not reserved

but are discovered dynamically when needed. The restoration time has to be less

than 50 msec after a failure has been detected in SONET/SDH networks [60].

In this chapter, we study the impact of the computational complexity of RWA with

QoT constraints for centralized networks. Connection management schemes for WDM

networks can be classified as centralized or distributed [4, 61]. In this chapter, only

centralized circuit-switched WDM networks, a type of connection-oriented network,

are considered. The reason is that the delay induced in the admission control for

distributed networks depends highly on the network topology and signaling control

protocols [62,63].

The RWA algorithms in Chapter 3 are extended to consider both QoT and latency

constraints. The merit of each RWA algorithm is evaluated by its performance as

measured by the blocking probability; complexity is penalized by the negative impact

it has on the network performance (measured by the latency blocking rate) resulting

from an excessively long queueing or call-setup time. To our knowledge, this is the first

study to include both QoT and latency thresholds when evaluating RWA algorithms.

Because both these crucial measures of quality are tested, we refer to our algorithms

as QoS-aware.

92

5.1 Impact of QoT Complexity

In this section, we first describe the centralized network architecture employed,

and then present our model and assumptions for calculating the latency. We consider

networks with bidirectional links, each of which supports W wavelengths in each

direction. In this paper we only consider fixed shortest path (SP) and fixed alternate

(ALT) routing algorithms and focus on showing the ability of WA algorithms to reduce

QoS-blocking in all-optical networks. In the ALT routing algorithm, the second route

(if it exists) is considered if the first route is busy or failed.

Instead of assuming perfect power compensation, we consider the more realistic

case where the EDFA is modeled as automatic gain controlled (AGC) [9,37]. Because

of the gain dependence of the AGC EDFA model on the total received power (due to

power saturation), the technique for estimating the QoT proposed in Chapter 2 and

3 cannot be utilized here and all noises have to be calculated on-line.

5.1.1 Centralized Network Architecture

Fig. 5.1 shows a simplified node architecture, including the data-plane and the

control plane. Via the control plane the user sends a message requesting a commu-

nication channel, i.e., a lightpath connecting one node in the network to another.

The controller checks the routing table, assuming that the routing table contains the

information on routing and wavelength usage for all current established routes, and

assigns an appropriate route and wavelength to each accepted request. It then sends

control messages to all nodes on the lightpath to configure the switches appropriately.

Last, the controller sends a reply message back to the user, informing it of its assigned

lightpath.

On the data plane, the data sent from the user enters the switch fabric by the

optical add/drop multiplexer (OADM). The switch fabric directs the demultiplexed

93

Control plane

Amplifier

...

Input link

Amplifier

...

Input link

Add

DropOptical add/drop

multiplexer (OADM)

Amplifier

...Output link

Amplifier

...

Output link

Routing table

BER estimator......

QueueProcessor

RWA and linkmanagementcontroller

all−opticalnode

Replies to other nodes

......

Data plane Reply m

essages

Request m

essages

......

Switch fabric

......

Data

Users

......Requests from other nodes ...

...

Control messages

Control messages to other switching nodes

λ1

λn

λn

λ1

λ1

λn

λ1

λn

Figure 5.1: All-optical network node architecture including control plane and dataplane. λi represents the ith wavelength.

pre-amplified input signals from other network nodes and the new signals from the

OADM to the appropriate output ports. The switch fabric could be either a single

multi-wavelength large-scale switch, or a set of small-scale single-wavelength switches.

More details can be found in [36, Chapter 3.7]. After traversing the switch fabric,

signals that have not reached their destination are amplified and transmitted out

through multiplexers to output links. Otherwise, the signals are switched to the drop

ports of the OADM and are received by the desired users [61, 64]. The functions of

the OADM and switching fabric are typically integrated within the switch, yet are

drawn separately in Fig. 5.1 for clarity.

The main purpose of the control plane is to reserve network resources (routes

and wavelengths) and program the switching fabric prior to data transfer. A route

is determined for the connection by consulting routing tables, which can be created

dynamically or statically. The structure of a centralized controller is simplified and

shown inside the control plane in Fig. 5.1. The lightpaths are reserved in a circuit

setup phase and released in a circuit tear-down phase. In centralized networks, the

controller allocates the resources over the entire lightpath for each request during the

94

connection admission control (CAC) procedure. Requests arrive at the controller’s

queue and are allocated resources using a first-come, first-served (FCFS) policy. We

assume that the queue has an infinite size yet users are willing to wait only a limited

time for a reply message from the controller. Similar to Chapter 3, out-of-band

control signaling is assumed to avoid the additional interference and crosstalk it would

otherwise generate.

Call requests are assumed to arrive at the network nodes according to a Poisson

process with mean arrival rate λa, and call durations follow an exponential distribu-

tion with mean value E[X]. Thus the offered load per node in the network is λaE[X]

Erlangs, which is assumed for notational simplicity to be equal for all nodes. Based

on the additive property of Poisson processes, the total call arrival rate offered to the

controller’s queue is Nλa, where N is the total number of network nodes.

5.1.2 Setup Latency

In delay-sensitive networks, the delay incurred during the CAC procedure, denoted

by Da, can be unacceptably long. We assume the presence of a timeout mechanism

with a user-adjustable delay bound Tmax, which depends on the application. The

controller processes the call at the head of the queue and iterates through candidate

lightpaths until it has found one satisfying the QoT constraint (if one exists), until

this allowed latency expires.

The total call admission time for call request k can be written as the sum of two

delays, a queueing delay and a processing delay,

Da(k) = Dq(k) + Dp(k). (5.1)

The queueing delay Dq(k), which is the time request k must wait in the queue, depends

on the sum of the processing delay of previous requests in the queue. The processing

95

delay Dp(k) includes the time required to check the routing table and the time to find

a viable wavelength (BER worse than threshold). The time required for calculating

the set of free wavelengths is denoted by τLP , and the time needed for checking if

the QoT of a candidate or interacting lightpath is worse than the QoT threshold is

denoted by τc. When using the fixed alternate routing algorithm, the time to find all

free wavelengths in primary and alternate routes is 2τLP . The time to estimate the

QoT of a call depends directly on the network traffic and the instantaneous network

state, and also indirectly on the number of hops in the lightpath and the severity of

the physical impairments. The delay in processing request k is calculated as

Dp(k) = aτLP +m∑

i=1

Yiτc, (5.2)

as long as the delay constraint is not exceeded, where a is equal to 1 if SP is applied

or a ≥ 1 (e.g., a = 2) if ALT is applied. m denotes the number of trials before

the processor finds a viable lightpath or finishes checking all candidate lightpaths.

Assuming there are Ei existing lightpaths that interact (share a link or node) with

lightpath i, Yi is equal to 1 + Ei if every interacting lightpath is tested for QoT

compliance. If one interacting lightpath fails the compliance test, the process is

terminated for the ith candidate lightpath, and Yi is then the number of interacting

lightpaths tested before the failure occurs. At the moment the delay exceeds Tmax,

the call is instantly dropped.

Fig. 5.2 shows the various delays as a timeline. When a request k is sent by a net-

work node to the centralized controller, transmission delay (the duration of the request

packet) and propagation delay (from the node to the controller) are incurred before

the request goes into the controller’s queue. Networks that ignore physical impair-

ments suffer primarily from transmission delay and propagation delay in their CAC

process [65]; the queueing and processing delays are small if no complex computation

96

controllerCentralized

nodeSwitching

propagation delay propagation delay

transmission delaytransmission delay

...... Ymτc

Request kReply k

Da(k)

Dq(k) Dp(k)

aτLP Y1τc Y2τc

Figure 5.2: The timeline of a call admission procedure for request k in centralizedWDM networks if Da(k) < Tmax.

is performed. The WA algorithms considered here impose a significant processing

delay because of the time needed to estimate the QoT. Since the transmission and

propagation delays are expected to be small in comparison to Dp(k), they are ignored

in this dissertation so as to simplify the derivation. Thus, the total latency for call

k, Da(k), is estimated as just the sum of the processing delay and queueing delay if

within the timeout threshold.

5.1.3 RWA with QoT and Latency Constraints

We denote as QoS-aware WA algorithms that find lightpaths satisfying both the

latency and QoT constraints (for the new call as well as every already-established

lightpath) by a process consisting of checking available wavelengths in the routes found

by the SP or ALT algorithms. Algorithms not identified as QoS-aware test a single

wavelength in the route found by SP or in the primary route and the alternate route (if

the first trial in the primary route fails) found by ALT for QoS compliance (QoS-

guaranteed) and then quit.

The flowchart in Fig. 5.3 illustrates the QoS-aware WA approach. The centralized

controller takes the first call in line from the queue, assigns it one or two routes

(from the routing table) and then starts an iterative process to select a wavelength.

In this work, the order in which wavelengths are tried (for both the QoS-aware and

97

No

A request arrives Wait in the queue

Block the request

the requestAccept

algorithm, FF, FFwO, or RP

Choose a new free wavelengthbased on wavelength assignment

BER < threshold ?

BER estimation

and existing LPsof the candidate

SP or ALTRouting

No free wavelength

YesNo

Yes

No

Yes

Tmax ?Dq <

Tmax ?Da <

Figure 5.3: Flowchart of QoS-aware WA algorithms using SP or ALT routing incor-porating both QoT and latency thresholds.

the QoS-guaranteed WAs) can either be RP, FF, or FFwO. At any point in the

CAC processing, if the timeout constraint is violated, the call is dropped. The WA

algorithm uses the QoT estimator to determine if a viable wavelength is available

that satisfies the QoT constraint. If a lightpath is found within the allotted time, the

call is accepted; otherwise, the connection request is rejected.

Note that the algorithms considered here accept a call on the first lightpath that

yields acceptable performance, thus risking the acceptance of connections with per-

formance close to the QoT threshold. We do not consider a Q factor maximizing

algorithm (such as “highest-Q” in [27]) that takes the best performing option within

the timeout limit. First, this greedy algorithm would take a longer time performing

optimization and would thus leave less time for calls in the queue to perform their

lightpath search, forcing more time-out blocking. Second, maximizing the Q factor

does not diminish blocking probabilities, even without a timeout constraint [26, 58],

because the increase in wavelength blocking seldom compensates for the decrease in

QoT blocking.

The QoS-guaranteed WA algorithms try a single lightpath (if one exists) in SP or

a primary and an alternate lightpaths (if the primary lightpath fails) in ALT using

the corresponding wavelength selection method; unlike the QoS-aware techniques,

98

they do not repeatedly try other candidate lightpaths. They are thus not as powerful

as the QoS-aware techniques, yet still guarantee the QoS for every communicating

lightpath, new and established.

5.2 Simulations and Results

We compare the algorithms presented above by means of simulation since there

are currently no known analytical techniques for evaluating complex RWA algorithms

with timeout. The only known performance bound is that obtained when QoS factors

are ignored, which is too loose a bound to be meaningful. The number of calls

generated is more than 5 × 106 in each simulation. The 95% confidence intervals

were computed but are not shown since they are all small compared to the scale of

the plots. The optical impairments considered in this section are node crosstalk, and

noise, including ASE noise from the EDFAs, shot noise, and thermal noise at the

receivers. Their impacts are estimated using the method described in [8, 9].

The impact of physical impairments depends not only on the physical layer pa-

rameters as described above, but also on the network topology. In a star network,

the center node can experience crosstalk-limited performance. In a ring network, the

major call request loss is from wavelength blocking instead of QoS blocking. To as-

sure that our results generalize to various types of networks, we evaluate our RWA

techniques on two different large networks. The popular 16-node mesh toroid network

is studied because of its high degree of symmetry and connectivity. We also consider

the NSF network as a more practical example to compare the WA algorithms. The

link lengths on the NSF network are scaled by 1/10 because the physical impairments

would otherwise be too strong for our link design, which is not optimized for long-

haul communications. The two network topologies are depicted in Fig. 5.4. For each

network, the baseline parameter values used in the simulations are listed in Table 2.1

99

with τLP = 100milliseconds and Tmax = 20 seconds. τc is varied in the first set of

simulations. We model the arrival process as Poisson, and the service time as expo-

nentially distributed with E[X] = 1 × 105 seconds. The latency is estimated using

the expressions in Section 5.1.2.

The allowed timeout Tmax and the service time in wavelength routed optical net-

works depend heavily on the application. In an effort to present numerically mean-

ingful results, we have chosen a timeout of 20 seconds. The transmission delay,

propagation delay and other delays are not included in the model. They can simply

be added to the timeout threshold if necessary. The time required to perform one

QoT calculation, τc, depends entirely on the hardware and software used. The base-

line value of τc was chosen so as to demonstrate the impact of latency and QoT on

the blocking probability. The results presented apply equally well to networks with

different temporal requirement by simply scaling all time values (E[X],τLP , τc, Tmax)

accordingly. Note that the physical model we have adopted for simulation is simple

and would not require extensive computational power. Employing a complex model

considering all types of physical impairments as would be done in practice would be

prohibitive. The delay used in the computations is derived from the simulations,

which is only indicative of what the real delay might be.

In the plots, the WA algorithm used is identified as QoS-aware (QoS-FF, QoS-

RP, and QoS-FFwO) or QoS-guaranteed (FF, RP, and FFwO). The routing technique

used is identified by appending either “SP” or “ALT” to the name of the WA algo-

rithm, e.g. QoS-FF-SP or QoS-FF-ALT.

For both QoS-guaranteed and QoS-aware WA algorithms, the measured blocking

probability includes call requests dropped due to wavelength blocking and to the

failure of the chosen wavelength to satisfy the QoS (QoT or latency) requirement.

We define Ptotal, PQoT , PT , and Pλ as the simulated overall blocking probability, the

blocking probability caused by an unsatisfactory QoT, the blocking probability due to

100

16

1 3 42

5 6 7 8

9 10 1211

13 14 15

(a)

75

CA1

WA

CA2

UT

CO

NE

TX

GA

MD

IL

PA NJ

MINY

75

300

120

12075

150

150

300

60 60

60

60

300

60

75 120

120

120

60

105

(b)

Figure 5.4: Network topologies used in simulation. (a) 16-node mesh toroid net-work (MESHnet) with identical link length of 100 kilometers and (b) Topology ofa downsized version of the NSF network (NSFnet), using link lengths 1/10 of theiroriginal size, with 14 nodes and 21 bidirectional links. The number on the linksrepresents the length of the links in kilometers. Each link is considered as a singlespan.

101

the timeout constraint, and the wavelength blocking probability, respectively. In our

simulation, each blocked event is counted as either wavelength blocked (Pλ), latency

blocked (PT ), or QoT blocked (PQoT ), so that Ptotal = Pλ + PT + PQoT .

5.2.1 Blocking vs. Processing Time

To see how the QoT estimation delay affects network performance, we examine

in Figs. 5.5-5.10 the various blocking probabilities for a range of τc for each routing

and WA algorithm. Without loss of generality, we define a dimensionless parameter

τ as τc = τE[X] so that τc scales with E[X]. The vertical dashed line in the figures

is used to indicate a common point in the different simulations. In each figure the

results are shown for the mesh toroid network in subplot (a) and the scaled version

of the NSF network in subplot (b), using the parameters as noted.

With SP routing, as shown in Fig. 5.5, QoS-FFwO-SP outperforms other QoS-

aware WAs for τ < 1.5× 10−5 and the QoS-FF-SP is better than QoS-RP-SP except

in the long delay case. When τ > 10−5, the centralized controller is overloaded and

the Ptotal of the three QoS-aware WAs increases steeply because of the short timeout.

In this case, the Ptotal for QoS-FF-SP and QoS-FFwO-SP grows faster than for QoS-

RP-SP. QoS-FF-SP causes more blocking than QoS-RP-SP when τ > 1 × 10−5 and

QoS-FFwO-SP causes more blocking than QoS-RP-SP when τ > 1.5 × 10−5. QoS-

FF-SP suffers most from long QoT estimation times because it needs more time to

find a lightpath fulfilling the QoT requirement.

QoS-guaranteed SP WA algorithms have nearly constant Ptotal performance be-

cause they do not iteratively try other candidates so that PT has less impact, which is

shown in Fig. 5.6. FFwO-SP performs the best, followed by RP-SP, and then FF-SP.

FF-SP tries to pack the traffic in the same few low-index wavelengths and therefore

meets the most severe demultiplexer crosstalk impairments. The wavelength order-

ing technique successfully removes a fraction of the crosstalk which helps FFwO-SP

102

achieve a better performance than RP-SP or FF-SP.

We quantify the effect of the timeout and QoT constraints by plotting results for

PT and PQoT in Figs. 5.6 and 5.7, respectively. For all values of τ , QoS-FF-SP has

the largest PT , followed by QoS-FFwO-SP and QoS-RP-SP. QoS-FFwO-SP benefits

from the wavelength ordering technique and has nearly the same PT as QoS-RP-

SP. The basic idea of RP is to choose channels randomly so the variable Yi in (5.2)

is lower for QoS-RP-SP than for QoS-FF-SP and QoS-FFwO-SP. This comes from

the fact that, since RP blocks more requests than FF, there are (on average) fewer

active paths in the network under RP and therefore the average Yi will be smaller.

QoS-FFwO-SP enjoys a lower PT than QoS-FF-SP because the number of trials

m in (5.2) for QoS-FFwO-SP is less than for QoS-FF-SP (and QoS-RP-SP). The

wavelength ordering technique improves the probability that the channel first chosen

(the first wavelength on the list available end-to-end) is a feasible one (satisfies the

QoT constraint) and thus QoS-FFwO-SP results in a smaller average latency than

QoS-FF-SP. Furthermore, since FF blocks more requests (on average) than FFwO,

the network load under FF tends to be lower. Therefore, the chance that a wavelength

is free in FF is higher than in FFwO, which generates more checking for the QoT and

therefore m is larger.

For the three QoS-guaranteed SP WA algorithms, FFwO-SP has a lower PT than

FF. Unlike the QoS-aware WAs, RP-SP performs much better than FFwO-SP in

terms of PT again because of a lower Ei (m = 1 in this case). In summary, the results

show that wavelength ordering decreases the blocking probability by increasing the

chances that the first channel selected meets the QoT requirement and by decreasing

the number of iterations in the wavelength search.

Fig. 5.7 shows that the QoT blocking for FFwO for SP routing is significantly lower

than for FF, which justifies our claim that wavelength ordering reduces crosstalk.

Surprisingly, the QoS-aware WAs do not follow the same trend as the QoS-guaranteed

103

10−6

10−5

10−5

10−4

10−3

10−2

10−1

100

τ

Pto

tal

FF−SPRP−SPFFwO−SPQoS−FF−SPQoS−RP−SPQoS−FFwO−SP

(a)

10−6

10−5

10−5

10−4

10−3

10−2

10−1

100

τ

Pto

tal


(b)

Figure 5.5: Simulation of Ptotal with QoT and latency constraints for the six WAalgorithms when SP routing is applied; (a) 16-node mesh toroid network with Xadj =−20 dB, Xsw = −40 dB, and total traffic load of 160 Erlangs; (b) NSF network withXadj = −25 dB, Xsw = −45 dB, and total traffic load of 100 Erlangs.

104

10−6

10−5

10−5

10−4

10−3

10−2

10−1

100

τ

PT


(a)

10−6

10−5

10−5

10−4

10−3

10−2

10−1

100

τ

PT


(b)

Figure 5.6: Simulation of PT with QoT and latency constraints for the six WA algo-rithms when SP routing is applied; (a) 16-node mesh toroid network with Xadj = −20dB, Xsw = −40 dB, and total traffic load of 160 Erlangs; (b) NSF network withXadj = −25 dB, Xsw = −45 dB, and total traffic load of 100 Erlangs. Missing pointsor lines indicate that the data fall below the ordinate values plotted.

105

10−6

10−5

10−5

10−4

10−3

10−2

10−1

100

τ

PQ

oT


(a)

10−6

10−5

10−5

10−4

10−3

10−2

10−1

100

τ

PQ

oT


(b)

Figure 5.7: Simulation of PQoT with QoT and latency constraints for the six WAalgorithms when SP routing is applied; (a) 16-node mesh toroid network with Xadj =−20 dB, Xsw = −40 dB, and total traffic load of 160 Erlangs; (b) NSF network withXadj = −25 dB, Xsw = −45 dB, and total traffic load of 100 Erlangs.

106

WAs. For instance, QoS-FF-SP has the same PQoT as QoS-FFwO-SP, but FF-SP is

much worse than FFwO-SP because FF only tests the first candidate and QoS-FF can

test other candidates so that QoS-FF finally does find a qualified lightpath (thereby

incurring a larger PT , as seen in Fig. 5.6).

QoS-RP-SP have the highest PQoT among the QoS-aware WAs, yet RP is better

than FF among the QoS-guaranteed WAs. The reason, as noted in the previous

chapters, is that the RP algorithm can reduce the physical impairments in exchange

for more different wavelengths used, causing higher wavelength blocking [9, 10, 16].

QoS-RP-SP does poorly because it has fewer candidate lightpaths than QoS-FF and

QoS-FFwO, which decreases its chance of finding a lightpath that satisfies the QoT

requirement. Notice that when τ is large, the PQoT of all WA algorithms decreases due

to a decrease in effective network traffic as a large percentage of calls have timed-out.

In Fig. 5.8, the performance of the various WA algorithms using the fixed alternate

routing algorithm are shown to be similar to those for SP routing in Fig. 5.5. QoS-

FFwO-ALT is superior until τ > 1.4 × 10−5. QoS-FF-ALT is worse than QoS-RP if

τ > 6×10−6 because PT dominates Ptotal for large τ , as shown in Fig. 5.9. Compared

to Fig. 5.5, each WA algorithm using ALT routing outperforms the corresponding WA

using SP routing because ALT can decrease Pλ [10]. We also observe that QoS-FFwO-

SP is better than FFwO-ALT in the 16-node mesh network, whereas FFwO-ALT is

better than QoS-FFwO-SP in the NSF network. Thus the performance comparison

of SP and ALT for different WA algorithms is dependent of the network topology.

However, the performance improvement from QoS-awareness is much larger than the

improvement from ALT routing algorithm. This is clearly seen by comparing the

gap between FF-SP and FF-ALT with the gap between FF-SP and QoS-FFwO-SP

in Figs. 5.5 and 5.8.

The blocking probabilities of the timeout and QoT constraints,PT and PQoT for

ALT routing, are shown in Figs. 5.9 and 5.10. The results are observed similarly to the

107

10−6

10−5

10−5

10−4

10−3

10−2

10−1

100

τ

Pto

tal

FF−ALTRP−ALTFFwO−ALTQoS−FF−ALTQoS−RP−ALTQoS−FFwO−ALT

(a)

10−6

10−5

10−5

10−4

10−3

10−2

10−1

100

τ

Pto

tal


(b)

Figure 5.8: Simulation of Ptotal with QoT and latency constraints for the six WAalgorithms when ALT routing is applied; (a) 16-node mesh toroid network with Xadj =−20 dB, Xsw = −40 dB, and total traffic load of 160 Erlangs; (b) NSF network withXadj = −25 dB, Xsw = −45 dB, and total traffic load of 100 Erlangs. Missing pointsor lines indicate that the data fall below the ordinate values plotted.

108

results for SP routing. For all values of τ , QoS-FF-ALT has the largest PT , followed

by QoS-FFwO-ALT and QoS-RP-ALT. Different from FFwO-SP, PT of FFwO-ALT

is slightly better than PT of RP-ALT because average of m in RP-ALT is larger than

that in FFwO-ALT (m can be one or two in this case). The wavelength ordering

technique again shows the ability to decrease the QoT blocking and decrease the

timeout. In Fig. 5.10, the QoT blocking rates for FFwO-ALT in both networks

are significantly lower than for FF-ALT, which again shows that wavelength ordering

reduces crosstalk. PQoT of three QoS-aware algorithms for ALT routing are too low to

observe. This indicates that routing algorithms help the network decrease the impact

of the physical degradation, which is also shown in the results of Chapter 2.

The performance for 16-node mesh toroid network and NSF network is similar,

which indicates that the QoS has the similar impacts in the two different networks.

5.2.2 Blocking vs. Network Traffic Load

To show how the twelve RWA algorithms perform in different network conditions,

in Figs. 5.11 and 5.14 we plot the total blocking probabilities while varying the total

network load. PT and PQoT results of SP and ALT routings are shown in Figs. 5.12-

5.16. In all simulations, we have selected a QoT estimation delay of τ = 7 × 10−6,

corresponding to τc = 700 msec.

Ptotal for SP routing is plotted in Fig. 5.11, showing that QoS-FFwO-SP performs

best among the six SP WAs, yielding the lowest average blocking probability in all

traffic load cases. QoS-FF-SP is second-best, except in light traffic (< 140 Erlangs

for the mesh network and < 80 Erlangs for the NSF network). In the low traffic case,

wavelength blocking is negligible and Ptotal is dominated by PT and PQoT as shown

in Fig. 5.11-5.13. PT is nearly zero for QoS-RP-SP so that it is missing in Fig. 5.12,

yet it is PQoT that is negligible for QoS-FF, as shown in Fig. 5.13. Thus, for QoS-

RP-SP Ptotal is bounded by PQoT and for QoS-FF-SP it is bounded by PT . Ptotal

109

10−6

10−5

10−5

10−4

10−3

10−2

10−1

100

τ

PT


(a)

10−6

10−5

10−5

10−4

10−3

10−2

10−1

100

τ

PT


(b)

Figure 5.9: Simulation of PT with QoT and latency constraints for the six WAalgorithms when ALT routing is applied; (a) 16-node mesh toroid network withXadj = −20 dB, Xsw = −40 dB, and total traffic load of 160 Erlangs; (b) NSFnetwork with Xadj = −25 dB, Xsw = −45 dB, and total traffic load of 100 Erlangs.Missing points or lines indicate that the data fall below the ordinate values plotted.

110

10−6

10−5

10−5

10−4

10−3

10−2

10−1

100

τ

PQ

oT

FF−ALTRP−ALTFFwO−ALT

(a)

10−6

10−5

10−5

10−4

10−3

10−2

10−1

100

τ

PQ

oT


(b)

Figure 5.10: Simulation of PQoT with QoT and latency constraints for the six WAalgorithms when ALT routing is applied; (a) 16-node mesh toroid network with Xadj =−20 dB, Xsw = −40 dB, and total traffic load of 160 Erlangs; (b) NSF network withXadj = −25 dB, Xsw = −45 dB, and total traffic load of 100 Erlangs. Missing pointsor lines indicate that the data fall below the ordinate values plotted.

111

for QoS-RP-SP is lower than for QoS-FF-SP in this simulation scenario, but this can

easily reverse depending on the delays and crosstalk levels. It can be seen that PT

and PQoT for QoS-FFwO-SP both diminish to nearly zero in the low traffic situation.

As the traffic increases, Pλ cannot be neglected and the performance of QoS-FF-SP

surpasses that of QoS-RP-SP since QoS-FF-SP has lower Pλ than QoS-RP-SP [10].

Note that QoS-FF-SP and QoS-RP-SP are always worse than QoS-FFwO-SP since

the wavelength ordering technique decreases the adjacent-port crosstalk impairment

without producing larger latency.

The results shown in Fig. 5.14 for ALT routing are similar to those for SP in

Fig. 5.11. Each ALT WA algorithm outperforms the corresponding SP WA algorithm.

The ALT algorithm can not only efficiently decrease Pλ, but also decreases PQoT as

shown in Fig. 5.15. This is because ALT routing has another alternate route that can

be used during CAC so that the number of candidate channels is larger than that

for SP. Moreover, PT for ALT is not significantly increased because Yi is decreased,

from the fact that the traffic is spread to two routes decreasing the existing traffic

in each. Compared Fig. 5.11 with Fig. 5.14, the decrease of Ptotal between FF and

QoS-FFwO is much larger than that between FF and FF-ALT. QoS-aware WAs are

more powerful than ALT routing algorithm in this scenario.

As expected, the performance of the three QoS-aware WAs for both SP and ALT

is superior to the performance of QoS-guaranteed WAs. Yet, the QoS-guaranteed

WAs have a faster response compared to their corresponding QoS-aware WAs, as

seen in Figs. 5.12 and 5.15, where FF, FFwO, and RP have negligible PT , in either

routing scheme. QoS-FF-ALT causes the highest PT among all WAs in medium or

high traffic. In low traffic cases QoS-FF-SP causes the highest PT among all WAs. In

ALT routing, the traffic spreads to two paths, which helps QoS-FF-ALT achieve a fast

response than QoS-FF-SP. However, as the traffic goes up, the help of spreading traffic

to two routes is limited and finally ALT routing runs longer than SP routing. For

112

140 150 160 170 180 190 200 210 220

10−5

10−4

10−3

10−2

10−1

100

Load, Erlangs

Pto

tal


(a)

90 95 100 105 110 115 120 125

10−5

10−4

10−3

10−2

10−1

100

Load, Erlangs

Pto

tal


(b)

Figure 5.11: Simulation of Ptotal with QoT and latency constraints for the six WAalgorithms when SP routing is applied, using τ = 7× 10−6; (a) 16-node mesh toroidnetwork with Xadj = −20 dB and Xsw = −40 dB; (b) NSF network with Xadj = −25dB and Xsw = −45 dB. Missing points or lines indicate that the data fall below theordinate values plotted.

113

140 150 160 170 180 190 200 210 220

10−5

10−4

10−3

10−2

10−1

100

Load, Erlangs

PT

QoS−FF−SPQoS−RP−SPQoS−FFwO−SP

(a)

90 95 100 105 110 115 120 125

10−5

10−4

10−3

10−2

10−1

100

Load, Erlangs

PT


(b)

Figure 5.12: Simulation of PT with QoT and latency constraints for the six WAalgorithms when SP routing is applied; (a) 16-node mesh toroid network with Xadj =−20 dB, Xsw = −40 dB, and total traffic load of 160 Erlangs; (b) NSF network withXadj = −25 dB, Xsw = −45 dB, and total traffic load of 100 Erlangs. Missing pointsor lines indicate that the data fall below the ordinate values plotted.

114

140 150 160 170 180 190 200 210 220

10−5

10−4

10−3

10−2

10−1

100

Load, Erlangs

PQ

oT


(a)

90 95 100 105 110 115 120 125

10−5

10−4

10−3

10−2

10−1

100

Load, Erlangs

PQ

oT


(b)

Figure 5.13: Simulation of PQoT with QoT and latency constraints for the six WAalgorithms when SP routing is applied; (a) 16-node mesh toroid network with Xadj =−20 dB, Xsw = −40 dB, and total traffic load of 160 Erlangs; (b) NSF network withXadj = −25 dB, Xsw = −45 dB, and total traffic load of 100 Erlangs. Missing pointsor lines indicate that the data fall below the ordinate values plotted.

115

140 150 160 170 180 190 200 210 220

10−5

10−4

10−3

10−2

10−1

100

Load, Erlangs

Pto

tal


(a)

90 95 100 105 110 115 120 125

10−5

10−4

10−3

10−2

10−1

100

Load, Erlangs

Pto

tal


(b)

Figure 5.14: Simulation of Ptotal with QoT and latency constraints for the six WAalgorithms when ALT routing is applied, using τ = 7×10−6; (a) 16-node mesh toroidnetwork with Xadj = −20 dB and Xsw = −40 dB; (b) NSF network with Xadj = −25dB and Xsw = −45 dB. Missing points or lines indicate that the data fall below theordinate values plotted.

116

QoS-RP in both SP and ALT routing, the randomness in wavelength selection tends

to spread the calls throughout the spectrum so that the probability that the chosen

wavelength meets crosstalk from other in-band signals is lower than that for QoS-FF.

Thus the average value of Yi in (5.2) for QoS-RP becomes lower than that for QoS-FF,

since Yi for QoS-RP is less than that for QoS-FF. However, the wavelength ordering

technique diminishes the probability that the chosen wavelength meets crosstalk from

adjacent wavelengths and decreases the average of m. Therefore, QoS-FFwO suffers a

similar delay as QoS-RP so that its PT is similar to that of QoS-RP, and yet remains

smaller than that of QoS-FF, as shown in Fig. 5.12 and 5.15.

In Figs. 5.13 and 5.16, QoS-FFwO-ALT has the lowest PQoT among all of algo-

rithms. Among the QoS-guaranteed algorithms, FFwO-ALT is the best algorithm.

Generally, the performance of FFwO WA is better than that of RP, which is better

than that of FF, as expected. FFwO is better than FF because the ordering tech-

nique alleviates crosstalk from the demultiplexers. Thus the PQoT for QoS-FF falls

lower than for QoS-RP in Figs. 5.13 and 5.16. The gap between QoS-aware FF and

QoS-aware RP is diminished as the traffic increases, where crosstalk introduced by

high traffic load may lead to all unsatisfactory candidate lightpaths in FF. Note that

QoS-aware FF may have lower PQoT than QoS-aware FFwO in light traffic situation,

because QoS-aware FF experiences more total blocking. In other words, QoS-aware

FF blocks more calls thereby decreasing the effective network load in the network so

that it experiences less physical impairments than QoS-aware FFwO.

5.2.3 Blocking vs. Crosstalk Level

As crosstalk is considered the dominant physical impairment in this paper, it is

important to determine how each algorithm performs under different crosstalk power

levels. The total blocking probabilities for the twelve RWA algorithms are plotted

in Figs. 5.17 and 5.20 for a fixed adjacent-port crosstalk level Xadj as the switching

117

140 150 160 170 180 190 200 210 220

10−5

10−4

10−3

10−2

10−1

100

Load, Erlangs

PT

FF−ALTFFwO−ALTQoS−FF−ALTQoS−RP−ALTQoS−FFwO−ALT

(a)

90 95 100 105 110 115 120 125

10−5

10−4

10−3

10−2

10−1

100

Load, Erlangs

PT

FF−ALTQoS−FF−ALTQoS−RP−ALTQoS−FFwO−ALT

(b)

Figure 5.15: Simulation of PT with QoT and latency constraints for the six WAalgorithms when ALT routing is applied; (a) 16-node mesh toroid network with Xadj =−20 dB, Xsw = −40 dB, and total traffic load of 160 Erlangs; (b) NSF network withXadj = −25 dB, Xsw = −45 dB, and total traffic load of 100 Erlangs. Missing pointsor lines indicate that the data fall below the ordinate values plotted.

118

140 150 160 170 180 190 200 210 220

10−5

10−4

10−3

10−2

10−1

100

Load, Erlangs

PQ

oT


(a)

90 95 100 105 110 115 120 125

10−5

10−4

10−3

10−2

10−1

100

Load, Erlangs

PQ

oT


(b)

Figure 5.16: Simulation of PQoT with QoT and latency constraints for the six WAalgorithms when ALT routing is applied; (a) 16-node mesh toroid network with Xadj =−20 dB, Xsw = −40 dB, and total traffic load of 160 Erlangs; (b) NSF network withXadj = −25 dB, Xsw = −45 dB, and total traffic load of 100 Erlangs. Missing pointsor lines indicate that the data fall below the ordinate values plotted.

119

fabric crosstalk level Xsw varies from −50 dB to −30 dB. Selected values of PT and

PQoT are shown in Figs. 5.18-5.22.

As seen in Fig. 5.17, among the SP routed systems, QoS-FFwO-SP has the best

performance and QoS-FF-SP is the second-best algorithm. QoS-RP-SP always per-

forms worst because it has the highest PQoT in Fig. 5.19, even though QoS-RP-SP

has much better PT than QoS-FF-SP, as shown in Fig. 5.18. As the level of crosstalk

increases, QoS-aware SP WA algorithms need more time to obtain a workable light-

path. PT for QoS-FFwO-SP increases faster than for QoS-RP-SP and QoS-FF-SP

as shown in Fig. 5.18. At the low level of crosstalk, wavelength ordering helps QoS-

FFwO-SP setup the lightpaths rapidly. In strong crosstalk (Xsw larger than −35

dB [38, 39]), physical impairments from Xsw force QoS-FFwO-SP to iterate more

times to find a workable lightpath so that QoS-FFwO-SP has the nearly the same

delay as QoS-FF-SP, as shown in Fig. 5.18.

In Fig. 5.20, the six ALT WA algorithms show the same trends as the six SP WA

algorithms in Fig. 5.17. As we expected, when Xsw is large, Ptotal for QoS-FFwO-ALT

is sometimes larger than for QoS-RP-ALT in Fig. 5.20 because PT for QoS-FFwO-

ALT is larger than for QoS-RP-ALT, as shown in Fig. 5.22. When Xsw ≥ −35 dB,

ordering technique does not help and switching crosstalk forces QoS-FFwO-ALT to

iterate more times to find a workable lightpath so that QoS-FFwO-ALT has the even

larger delay than QoS-FF-ALT. In low Xsw case, the alternate routing help FFwO-

ALT achieve the same performance as QoS-FFwO-ALT. This shows that ordering

technique combined with routing algorithms can greatly improve the performance

with adding a small complexity.

RP still benefits from its randomness property in all situations. We can observe

this phenomenon from the three QoS-guaranteed WA algorithms for both routing

algorithms in Fig. 5.17 and 5.20. Note that PT and Pλ for QoS-guaranteed WA

algorithms are negligible and PQoT is the dominant term of Ptotal. The Ptotal and

120

−50 −45 −40 −35 −30

10−5

10−4

10−3

10−2

10−1

100

Xsw, dB

Pto

tal


(a)

−50 −45 −40 −35 −30

10−5

10−4

10−3

10−2

10−1

100

Xsw, dB

Pto

tal


(b)

Figure 5.17: Simulation of Ptotal with QoT and latency constraints for the six WAalgorithms when SP routing is applied, using τ = 7× 10−6; (a) 16-node mesh toroidnetwork with Xadj = −20 dB and traffic load of 160 Erlangs; (b) NSF network withXadj = −25 dB and traffic load of 100 Erlangs. Missing points or lines indicate thatthe data fall below the ordinate values plotted.

121

−50 −45 −40 −35 −30

10−5

10−4

10−3

10−2

10−1

100

Xsw, dB

PT


(a)

−50 −45 −40 −35 −30

10−5

10−4

10−3

10−2

10−1

100

Xsw, dB

PT


(b)

Figure 5.18: Simulation of PT with QoT and latency constraints for the six WAalgorithms when SP routing is applied, using τ = 7× 10−6; (a) 16-node mesh toroidnetwork with Xadj = −20 dB and traffic load of 160 Erlangs; (b) NSF network withXadj = −25 dB and traffic load of 100 Erlangs. Missing points or lines indicate thatthe data fall below the ordinate values plotted.

122

−50 −45 −40 −35 −30

10−5

10−4

10−3

10−2

10−1

100

Xsw, dB

PQ

oT


(a)

−50 −45 −40 −35 −30

10−5

10−4

10−3

10−2

10−1

100

Xsw, dB

PQ

oT


(b)

Figure 5.19: Simulation of PQoT with QoT and latency constraints for the six WAalgorithms when SP routing is applied, using τ = 7× 10−6; (a) 16-node mesh toroidnetwork with Xadj = −20 dB and traffic load of 160 Erlangs; (b) NSF network withXadj = −25 dB and traffic load of 100 Erlangs. Missing points or lines indicate thatthe data fall below the ordinate values plotted.

123

PQoT for FF is worst. FFwO is better than RP when Xsw < −35 dB in SP routing

and Xsw < −38 dB in ALT routing. When Xsw is large, FFwO is worse than RP since

FFwO can only alleviate the crosstalk effects from the demultiplexer and yet results

in a large PT , as shown in Figs. 5.18-5.22. Note that current switching devices based

on MEMS technology can provide switching crosstalk levels as low as Xsw = −60

dB [66]. Thus FFwO outperforms RP in current devices.

5.2.4 Blocking vs. Path Length

The blocking probabilities for different path lengths (as measured by the number

of hops) are shown in Fig. 5.23 to verify that fairness amongst node pairs is not com-

promised by using a particular WA algorithm. Only SP routing is considered here

because the primary and alternate routes may have different lengths. Clearly, longer

paths are more likely to be blocked using any WA algorithm. Yet QoS-FFwO-SP

performs best among all WA algorithms for all path length values tested. Second

best is QoS-FF-SP, always beating QoS-RP-SP. Among the QoS-guaranteed SP algo-

rithms, for all path length cases, FFwO-SP outperforms RP-SP, and FF-SP performs

the worst. All results demonstrate that wavelength ordering effectively decreases the

blocking probabilities for paths with different lengths.

5.3 Summary

In this chapter, we study the impact of guaranteeing both QoT and latency con-

straints on the performance of WA algorithms in SP and ALT routing. The static

wavelength ordering algorithm to wisely allocate the wavelengths to calls/requests

removes a part of the crosstalk due to adjacent wavelength power leaking through

the WDM demultiplexers as described in Chapter 3. We show that this technique

not only alleviates the effects of physical impairments, but also decreases the latency

124

−50 −45 −40 −35 −30

10−5

10−4

10−3

10−2

10−1

100

Xsw, dB

Pto

tal


(a)

−50 −45 −40 −35 −30

10−5

10−4

10−3

10−2

10−1

100

Xsw, dB

Pto

tal


(b)

Figure 5.20: Simulation of Ptotal with QoT and latency constraints for the six WAalgorithms when ALT routing is applied, using τ = 7×10−6; (a) 16-node mesh toroidnetwork with Xadj = −20 dB and traffic load of 160 Erlangs; (b) NSF network withXadj = −25 dB and traffic load of 100 Erlangs. Missing points or lines indicate thatthe data fall below the ordinate values plotted.

125

−50 −45 −40 −35 −30

10−5

10−4

10−3

10−2

10−1

100

Xsw, dB

PT


(a)

−50 −45 −40 −35 −30

10−5

10−4

10−3

10−2

10−1

100

Xsw, dB

PT


(b)

Figure 5.21: Simulation of PT with QoT and latency constraints for the six WAalgorithms when ALT routing is applied, using τ = 7×10−6; (a) 16-node mesh toroidnetwork with Xadj = −20 dB and traffic load of 160 Erlangs; (b) NSF network withXadj = −25 dB and traffic load of 100 Erlangs. Missing points or lines indicate thatthe data fall below the ordinate values plotted.

126

−50 −45 −40 −35 −30

10−5

10−4

10−3

10−2

10−1

100

Xsw, dB

PQ

oT


(a)

−50 −45 −40 −35 −30

10−5

10−4

10−3

10−2

10−1

100

Xsw, dB

PQ

oT


(b)

Figure 5.22: Simulation of PQoT with QoT and latency constraints for the six WAalgorithms when ALT routing is applied, using τ = 7×10−6; (a) 16-node mesh toroidnetwork with Xadj = −20 dB and traffic load of 160 Erlangs; (b) NSF network withXadj = −25 dB and traffic load of 100 Erlangs. Missing points or lines indicate thatthe data fall below the ordinate values plotted.

127

1 2 3 4−6

−5

−4

−3

−2

−1

0

Route length in number of hops (a)

log 10

(Blo

ckin

g pr

obab

ility

)

1 2 3 4−6

−5

−4

−3

−2

−1

0

Route length in number of hops (b)

QoS−FF−SP

QoS−RP−SP

QoS−FFwO−SP

FF−SP

RP−SP

FFwO−SP

Figure 5.23: Total blocking probability with QoT and latency constraints for differentrouting path length for the six WA algorithms when SP routing is applied, usingτ = 7× 10−6; (a) 16-node mesh toroid network with Xadj = −20 dB, Xsw = −40 dB,and traffic load of 160 Erlangs; (b) NSF network with Xadj = −25 dB, Xsw = −45dB, and traffic load of 100 Erlangs.

128

in QoS-aware algorithms over a wide range of network parameters. The static wave-

length ordering can be done without any extra hardware or run-time computational

expense. Because of this ordering technique, QoS-aware FFwO performs better than

other QoS-aware WAs in all practical cases when SP or ALT routing is applied. QoS-

aware FF outperforms QoS-aware RP in many circumstances even though QoS-aware

RP induces less delay than QoS-aware FF.

If the design of the centralized network controller allows for the extra complexity

of a QoS-aware RWA algorithm, QoS-aware FFwO should be selected over the other

QoS-aware WAs considered in SP or ALT routing, for all traffic and levels of physical

impairments cases. If the use of a simpler QoS-guaranteed WA algorithm is necessary,

we suggest the FFwO algorithm for networks using switches with Xsw ≤ −35 dB.

Surprisingly, QoS-aware WA is powerful and brings a larger performance improvement

than ALT routing does if the latency constraint is enforced.

Chapter 6

Conclusions and Future Work

The dramatic increase in throughput demands from backbone transport systems

has propelled the development of all-optical networks. These so-called transparent

optical networks have eliminated the electrical/optical conversion bottleneck by us-

ing all-optical switches and routers. The impairments from other network layers,

which were totally ignored previously, are becoming an important and fundamental

limitation to the performance of optical networks.

6.1 Main Contributions

The goal of this dissertation is to study the impact of physical impairments on

WRONs. A QoT blocking constraint is introduced on the call setup procedure to

maintain the high quality of transmission in networks. We propose several techniques

to combat the performance degradation caused from the physical layer. We further

consider the impact of the complexity of the QoT estimation in terms of latency.

By carefully design of routing and wavelength assignment algorithms, the effects

of physical impairments can be alleviated. Using a simple ordering technique, the

latency in QoS-aware algorithms can also be reduced over a wide range of network

parameters.

129

130

One critical issue for anyone doing research in optical communications is the tech-

nology dependence. We expect WRONs will become the next generation backbone

and metropolitan networks. By extracting the dominant impacts from constraints

of the optical networks and keeping the math framework general, we can perform

farther-reaching and more fundamental research. We hope the work can be applied

in practice with current and future technological constraints.

The immediate contribution of this work is to provide a deep understanding of

the limitations and optimization of optical networks. The proposed mathematical

frameworks for static and dynamic traffic help researchers design and evaluate their

algorithms. Our analysis model is the first to allow the evaluation of FF WA with QoT

constraints. Furthermore, we consider the impact of complexity of the algorithms on

the implementation and give several simple but efficient techniques to mitigate the

effects of the QoT degradation.

6.2 Summary of Dissertation

In Chapter 2, we review the physical model used in this dissertation. By using

this physical model, the QoT of the lightpath can be estimated. We then propose an

optimal RWA with a QoT constraint for a set of static deterministic call provisioning

requests, so as to assess the role of RWA in combating physical degradations. Until

now no optimal formulation has considered QoT constraints. Our results show the

improvement from using an optimal RWA algorithm and validate that routing and

wavelength assignment algorithms can both help the network mitigate the impact of

physical impairments. We make our mathematical formulations as general as possible.

The cost constraints in the formulations can be extended to other cases. A QCQP

approximation for the optimal RWA is also proposed that makes it possible to find

optimal solutions for large networks.

131

Based on the results in Chapter 2, we study routing algorithms and WA algorithms

separately for dynamic traffic in centralized and distributed networks in Chapter 3.

Sub-optimal RWA algorithms are studied because of the NP-hard nature of optimal

RWA. Adaptive routing and adaptive wavelength ordering techniques are proposed to

achieve better performance in terms of blocking probability and other metrics. Our

RWA algorithms are able to mitigate the impact of the physical impairments at the

network layer, which is shown via simulation.

To thoroughly investigate the problem of RWA with QoT constraints, a new ana-

lytical technique is proposed in Chapter 4 to assess the performance of QoT-aware and

QoT-guaranteed algorithms using FF and FFwO. This model is the first of its kind to

include QoT blocking in FF WA. In spite of the inaccuracy of the wavelength blocking

model it relies on, our analytical model accurately predicts the blocking probabilities

indicated by the simulations. Moreover, our framework is easily extended to evalu-

ate other algorithms; in particular, we employ it to evaluate QoT-guaranteed FFwO.

Because of the relaxation of the wavelength equivalent assumption used by other

techniques, heterogeneous networks can be studied and different levels of degrada-

tions can be considered for each path. We demonstrate the flexibility of our approach

by incorporating different number of spans in the NSF network example. This ad-

vantage makes it possible to integrate other types of physical impairments into our

framework, which is left for future work.

The physical impairments not only impact the quality of a lightpath, but also

cause a significant delay due to channel bit-error-rate estimation or measurement

collection. In Chapter 5, the impact on RWA of computational complexity of the

QoT estimation procedure is studied by adding a timeout constraint to evaluate the

negative impact it has on the network performance.

132

6.3 Conclusions and Recommendations

We conclude that our new wavelength ordering technique is powerful yet simple

and easy to be implemented. The improvement is significant in various situations

we simulate and analyze. We recommend to researchers and developers to consider

this simple technique to improve the network performance. Several adaptive RWA

algorithms also show significant ability to mitigate the impact of physical impairments

by adding a small complexity. In addition, our mathematical framework for static

traffic and analytical model for dynamic traffic are both applicable to be extended to

consider other degradations. Using the approximation we propose, larger networks

are also possibly evaluated in a short time.

6.4 Future Work

Currently, all-optical regeneration is still at an experimental design stage and is

hence ignored in this dissertation. Considering that it might be available soon, future

work might include the enhancement gained from the all-optical regenerations. Other

impairments, such as polarization mode dispersion (PMD), have to be considered in

high data rates, such as 40 Gbps or higher, which is also left for the future work.

Ongoing work also includes employing a more accurate wavelength blocking model to

improve the accuracy of the analytical model.

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