- - -
- - -
Dépôt Institutionnel de l’Université libre de Bruxelles / Université libre de Bruxelles Institutional Repository
Thèse de doctorat/ PhD Thesis Citation APA:
De Vega Rodrigo, M. (2008). Modeling future all-optical networks without buffering capabilities (Unpublished doctoral dissertation). Université libre de Bruxelles, Faculté des sciences appliquées – Informatique, Bruxelles.
Disponible à / Available at permalink : https://dipot.ulb.ac.be/dspace/bitstream/2013/210455/4/52bc6712-5d19-4358-9d7c-ddeb89b38510.txt
(English version below)
Cette thèse de doctorat a été numérisée par l’Université libre de Bruxelles. L’auteur qui s’opposerait à sa mise en ligne dans DI-fusion est invité à prendre contact avec l’Université ([email protected]).
Dans le cas où une version électronique native de la thèse existe, l’Université ne peut garantir que la présente version numérisée soit identique à la version électronique native, ni qu’elle soit la version officielle définitive de la thèse.
DI-fusion, le Dépôt Institutionnel de l’Université libre de Bruxelles, recueille la production scientifique de l’Université, mise à disposition en libre accès autant que possible. Les œuvres accessibles dans DI-fusion sont protégées par la législation belge relative aux droits d'auteur et aux droits voisins. Toute personne peut, sans avoir à demander l’autorisation de l’auteur ou de l’ayant-droit, à des fins d’usage privé ou à des fins d’illustration de l’enseignement ou de recherche scientifique, dans la mesure justifiée par le but non lucratif poursuivi, lire, télécharger ou reproduire sur papier ou sur tout autre support, les articles ou des fragments d’autres œuvres, disponibles dans DI-fusion, pour autant que :
Le nom des auteurs, le titre et la référence bibliographique complète soient cités;
L’identifiant unique attribué aux métadonnées dans DI-fusion (permalink) soit indiqué;
Le contenu ne soit pas modifié.
L’œuvre ne peut être stockée dans une autre base de données dans le but d’y donner accès ; l’identifiant unique (permalink) indiqué ci-dessus doit toujours être utilisé pour donner accès à l’œuvre. Toute autre utilisation non mentionnée ci-dessus nécessite l’autorisation de l’auteur de l’œuvre ou de l’ayant droit.
--- English Version ---
This Ph.D. thesis has been digitized by Université libre de Bruxelles. The author who would disagree on its online availability in DI-fusion is invited to contact the University ([email protected]).
If a native electronic version of the thesis exists, the University can guarantee neither that the present digitized version is identical to the native electronic version, nor that it is the definitive official version of the thesis.
DI-fusion is the Institutional Repository of Université libre de Bruxelles; it collects the research output of the University, available on open access as much as possible. The works included in DI-fusion are protected by the Belgian legislation relating to authors’ rights and neighbouring rights.
Any user may, without prior permission from the authors or copyright owners, for private usage or for educational or scientific research purposes, to the extent justified by the non-profit activity, read, download or reproduce on paper or on any other media, the articles or fragments of other works, available in DI-fusion, provided:
The authors, title and full bibliographic details are credited in any copy;
The unique identifier (permalink) for the original metadata page in DI-fusion is indicated;
The content is not changed in any way.
It is not permitted to store the work in another database in order to provide access to it; the unique identifier (permalink) indicated above must always be used to provide access to the work. Any other use not mentioned above requires the authors’ or copyright owners’ permission.
D 03553
M odeling F uture
A ll -O ptical N etworks
WITHOUT B uffering C apabilities
M iguel de V ega R odrigo
Thèse présentée en vue de l’obtention du grade de docteur en sciences de l’ingénieur
2008
Université libre de Bruxelles Faculté des Sciences Appliquées
■'"iyef'fite Libre de Bruxelles
Miguel de Vega Rodrigo Université libre de Bruxelles
Département de Mathématiques de la Gestion Blvd du Triomphe CP 210/01
1050 Bruxelles Belgique
Email: [email protected]
Thèse de doctorat présentée en séance publique le 27 octobre 2008 à l’Université libre de Bruxelles.
Jury: Philippe Emplit, Président du jury, ULB Koenraad Laevens, UGENT
Guy Latouche, Co-promoteur, ULB
Marie-Ange Remiche, Promoteur, ULB
Yves De Smet, Secrétaire du jury, ULB
Lucia y Clara...
Contents
Introduction i
I Network 1
1 Functional Description of a Bufferless OPS/OBS Network 3
1.1 All-Optical Networks... 3
1.2 Optical Burst Switching Networks... 5
1.3 Optical Packet Switching Networks... 7
1.4 Modeling Considérations... 8
2 Hardware Implémentation of an OBS Network 11 2.1 The Main Technological Requirements in an OBS Network... 11
2.2 Hardware Implémentation of an Ingress Edge Node... 13
2.3 Hardware Implémentation of an Egress Edge Node ... 16
2.4 Hardware Implémentation of a Transmission Link... 18
2.4.1 The Operating Principle of an EDFA... 19
2.4.2 The Problem of Using EDFAs in an OBS Network... 19
2.4.3 State-of-the-art Solutions for Using EDFAs in an OBS Network 20 2.5 Hardware Implémentation of a Core Node... 22
2.5.1 Fiber Delay Lines... 23
2.5.2 OBS Switch Fabrics... 24
2.5.3 Wavelength Conversion... 26
2.6 Modeling Considérations... 27
3 Characterization of Highly-Aggregated Internet Traffic 31
3.1 Problem Setting... 32
3.2 The Measurement Platform... 32
3.3 The Poisson Process... 33
3.3.1 Définition... 33
3.3.2 Testing the Poisson Hypothesis... 33
3.3.3 Results From the UPC Traces... 34
3.4 Wavelet Transforms... 35
3.4.1 The Discrète Wavelet Transform... 37
3.4.2 Multiresolution Analysis... 39
3.4.3 The Discrète Wavelet Transform of Stochastic Processes . . 41
3.5 Self-Similar and Long-Rangé Dépendent Processes... 42
3.5.1 Définition... 42
3.5.2 The Logscale Diagram Estimator... 43
3.5.3 Results From the UPC Traces... 46
3.6 Performance Evaluation ... 50
4 Traffic Entering the Optical Domain in a BufFerless OPS/OBS Network 55 4.1 Problem Setting... 56
4.2 The Theoretical Logscale Diagram... 57
4.3 The Packet Count Aggregation Strategy... 59
4.4 The Buffer Limit Aggregation Strategy... 63
4.5 The Timeout Aggregation Strategy... 65
4.6 The Mixed Aggregation Strategy ... 66
4.7 Modeling Considérations... 68
III Modeling 71 5 Modeling a BufFerless OPS/OBS Network with Poisson Traffic 73 5.1 Mathematical Tools... 74
5.2 General Description of the Network Model... 76
5.3 Model Assumptions... 78
5.4 Analysis of the Model... 79
5.4.1 Ingress Links... 81
5.4.2 Output Links of Independent Nodes... 81
5.4.3 Output Links of Arbitrary Nodes... 82
5.4.4 Algorithms for the Constraint Matrix A and the Sets T and C 84
5.5 Blocking Probability... 86
5.5.1 Blocking of a Flow at a Node... 88
5.5.2 Blocking at the Output Link of a Node... 90
5.5.3 Blocking of a Flow... 92
5.6 Computational Issues... 93
5.7 Numerical Study... 94
5.8 Model Extensions and Future Work... 101
6 Modeling a Simplified OPS/OBS Network with LRD Traffic 105 6.1 Mathematical Tools... 106
6.2 Problem Description...107
6.3 The Direct Solution to the Simplified Problem... 110
6.4 The Superposition of 2 QBD Processes... 113
6.5 The Simplified BD of a QBD...118
6.6 The Proposed Solution to the Simplified Problem... 125
6.7 Complexity Evaluation...126
6.8 A Case Study with a Markovian pLRD Process ...129
6.8.1 Applying the Proposed Solution to the Simplified Problem . 131 6.8.2 The Fitting Process...132
6.8.3 A Numerical Example...133
7 Modeling a BufFerless OPS/OBS Network with LRD Traffic 143 7.1 The Direct Solution to the Complété Problem... 143
7.1.1 Ingress Links...144
7.1.2 Output Links of Independent Nodes... 144
7.1.3 Output Links of Arbitrary Nodes... 145
7.1.4 The Blocking Probability...146
7.2 The Proposed Solution to the Complété Problem ... 149
7.3 Complexity Evaluation...153
7.4 Numerical Study... 154
Bibliography 161
Acknowledgement s
I would like to extend my sincere thanks to my superviser Marie-Ange Remiche for having dedicated so mu ch effort and time to me and my work. Her teaching skills and profound knowledge hâve led me through many exciting adventures in stochastic processes. I can hardly realize how much I hâve learnt from her. Besides being an excellent superviser, she has also helped me feel at home at the ULB and in Brussels.
What can I say about Guy Latouche that it has not been said yet? Thanks to an inexplicable phenomenon, an hour of his thinking time is équivalent to days of mine. I suspect it has to do with relativity, but I haven’t figured out the details yet. Considering that he has dedicated me a countless number of hours, I shall never be able to thank him enough for his continuous help, support and insight during the last few years.
Many thanks to Philippe Emplit for following the évolution of this work over the years. His comments and suggestions hâve notably influenced and motivated some parts of this work.
I would also like to thank my colleagues and friends at the ULB, in particular Ana da Silva Soares, Sophie Hautphenne, Philippe Nemery, Yves De Smet and Arturo Calvo Devesa for being there and helping me in numerous occasions. My thanks also to Michelle Hof for proof-reading the English text.
I will not forget my family. They are always there when I need them and to them I owe what I am. Spécial thanks to my sister Inès for sharing her knowledge on some parts of this work. Many thanks also to my parents who support me in every way at any given time. I would like to express my gratitude also to Jelka Ovaska for convincing me to begin these studies.
Most especially, I would like to thank my daughters for making me see the
Last but not least, this work would not bave been possible without the support
and help from my loving wife Tanja. Thanks for understanding me and standing
by my side during the difficult moments (and during the easy ones too).
List of Acronyms
ADC Analog to Digital Converter
AS Aggregation Strategy (OBS algorithm) ASE Amplified Spontaneous Emission BD Birth-Death (stochastic process) BER Bit Error Rate
CWT Continuous Wavelet Transform
DWDM Dense Wavelength Division Multiplexing DWT Discrète Wavelet Transform
EDFA Erbium-Doped Fiber Amplifier
EFPA Erlag Fixed Point Approximation (network model) FDL Fiber Delay Line
FEC Forward Equivalent Class
IM/DD Intensity Modulation/Direct Détection IP Internet Protocol
LD Logscale Diagram (LRD estimation) LR Lewis Robinson (statistical test)
LRD Long-Range Dépendent (stochastic process) MEMS Micro-Electro-Mechanical System
MM PP Markov-Modulated Poisson Process
MRA Multi Resolution Analysis (wavelet ttieory) MWM Multifractal Wavelet Model (traffic model) OBS Optical Burst Switching (network)
O/E/O Opto-Electro-Optic
O PS Optical Packet Switching (network) OSI Open Systems Interconnection
PC N T Pairwise Comparison Nonparametric Test QoS Quality of Service
RAM Random Access Memory
SOA Semiconductor Optical Amplifier SNR Signal-to-Noise Ratio
TCP Transmission Control Protocol
TLD Theoretical Logscale Diagram (LRD analysis)
WDM Wavelength Division Multiplexing
Introduction
These days, optical networks can be found anywhere from the access level to the very core of the Internet. But it is in the transmission of large amounts of infor
mation over long distances that they provide indisputable advantages over other transport technologies. The following dissertation focuses on such long-distance optical networks, also referred to as backbone, long-haul or core networks [102].
Most current backbone optical networks are built on two main cornerstones.
First, they are circuit-switching networks. That is to say, user information is sent between a pair of source-destination nodes as a continuons constant-rate bitstream that follows the same route or path across the network. Here, a node represents a point in the network where information can be transmitted, received or forwarded.
Second, their data plane is not all-optical. In other words, the bitstream containing user information is sent optically through the links of the network, but is converted to electronic signais at its nodes.
This scénario is not static or permanent. Optical networks are constantly evolving in an attempt to meet the ever-increasing demand for bandwidth created by the expansion of the Internet. This expansion has been one of the main catalysts behind the unprecedented growth of optical networks in the past several years.
However, it has also created a demand for new dynamic and upgradeable optical networks.
The need for dynamic optical networks is confirmed by many empirical studies
reporting that Internet traffic is highly variable and bursty (see for instance [31,
55, 96, 42]). An efficient and natural way of coping with such variable traffic is
to use packet-switching optical networks [115]. In such networks, user information
is sent between a pair of source-destination nodes as a sériés of packets that may follow different routes, where a packet is a finite sequence of bits. Thus, one of the major trends in the design of future optical networks is to move from the current circuit-switching to the packet-switching paradigm [138, 83].
The need for upgradeable optical networks arises from the continuously-in- creasing demand for bandwidth prompted by the expansion of the Internet. An efficient way of designing an upgradeable network is to make it all-optical - that is, to use exclusively optical components for the transmission of user information across the network. Indeed, it is relatively simple to upgrade the data rate in all- optical networks by adding extra transmission channels [16]. Moreover, all-optical networks hâve at least two additional advantages. First, they can potentially reduce costs by saving on expensive electronics and opto-electro-optic (O/E/O) converters, and by reducing power consomption. Second, they can eliminate the so- called electronic bottleneck. This bottleneck is currently one of the major factors limiting capacity in an optical network. It is a resuit of the low processing speed of the electronic equipment at the nodes compared to the high transmission capacity at the optical links. Ail these advantages make all-optical networking another major trend in the design of future optical networks [136, 138, 83, 134, 121].
The two trends mentioned above give rise to the concept of a pure packet- oriented all-optical network, called an Optical Packet Switching (OPS) network in the literature [138, 83]. The main objective in the design of an OPS network is to maximize its performance. Secondary objectives are the cost and feasibility of the all-optical hardware components needed.
The term performance is somewhat ambiguous. It can refer to the efficiency with which bits are physically represented, transferred and received in a network.
Typical performance parameters in this case are the bit error rate (BER) or the signal-to-noise ratio (SNR) [4]. Performance can also refer to the efficiency with which packets are transferred through the network by the network protocols. Net
work protocols can delay and sometimes cause the loss of packets. The main performance parameters in this case are the average packet delay and the packet blocking probability, which basically refers to the probability that a packet will be lost in the network. In this dissertation, we are interested in the study of a packet-switching all-optical network at the packet level of abstraction (i.e., at the OSI network layer). Thus, the term performance will hereinafter be used in order to refer to the average packet delay and the packet blocking probability.
In order to maximize the performance of an OPS network, it is customary to
include the following three requirements in its définition [136, 138, 83]. First, not
only the data plane, but also the control plane must be all-optical. That is to
say, signaling information used to manage network bandwidth must be processed
optically. This allows the control plane to profit from the above-mentioned benefits
111 of an all-optical implémentation. Second, incoming electronic packets must be sent on the fly (i.e., as they arrive) through the optical domain. This minimizes packet delay at the ingress nodes in the network. Third, buffering must be available at the optical domain, permitting the réduction of the blocking probability and thereby increasing network throughput.
The downside of these three requirements is that they notably increase the complexity associated with the implémentation of an OPS network [83]. More specifically, the first requirement implies the use of extensive signal processing ca- pabilities at the optical domain, a technology that is not yet mature enough [19].
The second requirement implies that optical packets hâve the same size as incom
ing Internet (IP) packets. This sets the operating times of the optical components in the OPS network (e.g., the switching times) to the ns range [28], represent- ing a considérable challenge for current technology. The third requirement also represents a problem, because there is no optical équivalent to the random access memory (RAM) used to build the buffers in electronic packet-switching networks.
The best option available are fiber delay Unes (FDLs), which are more expensive and difficult to control than RAMs [44], and increase signal dégradation at the optical domain due to physical System impairments [116].
The fact that OPS networks are so difficult to implement créâtes room for alternative networking solutions, where lower performance is accepted in exchange for a less expensive and complex hardware implémentation. One such alternative solution is Optical Burst Switching (OBS).
The définition of an OBS network strategically avoids the use of the three requirements presented above, while still remaining faithful to the basic principles of a packet-switching all-optical network [134, 135]. First, the control plane is implemented electronically (although the data plane is still all-optical). Second, incoming electronic packets are buffered at the ingress nodes in the network in order to form large groups of packets called bursts, which are then transferred through the optical domain. This relaxes the operating time requirements from the ns to the //s range [67]. Third, as buffering is not available at the optical domain, the use of FDLs is avoided. These characteristics will most probably enable OBS networks to be implemented earlier and at a lower cost than OPS networks [121].
Research on OBS networks has been quite extensive in the last decade and focuses mainly on two questions. The first question is whether OBS networks can be deployed soon and in a cost-efficient manner. The second question is whether OBS networks can provide a clear advantage in terms of performance compared to current optical network architectures.
This thesis focuses on the second question formulated above. Our main objec
tive is to provide the research community with a tractable and reliable analytical
network model that can be used in order to assess the performance in OBS net- works in terms of the burst blocking probability. By tractable we mean a model from which the blocking probability can be computed within a reasonable time using a reasonable amount of computational resources. By reliable we mean a model that includes enough functional and structural details from the original OBS network in order to be realistic and accurate. The use of our analytical net
work model to actually evaluate the viability of OBS networks is out of the scope of this dissertation.
It turns out that the model developed for OBS networks in this thesis can also be used in order to model OPS networks without buffering capabilities (i.e., without FDLs), also denoted as bufferless OPS networks. These networks are of great practical importance, since their study can help to décidé whether it is necessary or not to invest resources in the development and use of FDLs for OPS networks [82, 81].
The blocking probability is the performance parameter of interest in our net
work model, since neither OBS nor bufferless OPS networks hâve FDLs to reduce blocking at the core nodes. It has also been the preferred performance parameter studied in the literature on OPS/OBS networks [167, 99, 167, 66].
The study of other performance parameters falls out of the scope of this doc
ument. Such is the case of the results published in [40]. In that paper, we présent a new framework to study the problem of planning an OBS network from scratch.
The objective is to ensure that flows in the network meet previously given QoS (Quality of Service) requirements in the form of maximum average packet delay and blocking probability.
In this thesis, we develop the analytical network model of a bufferless OPS/OBS network in three steps that we call the Network step, the Traffic step and the Modeling step. In the Network step, the objective is to study the optical network in detail and to décidé which aspects of its functionality and structure should be included in the network model. In the Traffic step, the goal is to study network traffic in detail and to décidé which statistical properties should be included in the network model. In both steps, the main critérium used to select the information to be included in the network model is an often difficult compromise between its resulting reliability and mathematical tractability. In the Modeling step, the goal is to produce the analytical network model based on the modeling considérations collected in the previous steps, together with the corresponding algorithm for the computation of the blocking probability.
The three steps mentioned above serve as the backbone for structuring this
work and are reflected in the three parts into which this thesis is divided. We
proceed now to explain each part.
V
Part I: Networks. This part présents functional and structural details con- cerning the bufFerless OPS/OBS network to be modeled here. As stated before, the main goal is to identify the most important features of a bufferless OPS/OBS network in order to take them into account in the network model developed in Part III of this thesis. This, and the associated literature survey are the main contributions from this part.
OPS and OBS networks constitute extremely active research fields. It is there- fore not surprising that many variants of these networks hâve been presented and studied in the literature. Designing a model for a particular variant has the dis- advantage of reducing its use to just that variant. Designing a model for each one of the different variants constitutes a lengthy task beyond the scope of any single dissertation. In this work, we hâve opted for a third possibility and designed a model for a basic or standard version of an OBS network, the origin of ail other variants. This standard version corresponds to the concept of OBS networking, as originally introduced by Qiao and Yoo in [134, 135]. The resulting model is also valid for a standard OPS network as presented in [108], but without FDLs at the core nodes.
Part I focuses on the description of the above-mentioned standard versions of a bufferless OPS/OBS network. This document does not include the study of any variants. Such studies can be found in [41] and [131], contributions from which will be briefly summarized here.
OBS core nodes use algorithms called réservation mechanisms in order to re
serve a portion of bandwidth on a link for the transmission of a burst upon the arrivai of its associated header packet. In [41] we présent a new réservation mech- anism for OBS networks. We show analytically that it performs better than the best state-of-the-art réservation mechanism in terms of burst blocking probability, and that it allows for a less complex and cheaper network implémentation.
Many authors predict performance problems if an OBS network uses the TCP (Transmission Control Protocol) as a transport protocol [72, 77, 168, 24, 43].
In [131] we put these results into perspective by reporting that when the num- ber of TCP end users is high (above 100) and a realistic version such as TCP Reno is used, performance is not severely afîected by the use of TCP in OBS networks.
Part I is divided into two chapters. Chapter 1 provides an introduction to OPS
and OBS networks as a particular type of all-optical network. The main focus is
on a functional or procédural description of their four basic éléments: ingress edge
nodes, transmission links, core nodes and egress edge nodes. Essentially, we limit
ourselves to the description of what these éléments do in order to transfer user
information through the network, and intentionally skip the details concerning
their structure and hardware implémentation. At the end of the chapter, we
identify the most relevant functional features of bufferless OPS/OBS networks in order to take them into account in the network model developed in Part III.
In Chapter 2 we study the hardware implémentation of an OBS network. The main goal is to identify the most important structural features to be considered in the analytical model in Part III. The idea here is to describe how the basic éléments in an OBS network can be modeled, based on their particular hardware implémen
tation. A secondary goal is to provide the reader with information concerning the state-of-the-art techniques for implementing an OBS network.
The hardware implémentation of our standard bufferless OPS network from [108]
is very similar to that of our standard OBS network from [134,135]. There are basi- cally only two main différences. First, hardware operating times for OPS networks are at least three orders of magnitude below those for OBS networks [67, 28]. Sec
ond, OPS networks require the development of new tailor-made optical hardware for the implémentation of the control plane in the optical domain. These différ
ences play a crucial rôle in the commercial potential of each one of the networking solutions. However, from the structural point of view, the hardware implémenta
tion of the data plane in these networks is the same in both cases [16]. For this reason, structural modeling features from the data plane identified in this chapter are assumed to be valid for bufferless OPS networks as well.
Part II: TraflBc. This part présents a study of the traffic inside a bufferless OPS/OBS network. The main goal is to identify which statistical properties of this traffic should be taken into account in the network model developed in Part III.
Bufferless OPS/OBS networks are not yet commercially available, and thus it is not possible to directly measure the statistical properties of their traffic. In Part II we overcome this problem by means of a two-step approach. In Chapter 3 we study the statistical properties of the traffic that is most likely to arrive at a bufferless OPS/OBS network. In Chapter 4 we deduce from the results of Chapter 3 the statistical properties of traffic entering the optical domain in a bufferless OPS/OBS network.
Bufferless OPS/OBS networks constitute backbone network solutions and as
such are expected to reçoive highly-aggregated Internet (or IP) traffic at their
ingress nodes ]74, 138, 26, 133]. That traffic exhibits a high throughput result-
ing from the aggregation of many individual IP flows. Thus, it is possible to
study current highly-aggregated traffic from the Internet backbone and assume
that similar traffic will arrive at future bufferless OPS/OBS networks. Accordingly,
our main goal in Chapter 3 is to gain insight on the statistical nature of highly-
vil aggregated IP traffic as représentative of the traffic entering a typical bufferless OPS/OBS network. Previous studies report contradictory results on this matter.
On the one hand, some authors hâve reported the existence of long-memory or long-range dépendent (LRD) properties in low-aggregated [107, 35] as well as in highly-aggregated IP traffic [126]. On the other hand, papers such as [22, 23, 96]
acknowledge the existence of LRD in low-aggregated IP traffic, but report that as the level of aggregation increases, LRD disappears and traffic progressively re- sembles a Poisson process. Perhaps inspired by this conclusion, the majority of publications in the field of backbone optical networks use models with Poisson traffic (see for instance [80, 46, 141]).
Theoretically, in order to settle the debate on the statistical nature of highly- aggregated IP traffic, one could simply perform a statistical analysis of network traffic in a high-capacity optical backbone link. In practice, two main difficulties arise when trying to accomplish such a task. First, due to confidentiality issues, it is difficult for the research community to access such information, owned in most cases by private network operators. Second, the efficient measurement of traffic at Gbps speeds is a very challenging technical task. Hardware limitations often reduce the précision of the packet time-stamps to /is, as in [96]. Software limitations hâve an impact on the amount of data that can be analyzed and therefore often reduce the significance of the results obtained.
Our contribution to this debate is a detailed statistical analysis of a set of two traffic traces provided by the Universitat Politècnica de Catalunya (UPC) within the framework of the European-funded research projects NOBEL I and NOBEL II [132]. These traces contain an unprecedent amount of accurate data taken from a highly-aggregated transmission link. More specifically, each trace contains approximately 800 million packet arrivai time and packet size measurements from a 2-Gbps link, where packet arrivai times are measured with ns-precision.
Our main resuit is a rejection of the Poisson hypothesis and strong evidence suggesting the presence of LRD in ail the traces analyzed. This resuit is important, since it is widely known that LRD has a significant négative impact on network performance, measured in terms of such parameters as the buffer dynamics and blocking probability [126, 63].
We conducted additional studies in order to détermine scaling properties in the traffic beyond LRD. In particular, in [42, 21] we studied the multifractal proper
ties of traffic (see [55]) by means of the Multiscale Diagram presented in [2, 164].
However, we do not include these results in the dissertation for two reasons. First, in [164] the authors express their réservations about the effectiveness of the Multi
scale Diagram and other standard tests for detecting the presence of multifractal
behavior. Second, even if it could be effectively detected, it is not clear that
multifractal traffic has a substantial impact on network performance [9].
In Chapter 4, we assume the existence of LRD IP traffic arriving at the ingress edge nodes in an OPS/OBS network (in line with the evidence reported in Chapter 3) and study if and how LRD is transferred to the departure traffic from these nodes. That is, we study whether LRD is injected into the optical domain in OPS/OBS networks. As mentioned before, this question is relevant because of the impact that LRD traffic has on network performance.
In OPS networks, the answer to this question is immediately évident. In these networks, incoming IP packets are sent directly through the optical domain as they arrive at the ingress edge nodes. An immédiate implication of this is that the statistical properties of incoming IP traffic are not modified by the ingress edge nodes in the OPS network. Thus, we conclude that LRD should be taken into account in the network model of Part III of this thesis, whenever it is used to model a bufferless OPS network.
In the case of OBS networks the situation is more complex. Indeed, the char- acteristics of traffic entering the optical domain in an OBS network are generally different from those of the incoming electronic traffic, due to the fact that incom
ing IP packets are buffered at the ingress nodes to form bursts. In OBS networks, buffering is controlled by an algorithm called the aggregation strategy (AS). The AS basically décidés how many incoming packets should be buffered in order to create a burst. Thus, the question of whether the burst traffic entering the OBS network inherits the LRD from the electronic input traffic is dépendent on the choice of the AS.
There are four main ASs presented in the literature: the Timeout, Buffer Limit, Racket Count and Mixed ASs [179, 69, 39, 172].
The impact of the Timeout AS on the degree of LRD of the burst traffic entering an OBS network has been studied in [69, 86, 179, 8, 78, 153). The methodology followed in [69, 8, 78,153] is the use of simulation techniques together with different Hurst parameter estimators to measure the degree of LRD. In [86, 179], several analytical approximations and asymptotic bounds are obtained. Except for some discrepancies (see [179, 78]), the general conclusion is that LRD does not seem to be substantially reduced by the buffering that takes place at ingress OBS nodes using the Timeout AS.
There do not appear to be any équivalent studies in the literature for the other three ASs, and thus the state-of-the-art picture of traffic entering an OBS network is incomplète. In Chapter 4, we complété this picture by extending the study to the Racket Count, Buffer Limit and Mixed ASs. Our methodology' includes both analytical and simulation studies. From the theoretical point of view, our main contribution is a new analytical approach based on the discrète wavelet transform (DWT) to study the presence of LRD in the burst traffic entering an OBS network.
In the case of the Racket Count AS, our approach provides exact results, which
IX
contrasts with the fact that until now only approximate results had been obtained for the Timeout AS in [86, 179]. In the case of the Buffer Limit AS, our approach provides approximate results.
The analytical and simulative results from this chapter ail suggest that LRD is neither eliminated nor modified (i.e., the Hurst parameter does not change) by the main four ASs in an OBS network. Therefore, our main conclusion from Part II is that LRD should be taken into account when modeling burst traffic entering a bufferless OPS/OBS network. This conclusion questions the common practice of using the Poisson traffic assumption in models of backbone optical networks [80, 46, 141[.
Part III: Modeling. This part présents the main results of this dissertation:
a new model of a bufferless OPS/OBS network together with an algorithm for the computation of the blocking probability at any point in the network. As was explained earlier in this introduction, our goal is to obtain a model that is both reliable and tractable. In order for the model to be reliable, it should incorporate the most important features from Part I concerning the functionality and structure of a typical bufferless OPS/OBS network, as well as those from Part II concerning the statistical properties of its traffic. In order for the model to be tractable, the algorithm for computing the blocking probability should converge within a reasonable time using a reasonable amount of computational resources.
Chapter 5 présents a preliminary model of a bufferless OPS/OBS network and shows how to compute the blocking probability at any point in it. The preliminary model includes ail the modeling features from Part I, but does not take into account the resuit from Part II concerning the LRD nature of burst traffic entering a bufferless OPS/OBS network. Instead, the main assumption in this chapter is that packets/bursts enter the optical domain (i.e., leave the ingress edge nodes) according to a Poisson process.
Although the assumption above goes against our findings in Part II the resulting model is by no means immediately évident, due to the fact that bufferless packet- switching networks exhibit complex behavior. In such networks, packets from a source interact on each link with packets from other sources routed through that link. The physical origin of this interaction is the loss of packets (i.e., blocking) caused by the fact that packets from different sources must share a finite number of transmission channels on each link. As a resuit of packet loss, the characteristics of a traffic source change whenever it is routed on a link together with other traffic.
Therefore, a complété description of the traffic on each link in the network requires
full knowledge of the changes accumulated as packets from each source share links
along their path with packets from other sources.
Previous models of bufFerless packet-switching networks, such as [46, 45, 173, 5, 141, 167, 163, 159], do not provide a complété description (in the sense given above) of the traffic on each link in the network for two reasons. First, in these models, packets are assumed to arrive at each node in the network according to the same type of process (e.g., a Poisson process). That is to say, the packet arrivai process is re-sampled at each node in the network. Second, in these models, packet transmission times (and therefore packet sizes) are assumed to be re-sampled at each node in the network (e.g., from an exponential distribution). Re-sampling of these two stochastic processes (sometimes referred to as link blocking indepen- dence [163]) inevitably implies the loss of information concerning the blocking events of packets along the routes in the network, which makes the description of traffic incomplète.
The most outstanding feature of our model is the fact that, to our knowledge, it incorporâtes for the first time a complété description (in the sense given above) of the traffic on each link in the network.
Our model belongs to the class of réversible Markov process models described in [144], and it is related to well-known stochastic network models used in circuit- switching networking scénarios, such as [129, 29, 104, 103]. The main différence is that in these circuit-switching models there is just one so-called multivariate birth-death (BD) process to describe traffic in the whole network, while in our case we hâve a different one to describe the traffic on each link in the network.
Regarding the computation of the blocking probability in our model, we show in this chapter that it ail cornes down to the computation of the well-known par
tition function [144, 129, 29, 104, 103]. This function has been studied over the last two décades within the framework of many models of circuit-switching net
works. In [109] it was demonstrated that its exact computation constitutes a [JF- complete problem, where the class [[F-complete is a subset of the A^F-complete problems. According to current notions in complexity theory, it is widely believed that no polynomial-time algorithm exists to solve any problem that belongs to the A^F-complete class [64]. This suggests serions scalability problems affecting the computation of the blocking probability in our model as the size of the network grows. In the case of the circuit-switching models presented above, such scalability problems hâve been solved with the use of Monte Carlo simulation techniques [62].
These techniques provide an estimation of the value of the partition function and thus of the blocking probability. Since their complexity does not dépend on the size of the network, they do not présent any scalability issues. In Chapter 5 we use a numerical example to demonstrate that the use of Monte Carlo simulation tech
niques from [104, 103] leads to an accurate estimation of the blocking probability
at different points in our network. This allows us to conclude that our model is
tractable, since the blocking probability can be accurately estimated, even in large
XI
OPS/OBS scénarios.
In Chapter 6, we présent an intermediate step towards the goal of computing the blocking probability at any point in a preliminary network model from Chapter 5, upgraded with LRD traffic. More specifically, we do consider the model from Chapter 5 upgraded with LRD traffic, but we do not seek to compute the block
ing probability at arbitrary points in the network. Instead, we address the less ambitions problem of computing the blocking probability at a spécifie point in the network. This point is chosen so that the problem is équivalent to the computation of the blocking probability in a queueing System with a single multi-server node receiving packets from a LRD traffic source and with no buffering capabilities.
LRD is a complex phenomenon that involves the presence of spécifie properties in network traffic over an infinité span of timescales. Thus, it cornes as no surprise that the exact computation of performance measures in queuing Systems that use pure LRD packet arrivai processes such as fractional Gaussian noise (fGn), remains analytically untractable for the time being [70, 122, 123].
In order to overcome this problem, it is customary to use what one might call a pseudo-LRD process {pLRD in short). A pLRD process emulates or mimics to a certain extent the scale invariance structure typical of a true LRD process. In spite of this simplification, the exact computation of performance measures in queuing Systems using pLRD packet arrivai processes is in some cases also not tractable using current techniques. This is the case of the B-MWM process introduced in [140, 63], for instance.
Markov-modulated Poisson processes (MMPPs) constitute a particular class of Markovian point processes [105]. They are adéquate for analytical studies like ours, since they usually lead to closed-form expressions for the exact computation of performance measures of interest in a large variety of queuing Systems. In the literature, several pLRD processes based on MMPPs hâve been presented. Many of them consist of the superposition of a finite number of independent MMPPs modeling the behavior at different timescales typical of a LRD process. An example of this can be found in [7, 176, 70, 120]. These processes provide a conceptually simple, élégant and accurate way of mimicking LRD. For these reasons, we use them to model LRD in the remainder of this dissertation, and refer to them using the term Markovian pLRD processes.
Accordingly, the problem addressed in Chapter 6 is équivalent to the compu
tation of the blocking probability in a MMPP/PH/W/W queuing System (see Kendalls notation in [101]), where MMPP stands for the Markovian pLRD pro
cess, PH stands for phase-type distributed service times [105], and IT is a finite in-
teger representing the number of servers in the node. The choice for PH-distributed
service times is motivated by the ability of PH distributions to mimic a wide va-
riety of distributions, like for instance heavy-tailed distributions [57]. We show in this chapter that standard matrix analytic methods solve this problem with a com- plexity that increases exponentially with the number N of independent MMPPs superposed. According to our numerical experiments, accurate approximations of LRD processes require N to take large values, which suggests the presence of scalability problems when using the standard solution.
The main contribution in Chapter 6 is a new algorithm to compute the block- ing probability in a MMPP/ PH /W/W queuing System, when the MM PP is a Markovian pLRD process. This algorithm exhibits a complexity that scales linearly with N, and thus does not suffer from the above-mentioned scalability problems.
This allows for the use of Markovian pLRD processes with high values of N, in order to accurately approximate the behavior of real LRD traffic.
Our algorithm provides exact results under the assumption that some related processes exhibit a property called reversibility [144]. We présent in this chapter a Markovian pLRD process, based on the results from [70]. This process does not fulfill the reversibility assumption, and thus our algorithm is in this case regarded as approximative. We show with a numerical example that our algorithm approx- imates the blocking probability very accurately. We offer a possible explanation based on the observation that with this Markovian pLRD process, the reversibility assumption is close to being fulfilled.
In Chapter 7 we study the problem of computing the blocking probability at any point in the network model from Chapter 5, upgraded with Markovian pLRD processes. That is to say, we address the problem of computing the blocking probability in a network model of a bufferless OPS/OBS network with LRD traffic.
We shall call this the LRD Network Problem (in short LRD-NP).
To our knowledge, the network model from the LRD-NP has not been pre- viously studied in the literature. Perhaps the closest model is the one recently presented in [163], since it does not make the usual assumption of Poisson traf
fic. Instead, this paper considers an ON-OFF traffic model with exponentially distributed ON and OFF periods. Besides this rather weak connection, the model in [163] differs fundamentally from our model, since, as previously stated in this introduction, it is not complété.
In this chapter, the blocking probability in the LRD-NP is computed according to two different methods. The first one uses standard matrix analytic methods such as the linear level réduction algorithm from [105, 68]. The second method constitutes the main contribution from this chapter. It uses the algorithm derived in Chapter 6 in order to reduce the complexity associated with the computation of the blocking probability.
Comparing the complexity of the two methods, we conclude that the complexity
Xlll
of the first increases exponentially with the number N of independent MMPPs
superposed, while that of the second increases linearly with N. This constitutes the
main resuit from this thesis. It permits the computation of the blocking probability
in the stochastic network model of Chapter 7 for LRD traffic with basically the
same complexity as the computation of the blocking probability in the preliminary
stochastic network model from Chapter 5 for Poisson traffic. The linear complexity
growth with N effectively means that the number of MMPP sources in our analysis
may be increased in order to closely emulate LRD by means of Markovian pLRD
processes, without compromising the complexity of the problem.
Part I
Network
C hapter 1
Functional Description of a Bufferless OPS/OBS Network
This chapter présents a general functional description of a bufferless OPS/OBS network. Our main objective is to identify the most important functional fea- tures of these networks in order to take them into account in the network model developed in Part III.
The chapter is structured as follows. In Section 1.1 we introduce all-optical networks as a subclass of télécommunication networks. Sections 1.2 and 1.3 présent a general functional description of an OBS and an OPS network, respectively. In Section 1.4 we identify the most important functional features from these networks in order to include them in the network model from Part III.
1.1 All-Optical Networks
In this section we begin with a general définition of a télécommunication network and then describe the main characteristics which identify all-optical networks as a subclass of télécommunication networks. Most of the material in this section is taken from [156].
A télécommunication network is a network of links and nodes arranged so that information can be passed from one part of the network to another over multiple links and through varions nodes. Télécommunication networks are complex objects which can be studied under many different approaches. Throughout this work we use mainly two approaches, which we now proceed to describe.
The first approach divides a télécommunication network in three different
planes: the data, control and management planes. The data plane (also referred to as user plane or transport plane) comprises the network components responsi- ble for carrying the information generated by the users across the network. User information is called in this context user traffic. The transmission of user traffic requires the use of bandwidth resources from the links in the network, which is controlled by the exchange of signaling information among the different network nodes. The network components responsible for generating, carry'ing and Process
ing signaling information form the control plane. Finally, the management plane is formed by the network components in charge of generating, carrying and Pro
cessing administrative information required for network management. A typical function provided by the management plane is accounting, that is, the processing and distribution of billing information.
According to this approach, an all-optical network (also called transparent net
work in the literature) is defined as a télécommunication network of which data plane is entirely implemented in the optical domain [135]. That is, user traffic is strictly carried by optical signais without conversion to the electrical domain. Note that this définition does not mention anything about the control and management planes in all-optical networks, which may use electronic components.
The second approach studies télécommunication networks with the help of reference models. A reference model interprets a network as a hierarchy of several layers. Each layer solves a sériés of problems and provides services to the layer immediately on top. The problems solved by lower layers are related to the way in which information is physically conveyed from one point of the network to another.
The problems solved by upper layers are related to the way in which information is presented to network users. The services provided by each layer to its upper layer are implemented through a sériés of methods or algorithms called protocols. The different protocol choices made at each layer resuit in different télécommunication networks (e.g., satellite, mobile or optical networks).
In this thesis we use the hybrid reference model from [156], which represents a mixture of the OSI (Open Systems Interconnection) and TCP/IP (Transmission Control Protocol/ Internet Protocol) reference models. The main reason for pre- senting one model instead of two is simplicity. There is also a number of technical reasons justifying this choice, and we refer the interested reader to [156, Chapter 1] for details.
The hybrid model is composed of five layers, which we describe from the bottom
to the top. The physical layer is concerned with the transmission of raw bits
over a link. The design issues here largely deal with the physical transmission
medium over which the bits are sent (e.g. the optical fiber). The main task of
the data link layer is to take a raw link and transform it into a link that appears
free of undetected transmission errors to the network layer. The network layer
1.2 Optical Burst Switching Networks 5 is concerned with the transmission of packets between source and destination, possibly over several links. The basic function of the transport layer is to accept data from the application layer, split it up into smaller units if needed, pass these to the network layer, and possibly ensure that the pièces ail arrive correctly at the other end. The application layer contains a variety of protocols which offer a common interface to the network services to the different types of user applications.
In all-optical networks, the protocols implemented in the lowest three layers are tightly connected to the optical technology used to implement these networks [135, 67]. This is usually not the case for protocols at the transport and application layers [147, 14]. For this reason, a necessary requirement for a télécommunication network to be considered all-optical is that its three lowest layers use exclusively optical technology for the transmission of user traffic from the data plane.
All-optical networks may be connected to a wide variety of electronic networks that typically use ATM (Asynchronous Transfer Mode), Ethernet and/or IP tech
nology. Traffic from electronic IP networks dominâtes by far the proportion of total traffic injected into current optical networks. This trend is expected to con
tinue in future all-optical networks due to the increasing demand for bandwidth of Internet applications [31, 56]. For this reason, throughout this work all-optical networks are assumed to be connected to electronic IP networks exclusively. In this thesis we use hereinafter the term "IP network" in order to refer to an elec
tronic IP network. The optical version of an IP network is basically what we call an OPS network.
All-optical networks may use a circuit-switching or a packet-switching para- digm [115]. Optical circuit switching (OCS) networks constitute the most impor
tant type of circuit-switching all-optical network [46]. Sometimes they also referred to as an OFS (Optical Flow Switching) [171] and a WROBS (Wavelength Routed OBS) networks [52, 169, 50, 51, 49]. The two most relevant types of all-optical packet-switching networks are OPS [83] and OBS networks [134, 121].
As stated in the introduction of this thesis, we are interested in OBS networks, as well as in OPS networks without buffering capabilities at the core nodes. We proceed now to describe these networks in more detail.
1.2 Optical Burst Switching Networks
An OBS network can be basically defined as an all-optical packet-switching net
work with a switching granularity of a burst, where a burst is a collection of IP
packets with the same destination in the OBS network. The basic éléments in
an OBS network are four: ingress edge nodes, transmission links, core nodes and
egress edge nodes [46]. In this section we describe how these éléments internet in
order to convey user information from one point to another in a standard OBS
Assembled Burst
Offset time
Header Blocked Burst
Ingress Egress
Edge Edge
N ode Node
Incomiri' IP Rackets
Transmission Link Core Node
utgoing IP Rackets
