PERFORMANCE EVALUATION AND PLANNING METHODS FOR THE NEXT GENERATION INTERNET
GERAD 25th Anniversary Series
Essays and Surveys in Global Optimization Charles Audet, Pierre Hansen, and Gilles Savard, editors Graph Theory and Combinatorial Optimization David Avis, Alain Hertz, and Odile Marcotte, editors Numerical Methods in Finance Hatem Ben-Ameur and Michele Breton, editors Analysis, Control and Optimization of Complex Dynamic Systems El-Kebir Boukas and Roland Malhame, editors Column Generation Guy Desaulniers, Jacques Desrosiers, and Marius M. Solomon, editors Statistical Modeling and Analysis for Complex Data Problems Pierre Duchesne and Bruno Remillard, editors Performance Evaluation and Planning Methods for the Next Generation Internet Andre Girard, Brunilde Sanso, and Felisa Vazquez-Abad, editors Dynamic Games: Theory and Applications Alain Haurie and Georges Zaccour, editors Logistics Systems: Design and Optimization Andre Langevin and Diane Riopel, editors Energy and Environment Richard Loulou, Jean-Philippe Waaub, and Georges Zaccour, editors
PERFORMANCE EVALUATION AND PLANNING METHODS FOR THE NEXT GENERATION INTERNET
Edited by
ANDRE GIRARD GERAD and INRS-Energie, Materiaux et Telecommunications
BRUNUJDE SANSO GERAD and Ecole Polytechnique de Montreal
FELISA VAZQUEZ-AB AD GERAD and Universite de Montreal
4y Springer
Andre Girard GERAD & INRS-Telecommunications Montreal, Canada
Brunilde Sanso GERAD & Ecole Polytechnique de Montreal Montreal, Canada
Felisa Vazquez-Abad GERAD and Universite de Montreal Montreal, Canada
Library of Congress Cataloging-in-Publication Data A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN-10: 0-387-25550-8 ISBN 0-387-25551-6 (e-book) Printed on acid-free paper. ISBN-13: 978-0387-25550-7 © 2005 by Springer Science+Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science + Business Media, Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now know or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if the are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 9 8 7 6 5 4 3 2 1 springeronline.com
SPIN 11053163
Foreword
GERAD celebrates this year its 25th anniversary. The Center was created in 1980 by a small group of professors and researchers of HEC Montreal, McGill University and of the Ecole Polytechnique de Montreal. GERAD's activities achieved sufficient scope to justify its conversion in June 1988 into a Joint Research Centre of HEC Montreal, the Ecole Polytechnique de Montreal and McGill University. In 1996, the Universite du Quebec a Montreal joined these three institutions. GERAD has fifty members (professors), more than twenty research associates and post doctoral students and more than two hundreds master and Ph.D. students. GERAD is a multi-university center and a vital forum for the development of operations research. Its mission is defined around the following four complementarily objectives: • The original and expert contribution to all research fields in GERAD's area of expertise; • The dissemination of research results in the best scientific outlets as well as in the society in general; • The training of graduate students and post doctoral researchers; • The contribution to the economic community by solving important problems and providing transferable tools. GERAD's research thrusts and fields of expertise are as follows: • Development of mathematical analysis tools and techniques to solve the complex problems that arise in management sciences and engineering; • Development of algorithms to resolve such problems efficiently; • Application of these techniques and tools to problems posed in related disciplines, such as statistics, financial engineering, game theory and artificial intelligence; • Application of advanced tools to optimization and planning of large technical and economic systems, such as energy systems, transportation/communication networks, and production systems; • Integration of scientific findings into software, expert systems and decision-support systems that can be used by industry. One of the marking events of the celebrations of the 25th anniversary of GERAD is the publication of ten volumes covering most of the Center's research areas of expertise. The list follows: Essays and Surveys in Global Optimization, edited by C. Audet, P. Hansen and G. Savard; Graph Theory and Combinatorial Optimization,
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edited by D. Avis, A. Hertz and O. Marcotte; Numerical Methods in Finance, edited by H. Ben-Ameur and M. Breton; Analysis, Control and Optimization of Complex Dynamic Systems, edited by E.K. Boukas and R. Malhame; Column Generation, edited by G. Desaulniers, J. Desrosiers and M.M. Solomon; Statistical Modeling and Analysis for Complex Data Problems, edited by P. Duchesne and B. Remillard; Performance Evaluation and Planning Methods for the Next Generation Internet, edited by A. Girard, B. Sanso and F. Vazquez-Abad; Dynamic Games: Theory and Applications, edited by A. Haurie and G. Zaccour; Logistics Systems: Design and Optimization, edited by A. Langevin and D. Riopel; Energy and Environment, edited by R. Loulou, J.-P. Waaub and G. Zaccour. I would like to express my gratitude to the Editors of the ten volumes, to the authors who accepted with great enthusiasm to submit their work and to the reviewers for their benevolent work and timely response. I would also like to thank Mrs. Nicole Paradis, Francine Benoit and Louise Letendre and Mr. Andre Montpetit for their excellent editing work. The GERAD group has earned its reputation as a worldwide leader in its field. This is certainly due to the enthusiasm and motivation of GERAD's researchers and students, but also to the funding and the infrastructures available. I would like to seize the opportunity to thank the organizations that, from the beginning, believed in the potential and the value of GERAD and have supported it over the years. These are HEC Montreal, Ecole Polytechnique de Montreal, McGill University, Universite du Quebec a Montreal and, of course, the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Fonds quebecois de la recherche sur la nature et les technologies (FQRNT), Georges Zaccour Director of GERAD
Avant-propos
Le Groupe cTetudes et de recherche en analyse des decisions (GERAD) fete cette annee son vingt-cinquieme anniversaire. Fonde en 1980 par une poignee de professeurs et chercheurs de HEC Montreal engages dans des recherches en equipe avec des collegues de PUniversite McGill et de PEcole Polytechnique de Montreal, le Centre comporte maintenant une cinquantaine de membres, plus d'une vingtaine de professionnels de recherche et stagiaires post-doctoraux et plus de 200 etudiants des cycles superieurs. Les activites du GERAD ont pris suffisamment d'ampleur pour justifier en juin 1988 sa transformation en un Centre de recherche conjoint de HEC Montreal, de PEcole Polytechnique de Montreal et de PUniversite McGill. En 1996, PUniversite du Quebec a Montreal s'est jointe a ces institutions pour parrainer le GERAD. Le GERAD est un regroupement de chercheurs autour de la discipline de la recherche operationnelle. Sa mission s'articule autour des objectifs complementaires suivants : • la contribution originale et experte dans tous les axes de recherche de ses champs de competence; • la diffusion des resultats dans les plus grandes revues du domaine ainsi qu'aupres des differents publics qui forment Penvironnement du Centre; • la formation d'etudiants des cycles superieurs et de stagiaires postdoctoraux ; • la contribution a la communaute economique a travers la resolution de problemes et le developpement de coffres d'outils transferables. Les principaux axes de recherche du GERAD, en allant du plus theorique au plus applique, sont les suivants : • le developpement d'outils et de techniques d'analyse mathematiques de la recherche operationnelle pour la resolution de problemes complexes qui se posent dans les sciences de la gestion et du genie; • la confection d'algorithmes permettant la resolution efficace de ces problemes; • Papplication de ces outils a des problemes poses dans des disciplines connexes a la recherche operationnelle telles que la statistique, Pingenierie financiere. la theorie des jeux et Pintelligence artificielle; • Papplication de ces outils a Poptimisation et a la planification de grands systemes technico-economiques comme les systemes energetiques, les reseaux de telecommunication et de transport, la logistique et la distributique dans les industries manufacturieres et de service;
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• Pintegration des resultats scientifiques dans des logiciels, des systemes experts et dans des systemes d'aide a la decision transferables a Pindustrie. Le fait marquant des celebrations du 25e du GERAD est la publication de dix volumes couvrant les champs d'expertise du Centre. La liste suit : Essays and Surveys in Global Optimization, edite par C. Audet, R Hansen et G. Savard; Graph Theory and Combinatorial Optimization, edite par D. Avis, A. Hertz et O. Marcotte; Numerical Methods in Finance, edite par H. Ben-Ameur et M. Breton; Analysis, Control and Optimization of Complex Dynamic Systems, edite par E.K. Boukas et R. Malhame; Column Generation, edite par G. Desaulniers, J. Desrosiers et M.M. Solomon; Statistical Modeling and Analysis for Complex Data Problems, edite par P. Duchesne et B. Remillard; Performance Evaluation and Planning Methods for the Next Generation Internet, edite par A. Girard, B. Sanso et F. Vazquez-Abad; Dynamic Games : Theory and Applications, edite par A. Haurie et G. Zaccour; Logistics Systems : Design and Optimization, edite par A. Langevin et D. Riopel; Energy and Environment, edite par R. Loulou, J.-P. Waaub et G. Zaccour. Je voudrais remercier tres sincerement les editeurs de ces volumes, les nombreux auteurs qui ont tres volontiers repondu a l'invitation des editeurs a soumettre leurs travaux, et les evaluateurs pour leur benevolat et ponctualite. Je voudrais aussi remercier Mmes Nicole Paradis, Francine Benoit et Louise Letendre ainsi que M. Andre Montpetit pour leur travail expert d'edition. La place de premier plan qu'occupe le GERAD sur l'echiquier mondial est certes due a la passion qui anime ses chercheurs et ses etudiants, mais aussi au financement et a Infrastructure disponibles. Je voudrais profiter de cette occasion pour remercier les organisations qui ont cru des le depart au potentiel et a la valeur du GERAD et nous ont soutenus durant ces annees. II s'agit de HEC Montreal, PEcole Polytechnique de Montreal, PUniversite McGill, l'Universite du Quebec a Montreal et, bien sur, le Conseil de recherche en sciences naturelles et en genie du Canada (CRSNG) et le Fonds quebecois de la recherche sur la nature et les technologies (FQRNT). Georges Zaccour Directeur du GERAD
Contents
Foreword Avant-propos Contributing Authors Preface 1 Design of IP Networks with End-to-End Performance Guarantees /. Atov and R.J. Harris
v vii xi xiii 1
2
Design of IP Virtual Private Networks under End-to-end QoS Constraints E.C.G. Wille, M. Mellia, E. Leonardi, and M.A. Marsan 3 Design of Protected Working Capacity Envelopes Based on p-Cycles: An Alternative Framework for Survivable Automated Lightpath Provisioning G. Shen and W.D. Grover
35
63
4
Network Traffic Engineering with Varied Levels of Protection in the Next Generation Internet S. Srivastava, S.R. Thirumalasetty, and D. Medhi
99
5 Balancing Traffic Flows in Resilient Packet Rings P. Kubat and J. MacGregor Smith
125
6 Game-Theoretic Resource Pricing for the Next Generation Internet B.M. Ninan and M. Devetsikiotis
141
7 A New Approach to Policy-Based Routing in the Internet B.R. Smith and J.J. Garcia-Luna-Aceves
165
Advanced Methods for the Estimation of the Origin Destination Traffic Matrix S. Vaton, J.S. Bedo and A. Gravey 9 Energy and Cost Optimizations in Wireless Sensor Networks: A Survey V. Mhatre and C. Rosenberg
189
227
x NEXT GENERATION INTERNET 10 Duality-Based TCP Congestion Control with Error Analysis 249 M. Mehyar, D. Spanos, and S.H. Low 11 Fast Algorithmic Solutions to Multi-dimensional Birth-Death Processes with Applications to Telecommunication Systems L. D. Servi 12 A New Paradigm for On-Line Management of Communication Networks with Multiplicative Feedback Control H. Yu and C.G. Cassandras 13 Comparing Locality of Reference - Some Folk Theorems for the Miss Rate and the Output of Caches A.M. Makowski and S. Vanichpun
269
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333
Contributing Authors IRENA ATOV
JAMES MACGREGOR SMITH
Swinburne University of Technology, Australia
University of Massachusetts, USA jmsmithOecs.umass.edu
[email protected] ARMAND M. MAKOWSKI JEAN-SEBASTIEN BEDO
Ecole Poly technique, Palaiseau, France j
[email protected] CHRISTOS G. CASSANDRAS
Boston University, USA cgc@bu . edu
University of Maryland armand®isr.umd.edu MARCO AJMONE MARSAN
Politecnico di Torino, Italy
[email protected] DEEP MEDHI
North Carolina State University, USA
University of Missouri-Kansas City, USA
[email protected] [email protected] MICHAEL DEVETSIKIOTIS
JOSE JOAQUIN GARCIA-LUNA-ACEVES
MORTADA MEHYAR
University of California, Santa Cruz, USA
[email protected] California Institute of Technology, USA
ANNIE GRAVEY
ENST Bretagne, France
[email protected] [email protected] MARCO MELLIA
Politecnico di Torino, Italy
[email protected] WAYNE D. GROVER
VIVEK PRAKASH MHATRE
TRLabs and University of Alberta, Canada
Purdue University, USA
[email protected] [email protected] BOBBY M. NINAN RICHARD J. HARRIS
North Carolina State University, USA
Massey University, New Zealand
[email protected],nz
[email protected] PETER KUBAT
University of Waterloo, Canada
[email protected] Verizon Laboratories, USA peter.kubatOverizon.com EMILIO LEONARDI
Politecnico di Torino, Italy leonardiOpolito.it
CATHERINE ROSENBERG
L. D. SERVI
MIT Lincoln Laboratory, USA
[email protected] STEVEN H. LOW
GANGXIANG SHEN
California Institute of Technology, USA
TRLabs and University of Alberta, Canada gshenQtrlabs.ca
[email protected] Xll
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BRADLEY R. SMITH
SARUT VANICHPUN
University of California, Santa Cruz, USA
University of Maryland
[email protected] bradOsoe.ucsc.edu SANDRINE VATON DEMETRI SPANOS
California Institute of Technology, USA demetriQcaltech.edu SHEKHAR SRIVASTAVA
University of Missouri-Kansas City, USA
[email protected] ENST Bretagne, France sandrine.vatonQenst-bretagne.fr EMILIO C.G.
WILLE
Centro Federal de Educagao Tecnologica do Parana, Brazil willeQprezzemolo.polito.it HAINING YU
Boston University, USA fernyuQbu.edu
SRINIVASA RAO THIRUMALASETTY
Ciena Corporation, USA
[email protected] Preface
Optimization techniques have been used for a long time in the planning of telecommunication networks. There is abundant work on the design of telephone and transmission networks going at least a half century back. The recent evolution towards an integrated, multi-service network based on the Internet and the IP protocol has occurred in a very different way and without much recourse to the traditional traffic engineering methods. Because the current core network is so much overprovisioned and all the services are operating on a best-effort service model, there has been no real need for sophisticated planning modeling and analysis. This situation is bound to change for a number of reasons. New services such as voice are being introduced with strong requirements for definite Quality of Service, the cost of over-provisioning private networks is becoming an issue and wireless access cannot be over-provisioned at all since the bandwidth is limited by the available spectrum. For all these reasons, we believe that all the classical problems of telecommunication network design will become more essential in the coming years. One such problem is network design which in turn is based on performance evaluation which is an essential element of all design algorithms. This trend is well illustrated by the contents of this book. We find a large number of areas where significant work is being done to address the issue of network design in the context of the new IP-based networks. The topics selected here will give the reader some idea of what is going on but is far from exhaustive for obvious space and time limitations. The design of IP networks will have to take into account the requirements of many applications for guaranteed performance. This problem is examined in "Design of IP Networks with End-to-end Performance Guarantees" by Atov and Harris. Their model takes into account the proposed QoS standards and can handle multiple QoS requirements. The numerical method based on multicommodity flows can compute networks of realistic size. A similar problem of network design is the subject of "Design of IP Virtual Private Networks under End-To-End QOS Constraints" by Wille, Mellia, Leonardi and Ajmone Marsan. This time, the network to be designed is a Virtual Private Network but the model takes into account both the transport and the network layer performances. The design itself is then done at the IP layer while offering all the required QoS guarantees at the transport layer.
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The concept of resilience or reliability is gaining importance as another aspect of the Quality of Service that will have to be provided by the Internet. The notion of survivability by using protection cycles is examined in "Design of Protected Working Capacity Envelopes Based on P-Cycles: an Alternative Framework for Survivable Automated Lightpath Provisioning" by Shen and Grover when applied to the underlying optical transport infrastructure. The model integrates both the IP and the transport layers to provide a unified design methodology for the capacity allocation, service provisioning and reserve network. A similar problem of network design where the notion of QoS is extended to include reliability is examined in "Network Traffic Engineering with Varied Levels of Protection in the Next Generation Internet" by Srivastava, Thirumalasetty and Medhi. In addition to traffic engineering, reliability is taken care of via a number of protection levels. The model is based on protection cycles and is solved via heuristics. The notion of resilience in transmission networks, an essential complement to IP-level techniques, is studied in"Balancing Traffic Flows in Resilient Packet Rings" by Kubat and Smith. Here fast restoration techniques based on ring topologies are used in conjunction with Ethernet technology to provide a robust network. The model optimizes the allocation of traffic to the ring directions both for deterministic and stochastic demands either via an IP formulation or using heuristics for large cases. Pricing and routing are two issues that can be closely tied to the management of QoS. In "Game-Theoretic Resource Pricing for the Next Generation Internet", Ninan and Devetsikiotis use pricing and billing to manage the bandwidth allocated to users competing for a share of the network resources. They show applications of their model to a variety of networks. In addition to a thorough review of existing QoS-based routing, the chapter " A New Approach to Policy-Based Routing in the Internet" by Smith and Garcia-Luna-Aceves describes a new routing algorithm based on distributed label-swapping that can support QoS more efficiently than the present techniques. Network design is based on a good estimation of the traffic matrix. This problem is examined in the context of IP networks in the paper "Advanced Methods for the Estimation of the Origin Destination Traffic Matrix" by Vaton, Bedo and Gravey. Current tools such as SNMP allow traffic measurement only on individual links. Statistical methods are used to take into account the time variation of traffic measured on the network links to construct an estimate of the end-to-end demands.
PREFACE
xv
Wireless networks are growing even more rapidly than the Internet and bring up a new set of design problems. The recent development of sensor networks is a case in point where the management of the energy budget of the batteries in the devices is a dominant issue. A thorough survey of the routing and design problems in this new context is the subject of "Energy and Cost Optimizations in Wireless Sensor Networks: A Survey" by Mhatre and Rosenberg. If they are to provide the QoS required by applications, network operators must be able to control congestion whenever it occurs in the network. An approach to congestion control based on the maximization of utility is used in "Duality-Based TCP Congestion Control with Error Analysis" by Mehyar, Spanos and Low. The model provides a unifying framework for a large number of congestion control algorithms. The authors also show that even in the presence on imperfect information, the control will converge to a region close to the optimal operating point if perfect information were available. Network design is based on decomposition techniques where the performance of output queues has to be computed separately before being recombined into a network performance measure. Thus queuing analysis is a fundamental component of network planning. With multi-service networks, this analysis requires the solution of large birth-death systems. An example of an efficient solution algorithm is given in "Fast Algorithmic Solutions to Multi-Dimensional Birth-Death Processes with Applications to Telecommunication Systems" by Servi where a new class of solution algorithms is presented that can be applied to systems of arbitrary dimensions. In "A New Paradigm for On-Line Management of Communication Networks with Multiplicative Feedback Control" by Yu and Cassandras, Stochastic Flow models are used for control. The model obviates the need to solve difficult queuing analysis problems by using fluid models. It provides an estimation of the gradients of the performance which in turn can be used to adjust the flow rates via a multiplicative feedback algorithm. The Internet has spawned a number of new applications with previously unknown operating characteristics. Caching techniques are often used to reduce the delay in accessing databases. Many such techniques have been designed based on empirical knowledge. The validity of this knowledge is formalized and evaluated in "Comparing Locality of Reference — Some Folk Theorems for the Miss Rate and the Output of Caches" by Makowski and Vanichpun where the authors model the op-
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eration of caches and examine the efficiency of various cache replacement policies. The wide range of topics covered in this book is a witness to the diversity of problems that have to be faced if we want to design the Next Generation IP Networks to meet their expected performance. This is a rich field where optimization techniques can provide significant gains. ANDRE GIRARD BRUNILDE SANSO FELISA VAZQUEZ-ABAD
Chapter 1 DESIGN OF IP NETWORKS WITH END-TO-END PERFORMANCE GUARANTEES Irena Atov Richard J. Harris Abstract
1.
In this paper, we examine the issues that surround IP network design with quality of service (QoS) guarantees and propose a new network design methodology. The proposed network design model takes account of the new QoS technologies (i.e., DifFServ/MPLS) and allows for multiple delay constraints so that guaranteed performance can be achieved for each of the traffic classes. After discussing the most crucial planning issues that must be addressed when QoS mechanisms are used in an IP-based network, a non-linear multicommodity optimisation problem is formulated and heuristics for its approximate solutions are described. The network design model is evaluated in terms of accuracy and scalability for each of the main components that the model employs. The computational results for each of the building blocks demonstrate that realistic size problems can be solved with the proposed method.
Introduction
The development of various Internet technologies, such as DiffServ and MPLS, has enabled support for various traffic classes with different QoS requirements on an integrated IP network (Wang, 2001). Now with the inclusion of QoS considerations, the paradigm for network design and planning must change to include multiple delay constraints so that differentiated performance can be achieved for the various traffic classes. The delay QoS metric is additive (i.e., QoS along a path is a sum of the QoS of its constituent links) and such a QoS class may cover a delay bound or random variation of delay (jitter). It is traditionally difficult to provide network design to meet varying QoS constraints. Assuming that the network topology is given, the ob-
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jective of network design is to determine link capacities combined with traffic routing, such that the total network cost is minimised while meeting demands and QoS constraints for each of the traffic classes. With the introduction of Asynchronous Transfer Mode (ATM) broadband networks in the late 80s a lot of research was triggered in this area. However, the network design models developed for ATM use a loss-based approach. That is, network planning-design is achieved so that the blocking (loss) probabilities of various types of traffic (classes) remain below a specified threshold, see for example Liang and Ross (1999); Puah (1999). These models exploit the connection-oriented nature of ATM and transform the multi-level traffic problem into a multirate circuit-switched problem by using the notion of equivalent bandwidth (Guerin et al., 1991). However, these multirate loss models do not present suitable tools for the design of IP-based broadband networks. In IP-based broadband networks (i.e., DiffServ/MPLS), due to the concept of class aggregates and static resource reservation, network design is primarily concerned with developing performance guarantees in terms of packet delay or packet delay variation for the various service types (i.e., class aggregates). In addition, the conventional methods for capacity planning of IP networks are limited, in that they only consider best effort service, or else a single delay constraint for all traffic (Gavish and Neuman, 1989). Thus, there is a need for new methods for capacity planning and design that take account of technologies and mechanisms that enable QoS in IP networks and, thus, allow for multiple delay constraints, so that guaranteed performance can be achieved for each of the traffic classes. This paper investigates the issues surrounding IP network design with QoS and proposes a new design methodology which would be applicable to such networks. Since the proposed design model deals in a unified way with both the flow and the capacity assignment issues, we shall refer to it in the following as a capacity and flow assignment problem (CFA problem) as it is of the same generic form as early ARPANET models identified by Kleinrock (1975). There are major challenges involved in the development of an IP network design methodology that supports guaranteed services on an endto-end basis. The technologies that provide QoS introduce new constraints and require that certain features be addressed by any generic design methodology. In Section 2, we first discuss the most crucial planning issues that must be addressed when QoS mechanisms are used in an IP-based network. Then we outline a network model and a cost model, which define the set of underlying assumptions used in the development of the proposed IP network design model with end-to-end performance guarantees. Section 3 provides the notation and formu-
1 Design of IP Networks with End-to-End Performance Guarantees
3
lation of the mathematics programming problem. The CFA problem is formulated as a non-linear multicommodity optimisation problem, which is hard to solve mathematically to optimum for practical sized networks. To be able to efficiently solve large problem instances, we develop a framework for the solution of the network design problem which employs a heuristic approach. Section 4 describes the disaggregation of the problem into simpler optimisation problems (components) that form the basis for a heuristic solution to the original problem. Finally, Sections 5 and 6 summarize computational results and provide concluding remarks.
2.
QoS mechanisms and implications for network planning
QoS mechanisms that are being employed in IP-based core networks can be generally classified into three main categories: traffic control, resource management and traffic engineering. In the following, we briefly overview these categories and discuss the implications that have to be considered for the planning process. Traffic control. Traffic control encompasses all mechanisms for handling and forwarding of packets within the edge and the core routers of the network. These mechanisms include: traffic classification and aggregation, scheduling and active queue management. Typically, based on the type of scheduling mechanism deployed at the routers, which can range from a simple priority queueing to a bandwidth allocation scheme (WFQ, WF2Q, WRR Floyd and Jacobson, 1995), the network provider can offer two types of service quality. The first type is prioritised service, where certain class of traffic receives priority over others as it is processed and routed over the network. The second type is guaranteed service, where the traffic classes are guaranteed certain share of resources, for example bandwidth or a given performance level e.g., delay. It is the latter meaning that we consider in this paper, as it represents more common implementation of DiffServ in the current service offerings. The use of bandwidth allocation type QoS queueing mechanism implies that fixed bandwidth partitioning, i.e., predictable capacity assignment to individual classes can be assumed for the network design process. Since the DiffServ technology is based on the aggregation of individual flows into classes at the ingress of the network and on provisioning of QoS to the service class instead of a single flow, it is important to model and characterise the external and the internal (or internode) traffic flows on a per class basis in order to plan and manage these networks to meet performance objectives (QoS) as required by the various traffic classes.
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Resource management. Resource management refers to mechanisms that manage the access to the network resources in order to prevent service degradation occurring from traffic overload. DiffServ employs static resource control approach, where the network operator establishes several traffic classes, for which it allocates adequate level of resources (in terms of bandwidth and buffer space) along the respective data paths through the network. In addition, traffic conditioning at the network edge is implemented in order to control the amount of traffic entering the network. Thus, resource management functions require that the network design process determines the amount of bandwidth, which needs to be allocated to each traffic class on every link in the network. Traffic conditioning functions have to be accounted for in the traffic modelling of the c/ass-based traffic aggregates offered to the network. Traffic engineering. Traffic engineering is the commonly used term for the process of network performance optimisation during network operation. Most commonly, this approach involves routing optimisation. It can be based on standard routing protocols, such as OSPF, or on more advanced protocol, such as MPLS. For network design the type of routing protocol plays an important role. In the first case, routing optimisation can be achieved by allowing link metrics to be customized (Fortz and Thorup, 2000). The latter case, on the other hand, allows for explicit routes, providing maximum flexibility in building a specific path through a network based on differentiated QoS. We consider MPLS routing mechanism deployed in an IP-based core network and, thus, in the design process we are concerned with the problem of determining static paths based on differentiated QoS requirements for the classes.
2,1
Network model
We consider a network design methodology for IP core networks based on DiffServ/MPLS technologies, and therefore, our main modelling assumptions comprise (1) a guaranteed service model for the classes (based on a prescribed performance level) and, (2) a fixed routing mechanism for the traffic classes in the network. Fixed (or static) routing policies are implemented by providing each origin-destination (OD) pair in the network with an ordered set of routes and we concentrate here on the choice of the primary route i.e., the recommended one in the candidate set. The network underlying the design problem is modelled as a graph G(V,JS), where |V| = n is the number of nodes and \E\ — m is the number of links (edges) in the network. Each link consists of a separate queueing facility for each class of traffic and a scheduler. In the
1 Design of IP Networks with End-to-End Performance Guarantees
5
standard service offerings, class-based WFQ has been used to enable guaranteed services. It enables the different delay criteria for each class to be met, by allocating a specified proportion of the service capacity to each class. For analysis of this system, each queueing facility can be treated as an independent FIFO queue, with a fixed capacity equal to its allocation, which enables us to confine the design problem to a network of single-server queues for each class of traffic, respectively. Note that, by modelling the network in this way, we effectively disregard the gains from the statistical multiplexing associated with the work-conserving scheduling mechanisms. Since this is a model for a network planning tool, this approximation is acceptable, as it would imply that the performance of the designed network would be as good or better than the QoS criteria required for the traffic classes. The purpose of modelling the network in the above fashion is to enable traffic to be categorized into classes based on their sensitivity to the delay performance of the network. In our model, we consider the delay QoS constraints for a traffic class to be specified in terms of the mean delay and the variance of the delay (or jitter) following ITU-T G.1010 Recommendation. Depending on the type of delay QoS constraint, the following sets of delay-sensitive classes of traffic are defined: (1) Delay sensitive class (DSC) - contains classes of traffic sensitive to delay (i.e., their mean delays are required to be less than or equal to their specified end-to-end delay limits), (2) Jitter sensitive class (JSC) - contains classes of traffic sensitive to variations in the delay (i.e., their delay variances are required to be less than or equal to their specified end-to-end delay variance limits), and (3) Delay and jitter sensitive class (DJSC) - contains classes of traffic that are sensitive to both delay and its variation.
2.2
Performance dependent cost model
We consider two distinct types of costs associated with the design of multiservice IP network that provides guaranteed services end-to-end: (1) queueing costs and (2) capacity costs. The first type of cost is associated with the cost of provisioning a certain delay and jitter queueing performance for the delay-sensitive traffic classes in the network. The second type of cost is associated with the setup cost of a link with specific capacity. For multiservice IP networks, the dominant factor in the cost of provisioning a particular delay-sensitive service class is dependent on the performance requirement (QoS) of that class. For example, the more stringent the delay requirement for a traffic class, the higher the cost of provisioning this service class. In order to model the queueing costs associated with the design of such a network, we assume a QoS
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framework where each link I G E can offer several delay d\ and jitter QoS guarantees i//, each associated with a different cost Q\{d\) {Qiiyi)). Specifically, in this framework, a performance dependent cost function is associated with each link in the network. Furthermore, these performance dependent cost functions i.e., the cost/delay and cost/jitter functions {Qi(d),Qi(v)}izE, are assumed to be non-increasing and they are of a general integer type. Such cost functions are being assumed as they better fit practical purposes, as discussed in Raz and Shavitt (2000) and references therein. Furthermore, considering that, in practice, the capacities of the links in the network are restricted to a discrete set of values, we assume discrete capacity costs associated with the links. Let I\ denote the index set of line types available for link /, I G E. The capacity and the cost [$/month] of line typefc,k G //, are denoted by 9f and 7^, respectively.
3.
Problem formulation
In order to be able to offer performance guarantees (in terms of delay) we build our model around the consideration that switches support classbased WFQ queueing and routing constraints are imposed by MPLS routing mechanism. We incorporate these features into an efficient network design model which includes primary decisions for determining class-based bandwidth allocations on the links, total link capacities and how traffic of each class is to be routed through the network. Note that, determining bandwidth allocations for the various traffic classes on the links is an important design issue as standard WFQ service disciplines can only provide tight end-to-end delay guarantees for the classes if an adequate level of bandwidth is allocated along their respective data paths through the network. Our modelling approach exploits a novel framework in which capacity provisioning is based on the partitioning of the end-to-end QoS constraints of each class-based traffic demand into local QoS constraints at each link in the network. In this context, a link delay (jitter) partition for a given delay-sensitive class represents a maximum allowable queueing and propagation delay on a link in terms of mean delay (variance of the delay), that can be tolerated by the class, so that the end-to-end delay (jitter) constraints of all traffic flows of the same class traversing that link are still satisfied1. We shall use a path-b&sed formulation for the underlying multicommodity networkflowmodel. Our experience shows the path-based model lr rhe delay is additive QoS metric and allows the end-to-end delay to be partitioned across the various links in the network.
1
Design of IP Networks with End-to-End Performance Guarantees
7
is both simpler to solve for realistic networks and explicitly allows service-based routing constraints. Let II be the set of all OD pairs (or commodities) with a demand between them. Each OD pair (u, v) G II, may have up to C different classes of traffic where C — C — 1 are delay-sensitive classes and the remaining one is the best-effort class. The set of candidate routes for OD pair {u, v) of class c, is denoted by K%v and the j-th route from this set is denoted by it^J, j = 1 , . . . , |i?|, with \R\ representing the cardinality of this set. The end-to-end delay (jitter) constraint for class c of OD pair (u,v) is denoted by D%v (V™v). A c = {^v}(u,v)eii represents the traffic demand matrix for class c, c G C. An entry in this matrix, AJfv, represents a vector itself, that defines the traffic demand for OD pair (Uj v) in terms of a specific set of parameters corresponding to the selected traffic descriptors for the dimensioning process, which is discussed in Section 4.2. The sets of decision variables are defined as follows: dc\ and vc\ are integer decision variables representing a delay partition and jitter partition for traffic of class c on link /, respectively; x^ is a binary decision variable that has value 1 if j - t h route is chosen from the given set of routes for OD pair (u, v) of class c (R^v) and 0 otherwise; yf is a binary decision variable, which has value 1 if line type k is assigned to link / and 0 otherwise. We introduce a weighted type variable 5C to provide user flexibility in specifying the type of the considered delay-sensitive class with respect to delay and jitter. It is defined as 0 < Sc < 1, having value 1 if the considered class is of type DSC, value 0 if the considered class is of type JSC, and having a value in between 0 and 1 for the D JSC type class. The symbol aT- is an indicator parameter with value 1 if link I lies on j-th route from the set K£v (R™) and is zero otherwise. rc = {rcV}(Uiv)eu denotes the routing matrix for class c, c G C. The primary route for OD pair (n, t>), r^v) is the set of links that comprise the route from the set R£v for which x™ = 1. The corresponding vector of the delay (jitter) partitions for class c on all links is denoted by dc (^c)« The propagation delay for link I is denoted by d/prOp. fc — {fcljleE represents a vector of link flows for class c, c G C. The vector fc is determined from the traffic demand and routing matrices (A c , rc) by applying an appropriate trafficbased decomposition model. In network design procedures, a maximum link utilization p is often specified at input and must also be satisfied. These constraints allow for variations in the load not accounted for at the network planning level to occur without affecting the performance of the network.
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The actual capacity required for a link 1,1 € E, is denoted by [//. Due to the fixed bandwidth partitioning assumption, the required capacity on a link is simply obtained as the sum of the individual bandwidth allocations for the classes on the given link, which we denote by bci. The bandwidth required for a delay-sensitive class on a link can be determined from the traffic descriptors of the total class flow on the link and its link QoS constraints by applying an appropriate link dimensioning model i.e., bc\ — ^F(fchdci^vci). The best-effort service class does not require any service guarantees, and therefore its required bandwidth on a link is readily determined from the mean rate of the best-effort link flow i.e., bci = J-'(fci)' Finally, 6 — {6f}ieE represents a vector of link capacities for which y\ — 1. Accordingly, the considered CFA problem can be stated as follows: Problem CFA: Given a network G(V,E), link cost/delay and cost/ a set of available link capacities jitter functions {Qi(d))Qi(v)}ieE, set of candidate {OfykeiiJeE, their corresponding costs {^}keihieE, routes {RcV}ceC end-to-end delay QoS requirements {D™, ^^^ced (uv)eu and traffic demands {A c } c € c- Find a set of primary routes {rc}cec, & set of delay and jitter allocations on the links {dc}ceQ, {yc$c(zG and a set of link capacities 6, such that the network cost is minimised while all OD pair traffic demands and QoS constraints for the traffic classes are satisfied. Mathematically, the optimisation problem can be formulated as finding the x^J, y^, dc/, uci values that satisfy the following:
Minimise: E E ™ ™j E E (u.v)eu leE x
a
[ScQi{dci) + (1 -
Sc)Qi{ud)\
v
Subject to: E
d
^ < X™D™ + (i - x$)M
Vj e i C , v(«, v) e n, Vc € 6 (1.1a)
E
v
d < xcjDT + (1 - x$)M Vj € E£v, V(u, v) e n, Vc € C (Lib)
E
= 1 V(«, v) € n, Vc € C
(l.lc)
1 Design of IP Networks with End-to-End Performance Guarantees * = 1 VZ eE
9 (Lid)
f + (l--yf)^} VZ G £
(Lie)
cec x™ = {0,1} \/j G i2™, V(tz, v) G n , Vc G C
(l.lf)
yf = {0,1} Vfceii, V Z G £
(l.lg)
dd > diprop
(l.lh)
i/d > 0 yieE,
VZ G £ , c e C ceC
(l.ii)
In the above formulation, the network cost represents the sum of all link costs, where the total cost of a link consists of two components: (1) queueing cost and (2) cost resulting from the total capacity required for the link. The queueing cost of a link is a sum of the costs incurred by the delay-sensitive classes only, as the best-effort class does not require any performance guarantees. The cost incurred by a specific delay-sensitive class on a link consists of a weighted sum of the delay and jitter costs (depending on the type of class considered), and is a function of the delay and jitter partitions on that link and the number of flows of the considered class that traverse the link. Accordingly, the first two terms in the objective function capture the total queueing cost in the network, while the third term refers to the total cost associated with the capacities of the links in the network, respectively. The set of constraints specified in (1.1a) and (Lib) guarantee that the end-to-end delay and jitter requirements for the delay-sensitive traffic classes are satisfied. The constant M is chosen such that if the j-th route from the set E%v is not selected (i.e., x™ = 0) then the sum of the delays (jitter) can be unbounded. This can be achieved by setting M to a sufficiently large value, such as, the sum of all end-to-end delay requirements, i.e., M = Yl(uv)eu-^cV' ^he constraints in (Lie) and (Lid) guarantee that only one route is chosen for each OD pair and only one line type for each link, respectively. The constraints in (Lie) guarantee the feasibility of the flow on each link in terms of the capacity assigned to it. Finally, the constraints given in (l.lf-l.li) define the solution space for the decision variables. The formulated mathematical program is a non-linear multicommodity flow problem in which the level of complexity arises from the nature of the decision variables that describe the possible solution (i.e., x^J, y\ are 0 — 1 type or binary integer variables and dci, vci are variables of integer type), as well as from the non-linearity of the associated set of constraints. The problem is defined with \E\\I\ binary line type selectors
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(y?)> IC'II-^I integer delay partition variables, as well as, jitter partition variables (dc/, vc\), and |C||II||i?| binary flow variables (x^). Since each flow associated with a delay-sensitive class defines a forcing constraint for the end-to-end QoS requirement, the number of constraints (1.1a) and (1.1b) is equal to |C||Il||i?|. The set of constraints (1.1c) is defined for each service class and OD pair, thus resulting in |C||II| constraints. The total set of constraints (l.ld) and (Lie) is determined from the number of links in the network \E\. In addition, there is a total of 2|C||JS| + |C||II||i?| + |£?||/| defining constraints (l.lf-l.li) in the model. It can be seen that the considered problem involves the interaction of three significant factors: the flow assignment (i.e., routing), the maximum delay and jitter allocation to each link, and the capacity allocation on the links. Determining all these factors i.e., all the decision variables (x^J, y^, dc/, vc\) simultaneously, for a network of any reasonable size represents a very challenging task. In fact, this problem is A/T^-complete, as it can be reduced to other problems which represent special cases of our problem that are known to be A/'P-complete. Namely, the problem studied in Holmberg (2000), represents a multicommodity minimal cost network flow problem with fixed charges on the links and is well known to be A/"P-complete. In this problem, there are two kinds of costs associated with the links in the network. The routing costs increase linearly with the amount offlowand aflowcost per unit of commodity on a link is predefined. Additionally, a fixed charge is incurred whenever a link is being used (by any amount of flow). Furthermore, each link has a limited capacity on the total flow. Two sets of variables are introduced in this model, continuous flow variables which reflect routing decisions for each commodity and binary design variables which define the set of links that are used in the network. The multicommodity capacitated versions of this general model, such as the model considered in Gendron et al. (1999), are thus also A/'P-complete. The capacitated version of the model allows, whenever a link is being used, additional facilities with fixed capacities to be installed on it, if needed. In this case, the design variables are of integer type representing the number of facilities installed on the links. Now, if we reduce our model to the case of a single service class, it then becomes a generalized version of the model (Gendron et al., 1999), where the cost per unit flow on a link is a function of a delay partition (and/or jitter partition) variable which further adds to the complexity. Furthermore, if we consider only the first term of the objective function we are left with two sets of decision variables defining the delay partitions andflowsin the network. The problem becomes that of deter-
1 Design of IP Networks with End-to-End Performance Guarantees
11
mining the routes and delay partitions on the links given the cost/delay functions, such that the end-to-end delay requirements are satisfied. This combined problem of QoS partitioning and routing when the cost/delay functions associated with the links are of general integer type has been shown to be AfP-complete even for the case of single commodity flows (i.e., single OD pair) (Lorenz et al., 2000).
4.
Solution procedure and heuristics
In this section, we outline our proposed framework for the solution of the CFA problem. When devising an effective algorithm for solving problems of this sort, it might be best to exercise some careful "strategic" planning. From experience, we know that a general-purpose integer programming code will fail in all but the easiest problem instances. Thus, we are interested in a fast method that can generate near-optimal solutions for large problems. From the discussion in the previous section, it is apparent that for a network of any reasonable size, determining all the decision factors simultaneously (i.e., routing information, link delay and jitter allocations, link capacities) represents a nearly impossible problem. Therefore, we choose a heuristic approach for solving the CFA problem, in which these factors are considered sequentially. Specifically, a heuristic solution method to the original problem is devised by performing disaggregation of the problem into the following three (simpler) optimisation problems (Figure 1.1):
Optimal QoS Partition and Routing (OPQR-G) Problem First, for each delay-sensitive class, determine the primary paths between the OD pairs and the partitions of the global end-to-end QoS constraints into local QoS constraints (on the links), by solving a combined QoS partition and routing optimisation problem. Capacity Allocation (CA) Problem Then, based on the local delay QoS constraints and the total amount of traffic for each class routed on each link, determine bandwidth allocations for the delaysensitive traffic classes, as well as the total bandwidth (capacities) of the links by solving a capacity allocation problem. Cost Minimisation (CM) Problem Finally, once the links are sized, perform a cost optimisation to account for the modularity of the link capacities. In this approach, we first interpolate the discrete costs with continuous costs and thus we simplify the model in favour of one with fewer integer decision variables. That is, we first determine the flow and QoS (delay, jitter) partition variables for each delay-sensitive traffic class, by
12
NEXT GENERATION INTERNET Stepl: Determine primary routes and link QoS partitions for all classe
Class/
• OPQR-G Algorithm 1—
Class 2
• OPQR-G Algorithm 1 —
f !i
! i I 1 !
L_
Class n
• OPQR-G Algorithm
|—
i i i
1 I !
Step 2: Determine class-based bandwidth allocations and total capacities on links
1 —-J— CA Algorithm
Step 3: Perform optimization to account for the discrete set of link capacities
CM Algorithm
I
i
J
Figure 1.1. Capacity planning framework
applying an algorithm for solution of the OPQR-G problem. This provides the basis for the solution of CA problem i.e., for determining the required bandwidth for the delay-sensitive traffic classes on the links. The continuous link capacities, obtained as a linear sum of the bandwidth allocations for the delay-sensitive classes, are then transformed to the higher (feasible) discrete values of the link capacities. Once the links are sized for capacity (based on application of the CA algorithm), a cost optimisation is performed, where we concentrate on a flow assignment optimisation problem for the best-effort (BE) service class only. That is, we want to achieve a minimum cost placement of all OD pair BE traffic demands on the existing capacitated links and/or to install additional link capacities in the network if required. The optimisation subproblems, although more manageable than the original problem, also pose significant modelling and algorithmic challenges. Each of the main steps and algorithms employed in the proposed framework are discussed in the following subsections.
4,1
Problem OPQR-G
The algorithm for the solution of the OPQR-G (Optimal QoS Partition and Routing in General topology networks) problem, when applied to each class of traffic independently, will determine the required input for the capacity allocation problem; that is, the primary routes between the OD pairs and the QoS partitions on the links for each class of traffic, respectively. The combined QoS partition and routing optimisation
1 Design of IP Networks with End-to-End Performance Guarantees
13
problem for the DSC and JSC class will be solved by considering delay and jitter as a QoS metric, respectively. For the DJSC class, the QoS requirement is defined by a combination of two QoS metrics i.e., delay and jitter bound, thus, we need to find the partitions of the two metrics on the links simultaneously. This is achieved by applying the following two-step heuristic approach: (1) first solve the OPQR-G problem by considering delay as a QoS metric to determine the routes and the delay partitions on the links for the class, and subsequently, (2) given the routes, solve the problem of optimal QoS partitioning only (Problem OPQ-G) to determine the jitter partitions on the links. The combined routing and QoS partitioning optimisation problem has been addressed in the literature in the context of unicast connections and multicast trees only, see Lorenz et al. (2000); Lorenz and Orda (2002) and references therein. In addition to this, several other studies have considered the QoS partitioning part of the problem only, where the routing information is given at input (Ibaraki and Katoh, 1988; Monma et al., 1990). Again, these studies solve the problem for the case of unicast connections and multicast trees only. Moreover, they only provide solutions for convex cost functions. We consider the more general case of a multicommodity network flow problem. In addition, it is assumed that the performance dependent cost functions are non-increasing and they are of a general integer type. Problem OPQR-G needs to be solved for each delay-sensitive traffic class independently and, therefore, we provide its formulation in the context of a single service class. As a result, in the following we omit the subscript c for clarity. Furthermore, without loss of generality, the definition of the OPQR-G problem is described by considering a DSC type of service class i.e., we make use of a delay as a QoS metric. Problem OPQR-G: Given a network GiV^E), a cost/delay function for each link {Qi(d)}ieE, end-to-end delay requirements for all OD pairs and a set of candidate routes for all OD pairs in the net{Duv}(uv}en, work {Ruv}(Uyv)eU- Find a partition d — {di}ieE and set of routes r = {ruv}(UrV) dlprop
V(n, v) e n
He ; E
(1.3a) (1.3b)
The algorithm LP1 and the heuristic OPQR-G are conceptually the same. Both LP1 and the heuristic use INITIALISATION to compute the routes for all OD pairs and then re-adjust the delay partition such that the new partition does not violate end-to-end delay constraints. The only thing that differentiates between the two algorithms is how re-adjustment of the delay partition is achieved. In the case of LP1 the delay partition achieved on the given set of routes is guaranteed to be optimal. However, there is a trade-off when using the LP approach for solving the problem, in that, it will more-than-likely require a longer time to run than the heuristic. 4.1.3 Algorithm LP2. A limitation to both of the previous heuristics is that the routes are kept unchanged after the INITIALISATION step. In the case where these routes have many common links 2 Note that, the formulation of the OPQR-G-LP1 problem defines the optimal QoS partitioning problem in the context of a multicommodity flow network (OPQ-G problem). The heuristic algorithm OPQR-G can be easily modified to provide the solution for the OPQ-G problem. The only modification required is that the INITIALISATION algorithm runs the OPQ algorithm instead of OPQR for unicast connections for each given route between the node pairs in the network.
1
Design of IP Networks with End-to-End Performance Guarantees
19
LP2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
for alllEE ni « - 1
for
all (u,v) e
n
all (u,v) e
n
generate a set of routes {Ruv} determine {x^ v} and {dt} by solving OPQR-G-LP2 for
if x™ = 1 ^_
ruv
{r^|j-th from Ruv}
for oXiieE
nj-0 for all {u,v) £ n
for alH € ? n'{ *— n
A:
- n\)2
if A > r
for all /, ni diprop
VI eE
(1.4c)
(
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NEXT GENERATION INTERNET
The variable n\ in the formulation above represents the total number of routes that traverse link L The algorithm starts by initialising the vector n = {ni}ieE by a unit vector. Then it determines the set of routes and delay partitions in the network by solving the OPQR-G-LP2 problem. In addition, the vector n is updated by the number of routes that traverse each link, as computed in the previous step. The algorithm iterates until the vector n converges. 4.1.4 Discussion. It is easy to see that the lower bound, LB, on the optimal cost can be computed by LB = E f u ^ e n E i G r ^ ^ " ' where ruv and {diruv}ieruv are the route and delay partitions on its links found by running OPQR for an OD pair (u, v). We shall use the LB as a benchmark for the performance analysis of the three proposed heuristic algorithms in the next section. The heuristics can always provide a solution (if a feasible solution exists) as mentioned before. However, like other heuristics, the heuristic cannot guarantee optimal solutions. When the routes found in INITIALISATION are link disjoint, the heuristic will not change either the routes or the delay partitions, hence, the results are guaranteed to be optimal. If the routes have common links, the solution may not be optimal. The solution is guaranteed not to exceed the optimal cost by T,(u,v)en J2ier^[Ql(dd ~ Ql(dir™)}, where {d[}ieE is the delay partition computed by the heuristics. According to the above analysis, the heuristic is not expected to work very well when the routes found by running OPQR algorithm separately for each OD pair have many common links or when Qi(d[) — Qi(diruv) is large. For example, the heuristic may have trouble with a network that consists of two parts connected via a single link and the (non-increasing) cost function of that link is very steep.
4.2
Problem CA
The CA problem poses the challenge of performing appropriate link dimensioning in order to balance quality of service against costly overprovisioning. From a mathematical modelling point of view, a major challenge is to incorporate a tractable mathematical characterisation of IP data traffic and tractable stochastic model of QoS queueing mechanisms used at the routers. Traditionally, for ease of tractability Poisson traffic descriptor has been used for representation of the external traffic sources and consequently the Jackson's network performance model has been used in network design. However, it is very important that the chosen traffic descriptor is able to capture burstiness of the packet arrivals,
1 Design of IP Networks with End-to-End Performance Guarantees
21
as real IP traffic exhibits such characteristic. The dimensioning model applied for the solution of the CA problem in the proposed framework, incorporates procedures that allow burstiness of multi-class IP traffic to be effectively modelled. The choice of a renewal traffic model i.e., GI arrival process, for this purpose, represents a reasonable balance between the accuracy and the efficiency required by a network design tool, especially when large networks, as well as large aggregates of individual flows into service classes are considered. This is due to the multiplexing which occurs on a very large scale in this case and, as a result, the correlations significantly reduce due to the inter-mixing of packets from different traffic streams. We model a class flow (i.e., single class of traffic between an OD pair) as a GI arrival process characterised with the following set of parameters {Ac, c^, XC) X^}ruverc. The first two-parameters denote the mean packet arrival rate and the squared coefficient of variation (SQV) of the packet inter-arrival times of the class c flow (c = 1,2,... C), which has been assigned a route r^v. The third and fourth parameter denote the first two moments of the packet size of class c flow, respectively. For this renewal process, the coefficient of variation is used to characterise traffic burstiness, i.e., the variability of the arrival stream. IP traffic is bursty in the sense that its squared coefficient of variation is always greater than or equal to unity. In Atov and Harris (2002a), we have presented models, which can be used to translate the OD pair traffic demands for each class of traffic, as obtained from traffic measurement data, into equivalent GI arrival process parameters for direct application into the dimensioning procedures. Due to the aggregation of individual flows into traffic classes at the ingress of the network, first individual flows are modelled by distinguishing between TCP-based and UDP-based flows, respectively. The model also takes account of the traffic aggregation and conditioning functions at the ingress of the network. From the offered class flows to the network and the given routing information (obtained from the OPQR-G problem solution), characterisation of the internal class flows can be obtained by applying the methods for superposition, departure and splitting of GI traffic arrival processes as provided by the well-known QNA analysis (Whitt, 1983). However, the internal class flows cannot be derived in a single iteration step (i.e., after single analysis of each node in the network), as their traffic descriptors depend on the service capacities that are allocated on the links, which are not known and need to be determined in the CA procedure. In order to deal with this interdependence, we calculate the internal flows for the classes, as well as, their bandwidth allocations on the links, iteratively as part of the CA procedure.
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NEXT GENERATION INTERNET
Input: A c = {(Ac, c^, XCi^c)}ruverc for c E C. Output: bci = {bci}i£E f° r a ll Q°S sensitive classes. 1 2
for class c = 1 to C — 1 for all link (I e £7)
4 for class c = 1 to C — 1 5 switch (qc) 6 case qc = {rf c /} i€£ ; 6a for all link (/ e E) 6b Calculate internal flows: {(A c /,c^)}; 6£ ;, 6c Invert the delay formula to derive 6C/, >€ 6d if max { b^zb^1 \ 6e 7 7a
6C^ •— 6C/ for V7 and repeat steps 3,6. case
