routing flow and capacity design in communication and computer networks

Ro uting, Flow, and Capacity Design
in
Communic ation and Computer Networks
The Morgan Kaufmann Series in Networking
Series Editor, David Clark, M.I.T.
Routing, Flow, and Capacity Design in
Communication and Computer Networks
Michal Pióro and Deepankar Medhi
Wireless Sensor Networks: An Information
Processing Approach
Feng Zhao and Leonidas Guibas
Network Recovery: Protection and Restoration
of Optical, SONET-SDH, IP, and MPLS
Jean Philippe Vasseur, Mario Pickavet, and Piet
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Communication Networking: An Analytical
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Anurag Kumar, D. Manjunath, and Joy Kuri
The Internet and Its Protocols: A Comparative
Approach
Adrian Farrel
Modern Cable Television Technology: Video,Voice,
and Data Communications, 2e
Walter Ciciora, James Farmer, David Large, and
Michael Adams
Bluetooth Application Programming with the Java
APIs
C Bala Kumar, Paul J. Kline, and
Timothy J. Thompson
Policy-Based Network Management: Solutions for

the Next Generation
John Strassner
Computer Networks: A Systems Approach, 3e
Larry L. Peterson and Bruce S. Davie
Network Architecture, Analysis, and Design, 2e
James D. McCabe
MPLS Network Management: MIBs, Tools, and
Techniques
Thomas D. Nadeau
Developing IP-Based Services: Solutions for
Service Providers and Vendors
Monique Morrow and Kateel Vijayananda
Telecommunications Law in the Internet Age
Sharon K. Black
Optical Networks: A Practical Perspective, 2e
Rajiv Ramaswami and Kumar N. Sivarajan
Internet QoS: Architectures and Mechanisms
Zheng Wang
TCP/IP Sockets in Java: Practical Guide for
Programmers
Michael J. Donahoo and Kenneth L. Calvert
TCP/IP Sockets in C: Practical Guide for
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Kenneth L. Calvert and Michael J. Donahoo
Multicast Communication: Protocols,
Programming, and Applications
Ralph Wittmann and Martina Zitterbart
MPLS: Technology and Applications
Bruce Davie and Yakov Rekhter
High-Performance Communication Networks, 2e

Jean Walrand and Pravin Varaiya
Internetworking Multimedia
Jon Crowcroft, Mark Handley, and Ian Wakeman
Understanding Networked Applications: A First
Course
David G. Messerschmitt
Integrated Management of Networked Systems:
Concepts, Architectures, and their Operational
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Heinz-Gerd Hegering, Sebastian Abeck, and
Bernhard Neumair
Virtual Private Networks: Making the Right
Connection
Dennis Fowler
Networked Applications: A Guide to the New
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David G. Messerschmitt
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Robert S. Cahn
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Routing, Flow, and Capacity Design
in
Communication and Computer Networks
Micha Pióro
Warsaw University of Technology, Warsaw, Poland
Lund University, Lund, Sweden
Deepankar Medhi

University of Missouri-Kansas City
Kansas City, Missouri, USA
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CONTENTS
B
Foreword
xix
Preface

xxi
PART I INTRODUCTORY NETWORK DESIGN
1
C HAPTER1
Overview 3
1.1 A Network Analogy 4
1.2 Communication and Computer Networks, and Network
Prov iders

9
1.3 Notion of Traffic and Traffic Demand
11
1.3.1 Traffic in the Internet 12
1.3.2 Traffic in the Telephone Network
17
1.3.3 Demand in the Transport Network 20
1.3.4 Distinction between Traffic and Transport Network
22
1.3.5 Generic Naming for Demand Volume and Capacity 22
1.4 A Simple Design Example 22
1.5 Notion of Routing and Flows

23
1.6 Architecture of Networks: Multi-Layer Networks

25
1.7 Network Management Cycle
27
1.8 Sc ope of the Book
31
1.9 Naming and Numbering Convention
35
1.10 Summary
36
C HAPTER2
Network Design Problems—Notation and
Illustrations

37
2.1 A Network Flow Example in Link-Path Formulation 38
2.2 Node-Link Formulation
43
2.3 Notions and Notations
45
2.4 Dimensioning Problems
50
2.5 Shortest-Path Routing
60
2.6 Fair Networks

62
v iii Contents
2.7 Topological Design
65
2.8 Restoration Design

66
2.9 *Multi-Layer Networ ks Modeling
68
2.10 Summary
74
Exercises for Chapter 2

76
C HAPTER3
Technology-Related Modeling
Examples

77
3.1 IP Networks: Intra-Domain Traffic Engineering
78
3.2 MPLS Networks: Tunneling Optimization

82
3.3 ATM Networks: Virtual Path Design
84
3.4 Digital Circuit-Switched Telephone Networ ks: Single–
Busy Hour and Multi–Busy Hour Network Dimensioning
86
3.5 SONET/SDH Transport Networ ks: Capacity and
Protection Design

90
3.6 SONET/SDH Rings: Ring Bandwidth Design
94
3.7 WDM Networks: Restoration Design with Optical
Cross-Connects

96
3.8 IP Over SONET: Combined Two-Layer Design

98
3.9 Summary an d Further Reading

101
Exercises for Chapter 3
102
PART II DESIGN MODELING AND METHODS 103

C HAPTER4
Network Design Problem Modeling 105
4.1 Basic Uncapacitated and Capacitated Design Problems 106
4.1.1 Uncapacitated Problems
106
4.1.2 Capacitated Problems
112
4.1.3 Mixed Problems 115
4.2 Routing Restrictions
115
4.2.1 Path Diversity 116
4.2.2 Lower Bounds on Non-Zero Flows 117
4.2.3 Limited Demand Split
118
4.2.4 Integral Flows 123
4.3 Non-Linear Link Dimensioning, Cost, and Delay Functions 124
4.3.1 Modular Links 124
4.3.2 Convex Cost and Delay Functions

128
Contents ix
4.3.3 Concave Link Dimensioning Functions 134
4.4 Budget Constraint
140
4.5 Incremental NDPs
141
4.6 Extensions of Problem Modeling
142
4.6.1 Representing Nodes
143

4.6.2 Capabilities of Link-Path Representation
144
4.7 Summary an d Further Reading
145
Exercises for Chapter 4
148
C HAPTER5
General Optimization Methods for Network
Design

151
5.1 Linear Programming 152
5.1.1 Basic Facts About LP 152
5.1.2 Duality in LP
154
5.1.3 Simplex Method 158
5.1.4 Interior Point Methods (IPM)
160
5.2 Mixed-Integer Programming 162
5.2.1 The Branch-and-Bound (BB) Method 162
5.2.2 The Branch-and-Cut (BC) Method
166
5.2.3 The Cutting-Plane Method 167
5.2.4 Dynamic Programming
168
5.3 Stochastic Heuristic Methods 169
5.3.1 Local Search 169
5.3.2 Simulated Annealing (SAN) 170
5.3.3 Evolutionary Algorithm (EA) 172
5.3.4 Simulated Allocation (SAL)

173
5.3.5 Tabu Searc h (TS) 176
5.3.6 Other Methods

177
5.4 LP Decomp osition Methods 178
5.4.1 Lagrangian Relaxation (LR) 178
5.4.2 Column Generation Technique for Candidate Path List
Augmentation (CPLA)
184
5.4.3 Benders’ Decomposition

192
5.5 Gradient Minimization and Other Approaches for
Convex Programming Problems

194
5.5.1 The Flow Deviation (FD) Method 195
5.5.2 The Gradient Projection (GP) Method 196
5.5.3 Dual Method
198
x Contents
5.6 Special Heuristics for Concave Programming Problems
199
5.6.1 Minimum First Derivative Length Path (MFDLP) Method
200
5.6.2 Greedy Descent (GD) Method 201
5.6.3 Numerical Example
202
5.7 Solving Multi-Commodity Flow Problems

203
5.7.1 LP Formulations
204
5.7.2 Non-Bifurcated Flows

204
5.7.3 Modular Links
205
5.8 Summary an d Further Reading 206
Exercises for Chapter 5

208
C HAPTER6
Lo cation and Topological Design
211
6.1 Node Location Problem 212
6.1.1 Add Heuristic 214
6.2 Joint Node Location and Link Connectivity Problem
217
6.2.1 Design Formulation: One-Level 218
6.2.2 Design Formulation: Two-Level 223
6.2.3 Design Results

226
6.3 Topological Design
230
6.3.1 Discussion 231
6.3.2 Design with Budget Constraint 232
6.3.3 Design with Extended Objective
234

6.3.4 Transit Nodes and Links Localization Problem
235
6.3.5 Heuristic Algorithms
239
6.3.6 Numerical Results
242
6.4 Lower Bounds for Branch-and-Bound 243
6.4.1 Case: Topological Design with Budget Constraint
244
6.4.2 Case: Transit Node and Link Localization Problem 246
6.5 Summary an d Further Reading 249
Exercises for Chapter 6
251
C HAPTER7
Networks With Shortest-Path Routing
253
7.1 Shortest-Path Routing Allocation Problem 256
7.1.1 Basic Problem Formulation 256
7.1.2 Adjustments of the Basic Problem
260
7.1.3 Minimum-Hop Routing versus Network Delay: An Illustration 264
Contents xi
7.2 MIP Formulation of the Shortest-Path Routing Allocation
Problem and Dual Problems
266
7.2.1 MIP Formulation of the Shortest-Path Routing Allocation
Problem

266
7.2.2 Duality and Shortest-Path Routing 268

7.3 Heuristic Direct Methods for Determining th e Link
Metric System

271
7.3.1 Weight Adjustment (WA)
271
7.3.2 Simulated Annealing (SAN)

272
7.3.3 Lagrangian Relaxation (LR)-Based Dual Approach
273
7.4 Two-Phase Solution Approach 276
7.4.1 Formulation of the Two-Phase Optimization Problem
276
7.4.2 Solving Phase 1

278
7.4.3 Solving Phase 2
282
7.5 Impact Due to Stochastic Approaches 283
7.6 Impact of Different Link Weight System
285
7.7 Impact on Different Performanc e Measures
289
7.8 Uncapacitated Shortest-Path Routing Problem

291
7.9 Optimization of the Link Metric System under Transient
Failures
292

7.10
*NP-Completeness of the Shortest-Path Routing
Allocation Problem
295
7.11
*Selfish Routing and its Relation to Optimal Routing 298
7.12 Summary an d Further Reading
303
Exercises for Chapter 7
305
C HAPTER8
Fair Networks
307
8.1 Notions of Fairness 308
8.1.1 An Example 308
8.1.2 Max-Min Fairness (MMF) Allocation Problem for Fixed Paths 309
8.1.3 Proportional Fairness (PF) Allocation Problem for Fixed Paths

314
8.2 Design Problems for Max-Min Fairness (MMF)
316
8.2.1 Capacitated Problems for Flexible Paths
316
8.2.2 Uncapacitated Problems for Flexible Paths 330
8.2.3 Capacitated Problems With Non-Bifurcated Flows
330
8.3 Design Problems for Proportional Fairn ess (PF) 331
8.3.1 Capacitated Problems for Flexible Paths 332
8.3.2 Uncapacitated Problems With a Budget Constraint
332

xii Contents
8.3.3 Uncapacitated Problems With an Extended Objective Function 338
8.3.4 Numerical Examples
340
8.3.5 Minimum Delay 345
8.3.6 Non-Bifurcated Flows 346
8.4 Summary an d Further Reading
346
Exercises for Chapter 8

348
PART III ADVANCED MODELS
351
C HAPTER9
Restoration and Protection Design
of Resilient Networks

353
9.1 Failure States, Protection/Restoration Mechanisms, and
Diversity 354
9.1.1 Characterization of Failure States 354
9.1.2 Re-Establishment Mechanisms 355
9.1.3 Protection by Diversity
358
9.2 Link Capacity Protection/Restoration 361
9.2.1 Link Restoration 361
9.2.2 Hot-Standby Link Protection 364
9.3 Demand Flow Re-Establishment 365
9.3.1 Unrestricted Reconfiguration 365
9.3.2 Restricted Reconfiguration 368

9.3.3 *
Path Restoration With Situation-Dependent Back-up Paths 372
9.3.4 *Path Restoration With Single Back-up Paths 373
9.3.5 Hot-Standby Path Protection
376
9.4 Extensions
377
9.4.1 Non-Linear Cost/Dimensioning Functions 377
9.4.2 Modular Link Capacities and/or Integral Flows
377
9.4.3 Budget Constraint 379
9.4.4
*Routing Restrictions 380
9.4.5 Separating Normal and Protection Capacity 384
9.4.6 Separated Normal an d Protection Design

385
9.5 Protection Problems
386
9.5.1 Link Capacity Restoration 386
9.5.2
*Path Restoration 389
9.6 Applicability of the Protection/Restoration Design Models 392
9.6.1 Dynamic Routing Circuit-Switched Networks 392
9.6.2 Backbone IP, MPLS, and ATM Networ ks
394
Contents xiii
9.6.3 Optical Systems, SONET/SDH, and WDM Networks 397
9.7 Summary an d Further Reading
398

Exercises for Chapter 9
400
C HAPTER10
Application of Optimization Techniques
for Protection and Restoration Design

403
10.1 Path Generation
404
10.1.1 Unrestricted Reconfiguration 404
10.1.2 Restricted Reconfiguration 407
10.1.3 Back-up Path Restoration

41 1
10.1.4 Numerical Results
413
10.2 Lagrangian Relaxation (LR) With Subgradient Maximization
415
10.2.1 Unrestricted Reconfiguration 417
10.2.2 Restricted Reconfiguration 420
10.2.3 Back-up Path Restoration
422
10.3 Benders’ Decomp osition 423
10.3.1 Unrestricted Reconfiguration 423
10.3.2 Restricted Reconfiguration
429
10.3.3 Numerical Results 432
10.4 Modular Links
435
10.5 Stochastic Heuristic Methods

438
10.5.1 Simulated Allocation (SAL) 438
10.5.2 Simulated Annealing (SAN)
444
10.5.3 Evolutionary Algorithm (EA) 445
10.6 *Selected Application: Wavelength Assignment Problem
in WDM Networks 446
10.6.1 Design Problems 446
10.6.2 Design Methods 449
10.6.3 Numerical Results
450
10.6.4 Remarks 452
10.7 Summary an d Further Reading
453
Exercises for Chapter 10
453
C HAPTER11
Multi-Hour and Multi–Time-Period
Network Modeling and Design
455
11.1 Multi-Hour Design 45 6
11.1.1 Illustration of Multi-Hour Dimensioning 45 6
11.1.2 Multi-Hour Dimensioning Models
458
xiv Contents
11.1.3 Multiple Services Case 464
11.1.4 Algorithmic Approaches
465
11.1.5 Computational Results 467

11.1.6 Capacitated Case: Multi-Hour Routing 472
11.2 Multi-Period Design
474
11.2.1 Capacity Planning
475
11.2.2 Multi-Period Flow Routing Problem

480
11.2.3 Model Extensions
483
11.2.4 Algorithmic Approaches

486
11.2.5 Dynamic Programming
486
11.2.6 A Hybrid Method

487
11.3 Summary and Further Reading
491
Exercises for Chapter 11

493
C HAPTER12
Multi-Layer Networks: Modeling and
Design
495
12.1 Design of Multi-Layer Networ ks
497
12.1.1 Multi-Layer Technology-Related Example 497

12.1.2 Network Dimensioning Involving Two Resource Layers
500
12.1.3 Allocation Problems with Two Layers of Resources
506
12.1.4 Extensions to More than Two Layers

510
12.1.5 Optimization Methods for Multi-Layer Normal Design Problems

513
12.2 Modeling of Multi-Layer Networks for Restoration Design 515
12.2.1 The Case of Two Reconfigurable Layers
515
12.2.2 Restoration Involving Only Reconfiguration of Lower Layer 521
12.2.3 Restoration Involving Only Reconfiguration of Upper Layer

522
12.2.4 Extensions
523
12.2.5 Optimization Methods for Multi-Layer Restoration Design
524
12.3 Multi-Layer Design With Multi-Hour Traffic
525
12.3.1 Mixed Two-Resource Layer Design With Multi-Hour Traffic and
Restoration

525
12.3.2 Multi-Layer Design Problems With Multi-Hour, Multi-S ervic e
Traffic

529
12.3.3 Multi-Layer Design Through Layer Separation 533
12.3.4 Failure Propagation
534
Contents xv
12.4 Application of Decompo sition Methods for Two-Layer Design 535
12.4.1 LR With Subgradient Maximization of the Dual Function
536
12.4.2 Benders’ Decomposition 540
12.4.3 Path Generation
549
12.5 Numeric al Results
553
12.6 Cost Comparison

559
12.6.1 Diversity an d Restoration (with Multi-Hour Traffic)
559
12.6.2 Gain With Dynamic Transport Over Static Transport
(with Multi-Service, Multi-Hour Traffic)
563
12.7 Grooming/Multiplex Bundling
565
12.7.1 Illustration of Multi-Layer in the Presence of Grooming
566
12.7.2 Special Cases when Grooming Nodes are Known
568
12.7.3 A General Two Layer Formulation
571
12.7.4 Remark 574

12.8 Summary an d Further Reading 574
Exercises for Chapter 12
577
C HAPTER13
Restoration Design of Single- and
Multi-Layer Fair Networks

581
13.1 Restoration Design of Single-Layer PF Networks
582
13.1.1 Problem Formulation and Iterative Solution
582
13.1.2 Algorithm With Dual Non-Blocking Tests

585
13.1.3
*Regular Sets of Blocking Situations 587
13.1.4 Numerical Results 591
13.2 Decomp osition Methods for the Single-Layer
Restoration Problems
597
13.2.1 Benders’ Decomposition
597
13.2.2 Path Generation

598
13.3 Design of Resilient Two-Layer PF Networks 600
13.3.1 Three Basic Problems for Unrestricted Flow Restoration 600
13.3.2 Numerical Examples
603

13.3.3 Decomposition Methods for Two-Layer Networks
608
13.4 Extensions
609
13.5 Summary an d Further Reading

610
Exercises for Chapter 13

611
xv i Contents
APPENDICES
APPENDIX A
Optimization Theory Refresher 613
A.1 Basic Notions
613
A.2 Karush-Kuhn-Tucker (KKT) Optimality Conditions

614
A.3 Interpretation of th e Lagrange Multipliers in the
KKT Conditions
616
A.4 Numeric al Methods for Finding Minima of
Differentiable Problems
616
A.5 Duality
617
A.6 Duality for Convex Programs

618

A.7 Duality for Convex Objective and Linear Constraints

619
A.8 Subgradient Maximization of the Dual Function

620
A.9 Subgradient Maximization of the Dual Function of
Linear Programming Problems
622
APPENDIX B
Introduction to Complexity Theory and
NP-Completeness
62 5
B.1 Introduction
625
B.2 Complexity of a Problem
626
B.3 Deterministic and Non-Deterministic Machines

627
B.4 The Classes of Problems Known as
P and NP 629
B.5 Reducibility Relation between Problems

630
B.6 The Class of
NP-Complete Problems 631
B.7 The Satisfiability Problem and Cook’s Theorem
631
B.8 Network Flow Problems

632
B.8.1 The D2CIF problem
633
B.8.2 The U2CIF problem 636
B.9 Final Remarks 637
APPENDIX C
Shortest-Path Algorithms 639
C.1 Introduction and Ba sic Notions
639
C.2 Basic Shortest-Path Problem
640
C.2.1 Dijkstra’s Algorithm for Non-Negative Weights 641
C.2.2 Shortest Paths With a Hop Limit
642
C.2.3 Negative Weights 644
Contents xv ii
C.3 K-Shortest Paths and All Optimal Paths 646
C.3.1 K-Shortest Paths
646
C.3.2 All Optimal Paths 647
C.4 Shortest Sets of Disjoint Paths
648
C.4.1 Shortest Sets of Edge-Disjoint Paths
648
C.4.2 Shortest Sets of Vertex-Disjoint Paths

650
APPENDIX D
Using LP/MIP Packages
653

D.1 Solv ing Linear Programming Problems using Maple,
Matlab, and CPLEX

653
D.2 Solving (Mixed) Integer Programming Problems Using CPLEX

656
D.3 Modeling Using AMPL

658
D.4 Final Remark
660
List of Acronyms

661
Solutions to S elected Exerc ises

663
Bibliography
679
Index 713
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FOREWORD
B
Debasis Mitra
Vice President, Mathematical Sciences Research,
Bell Laboratories, Lucent Technologies
Michał Pi
´
oro and Deepankar Medhi have written a book that will be welcomed by

members of the networking community who have an interest in network design. Network
design has traditionally played an important, perhaps even a central, role in telecommu-
nications. There are several reasons for this, and one is that network design is the bridge
between demand estimates and capital investments in network infrastructure. Its reach also
extends to the design of network operations. Thus, network design has much to contribute
in optimizing a service provider’s capital expenditure (CAPEX) and operational expendi-
ture (OPEX). The span of the book splendidly captures the breadth of the role of network
design. For instance, major portions deal with least cost network design, which is aimed at
CAPEX reduction, while other parts of the book address issues of restoration, routing, and
provisioning, which affect OPEX.
The definitions of problems in network design and the algorithms for their solutions
have evolved over time to keep up with the changes in technologies and their roles in
telecommunications. Importantly, this book reflects the all-important dynamism of net-
working. The reader will find in it, for instance, the essentials of design of circuit-switched
networks, the mainstay of telephony for many decades, as well as the design issues in more
recent technologies, such as IP and optical networking. The book provides the reader with a
kaleidoscopic view of technologies and protocols seen through the lens of network design.
The heart of the book is its treatment of modeling and algorithms. It is also the unifying
force. The authors have wisely chosen to focus on a multi-commodity flow-based approach.
While the inclusion of multiple approaches, such as probabilistic modeling and performance
evaluation, must have appealed, the cost would have been a loss of focus and depth. As
it is, the book provides an in-depth treatment of an important segment of network design
algorithms, including their theoretical bases and role in design tools.
The reader will find many unique insights and pointers to research and problem solving
in this book. The following topics will serve to illustrate this point. The authors bring
a special perspective to the design for protection and restoration of optical and MPLS
networks. The treatment of multi-layer network design, such as IP over SONET, is also
quite special. Fairness in networks is, of course, a topic that has an extensive literature,
but the book’s thorough coverage of the implications on design represents another special
feature. The design of weights for OSPF routing in IP networking is yet another example

of a special feature found in the book.
Researchers, students, and practitioners of network design will warmly welcome the
book to their shelves. It will serve as a beacon and be consulted for many years to come.
This page intentionally left blank
PREFACE
B
Modeling and design of large communication and computer networks has always been
an important area to both researchers and practitioners. The interest in developing efficient
design models and optimization methods hasbeenstimulated by high deployment and main-
tenance costs of networks, which make good network design potentially capable of securing
considerable savings. For many decades, the area of network design had been relatively
stable and followed the development of telephone networks and their smooth transition
from analog to digital systems. In the past decade, however, the networks have undergone
a substantial change caused by the emergence and rapid development of new technologies
and services, an enormous growth of traffic, demand for service availability and continuity,
and attempts to integrate new networking and system techniques and different types of
services in one network. As a consequence, today’s network designers face new problems
associated with diverse technologies, complicated network architectures, and advanced re-
source and service protection mechanisms. In the context of this book, these problems can
be broadly divided into three classes: 1) developing adequate design models specific for
different technologies such as transmission control protocol/Internet protocol (TCP/IP),
digital telephony (i.e., integrated digital network—IDN), multi-protocol label switching
(MPLS), asynchronous transfer mode (ATM), synchronous optical network/synchronous
digital hierarchy (SONET/SDH), and wavelength division multiplexing (WDM); 2) proper
multi-layer modeling across the network layers using different technologies (such as IP over
ATM over SONET, IP over WDM, or IDN over SONET); and 3) considering restoration
design, accounting for recovery from failures (such as cable cuts and switch breakdowns)
of large capacity transport links and transit nodes.
As reflected in the title of the book, by network design we broadly refer to the optimal
determination of traffic routing, traffic flow, and capacity of links and nodes in one or several

resource layers of an expanding network,takinginto account different network states related
to failures and time-dependent traffic matrices. The number of papers and books on network
design has constantly increased over the past decades. As a result of the collective effort, a
considerable knowledge has been built, covering virtually all aspects of the field forall types
of networks. Still, in general, there is a large gap between what is achievable through exist-
ing mathematical methods and what is actually used in practice for network design. The use
of mathematical modeling and the application of efficient optimization algorithms to those
models has not been fully utilized—in practice one often observes simplified approaches
leading to too costly solutions. At the same time, it is important to recognize that much valu-
able theoretical work related to network design available in the existing literature may not be
xxii Preface
applicable in practice. Certainly, the relation between theory and practice of network design
is not simple. In a sense, network design is a kind of art; the designer has to make selective
use of various available theoretical models and approximations using his abilities, skills,
and knowledge. At the same time, implementable solutions need to take into account vari-
ous practical constraints which are difficult to consider in more general and abstract models.
In effect, the designer is required to apply and tailor theoretical models in a way leading to
solutions which can be then made useful in practice. We are convinced that in this process
available mathematical developments play an important role and must be well understood.
Clearly, one way to achieve this is by providing a dedicated systematic presentation of the
knowledge on the network design optimization models and methods gathered in one place.
This can substantially help not only a novice reader, but also an expert and a practitioner,
understand where to begin, develop, and refresh their knowledge, if one were to study
network design. Needless to say, our aim is at providing such an exposition in this book.
PURPOSE OF THIS BOOK
The main purpose of this book is to present basic principles and methods for develop-
ing optimization models for contemporary communication and computer network design.
The book is focused on optimization problems and methods for traffic routing, flow, and
resource capacity optimization. We aim at developing a general framework applicable to
such technologies as IP, IDN, MPLS, ATM, SONET/SDH, and WDM, and capable to cope

with new network technologies that will emerge in the future. The design models and meth-
ods considered here are mainly for backbone or core networks
1
as these are among the
most challenging due to their scale, complexity, and cost. Certainly, some of the methods
presented in this book can be used, after some modification, for other types of networks,
e.g., access and local networks.
The current situation in network design is significantly different from that of the 1960s
and 1970s, when the design methodology for the then dominant telephone networks was
very well understood, described in manuals, and applied in practice. Today, with a great
variety of network technologies and services, the knowledge on network design is spread
over a large number of papers and books. There are many fine works that contain excellent
models and methods; still, in most cases, their comprehension requires solid background
in modeling and optimization, which is not common among network designers. In fact,
it is hard to find works that present the material in a manner so that both beginners and
experts can read and understand how different modeling and optimization techniques can be
employed. Our book attempts to explain the principles and methods of network modeling
and optimization in a comprehensive, unified, generic, and precise manner. To achieve
this goal we present the problems on a level of abstraction that avoids unnecessary and
tedious technological details, aiming at helping students, new employees, practitioners,
and network designers to understand the basics, developments, and recent advances in
network design.
1
By backbone or core networks, we refer to networks, spread over a wide geographical area and carrying
large volumes of traffic, that interconnect access or local networks.
Preface xxiii
Network design problems (NDPs) require mathematical formulations to become un-
ambiguous and understandable to others; also, once the problem at hand is stated in a formal
way, it reveals what optimization methods are applicable and appropriate. In our experi-
ence, most problems of routing, flow, and capacity design studied in this book are directly

related to, and best tractable by the branch of optimization known as multi-commodity
flow networks, extensively studied in the operations research and optimization literature
for many different applications, including communication and computer networks. In fact,
the multi-commodity flow network approach, with its flexibility in problem modeling and
solid optimization background, is virtually the only way for achieving our target: providing
general, precise, and effective means for efficient optimization-oriented modeling of the
(enormously rich) family of valid NDPs.
Network designers usually have excellent knowledge of networking technologies (in-
cluding communication and computer systems technologies, networking techniques, pro-
tocols, service implementation, traffic characterization, and so on), but may not have
extensive background in optimization. On the other hand, specialists in optimization/
operations research may not posses sufficient technological knowledge to develop and
validate models for particular networks. With this in mind, our book tries to bridge the gap
between the two “parallel” worlds: the people involved in networking technology and the
people devoted to system modeling and optimization. In the process, when discussing the
multi-commodity flow network concepts in Chapter 2, we have introduced a uniform no-
tation and provided several problem-modeling examples. Symmetrically, in Chapter 3, we
have formulated a number of problems related to specific network technologies to explain
how to use the generic multi-commodity flow network modeling approaches for communi-
cation and computer networks. The subsequent chapters, devoted mostly to the presentation
and development of the modeling and optimization methods for network design, are illus-
trated with further technology-related examples.
In an attempt to cover the major issues in the design of contemporary communica-
tion backbone networks, we have used a “three-dimensional” approach discussing the three
main broad directions in network design: 1) modeling techniques for developing and formu-
lating various design problems; 2) multi-layer modeling of networks comprising different
technologies (and functionalities); and 3) incorporating network protection and restoration
mechanisms. While dealing with these three dimensions, the book conveys techniques for
precise modeling and formulating of valid design problems, optimization methods and al-
gorithms applicable for the elaborated problems, and examples illustrating the efficiency of

the resulting optimization models. Although the book does not attempt to answer questions
whether one technology should be used instead of another for the best network design, the
models and methods presented in this book can be useful in developing tools for answering
such questions.
This book assumes a background in calculus and linear algebra on a level of a student
with undergraduate degree in electrical engineering or computer science. Certainly, some
knowledge of networking and telecommunications technology will be helpful in under-
standing the reasons for various modeling details.
To conclude, our attempt was to write a book that can be useful for graduate students
in telecommunications, electrical engineering, computer science, and operations research,
as well as for researchers in academia and industry in exploring the sometimes difficult
xxiv Preface
area of contemporary communication and computer network design through mathematical
optimization-oriented modeling. The topics covered in this book can hopefully be of in-
terest to scientists and doctoral students in identifying fruitful areas for original theoretical
research. Our aim was also to reach out to practitioners by illustrating various modeling
techniques through technology-oriented examples. At the same time we believe that this
book may be useful for the practitioners in their efforts to make advances in the area of
network design through systemizing and deepening their theoretical background. For that
matter, we cannot think of a better way for a network designer to extend his basic back-
ground knowledge than to study principles of the models and methods of multi-commodity
flow networks, to which this book is mostly devoted.
CONTENTS AND ORGANIZATION
The book is divided into three parts. Part I—Introductory Network Design—is composed
of three chapters and serves as the Introduction. Chapter 1 introduces the basic notions and
concepts of network modeling and design by providing an analogy to airline networks and
explaining these concepts through simple examples. In Chapter 2, we discuss and introduce
the multi-commodity flow network notation used throughout the book, and illustrate the
principles of building network models using representative examples, further developed
in Parts II and III. Finally, in Chapter 3, we present a set of specific technology-related

examples, showing how to apply multi-commodity flow network modeling techniques to
selected up-to-date networks based on different technologies, such as IP, IDN, MPLS, ATM,
SONET/SDH, WDM, and IP over SONET.
Part II—Design Modeling and Methods—consists of five chapters and is devoted to
the most common case of designing single-layer networks for the normal state
2
. Chapter 4
presents various important general multi-commodity flow network models, starting with
simple examples, and gradually extending them, showing how different types of constraints
and variables can be used to express different desired characteristics of the models, such as
single-path routing or modular link capacity. We discuss specific types of multi-commodity
formulations, such as the node-link and the link-path formulation. In Chapter 5, we present
various basic optimization approaches applicable to design problems formulated in Chap-
ter 4 and in subsequent chapters. We discuss linear programming (including the simplex
method and interior point approaches), branch-and-bound and branch-and-cut for mixed
integer programming, decomposition methods for linear and mixed integer programming
(Lagrangian relaxation, column generation, and Benders’ decomposition), stochastic meta-
heuristics (simulated annealing, evolutionary algorithms, and others), and special methods
for convex and concave problems. These methods are used and illustrated in the subsequent
chapters. The remaining three chapters of Part II are devoted to three important classes
of design models not considered in Chapter 4. Each of these chapters develops relevant
design models, applies appropriate optimization methods, and shows numerical examples.
Chapter 6 considers a class of design problems related to location and topological design
which take into account the installation cost of links and nodes. Then we move to recent
2
By the normal state of network operation, we mean the situation when all resources are available and fully
operative, and when the demand matrix is fixed. A single-layer network is the network that utilizes one technology.