Queuing Theory and Telecommunications

Giovanni Giambene

Queuing Theoryand Telecommunications

Networks and Applications

Second Edition

Giovanni GiambeneDepartment of Information Engineeringand Mathematical Sciences

University of SienaSiena, Italy

Additional material to this book can be downloaded from http://extras.springer.com

ISBN 978-1-4614-4083-3 ISBN 978-1-4614-4084-0 (eBook)DOI 10.1007/978-1-4614-4084-0Springer New York Heidelberg Dordrecht London

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This second edition of the book is dedicatedto my son Francesco, my joy.

This book is in loving memory of my fatherGianfranco and my uncle Ilvo. A specialdedication is to the persons nearest to myheart: my mother Marisa and my wifeMichela.

Preface to the Second Edition

From the invention of the telegraph and of the telephone networks the importance

of telecommunication technologies has been clearly evident. Human beings need

to interact continuously. The exchange of information of different types is today

an absolute necessity. Telecommunications favor the development of countries

and the diffusion of knowledge, and they are playing and will play a pivotal role

in the society.

Originally, telecommunication systems were simply conceived as links to trans-

mit information between two points. At present, telecommunication systems are

characterized by networks with nodes, where information is processed and correctly

addressed to output links, interconnecting nodes.

The first telecommunication networks for telegraphy supported the transmission

of messages. Then, telephone networks were conceived to establish a physical

circuit at call set up in order to connect source and destination for the whole duration

of the conversation. Today’s networks are digital and based on the transmission of

information organized in blocks, called packets, which are either independently

routed along the nodes or forwarded through a virtual path from source to destina-

tion. Transmission media are typically differentiated on the basis of the network

hierarchy; in particular, twisted pairs (copper) or wireless transmissions are used for

the user access, whereas, optical fibers are adopted in the core network.

Telecommunication systems have reached a worldwide diffusion on the basis of

the efforts of international and regional standardization bodies, which have done a

significant work, allowing different pieces of hardware to interoperate on the basis

of well-defined protocols and formats.

Instead of having a specialized network for each traffic type, the digital repre-

sentation of information has made it possible to efficiently integrate different traffic

types and then services (from voice, to video to data traffic, etc.) in the same

network.

At present, the network of the networks, that is the Internet, has a tremendous

worldwide-increasing diffusion. The outcome of this impressive process is that the

Internet protocol has become the glue, unifying different network technologies,

from mobile to fixed and from terrestrial to satellite.

vii

The central issue for modern telecommunication networks is the provision of

multimedia services with global-scale connectivity (also including mobile users),

guaranteeing several Quality of Service (QoS) requirements, differentiated

depending on the application the user is running (i.e., traffic classes). Network

resources are precious and costly and must be efficiently utilized. On the other

hand, digital information and data traffic worldwide are experiencing an exponen-

tial growth that represents a challenge to be addressed by the system designer and

the network planners. In this scenario, wireless access will play a major role since

from 2011 wireless connections have surpassed broadband wired ones.

The design of modern networks requires a deep knowledge of network charac-

teristics, transmission media types, traffic demand statistics, and so on. On the basis

of these characteristics, analytical methods can be adopted to determine the appro-

priate transmission capacity of links, the number of links, the management strategy

for sharing resources among traffic classes, and so on.

The main interest of this book is in providing a basic description of important

network technologies (in the first part of the book) as well as some analytical

methods based on queuing theory to model the behavior of telecommunication

systems (in the second part of the book). The aim and ambition is to provide the

most important tools of teletraffic analysis for telecommunication networks.

As for Part I of this book, the focus is on network technologies (and related

protocols) according to their time evolution. In particular, this part is mainly

organized according to a bottom-up approach, referring to the ISO/OSI stacked

protocol model, since we start from almost-layer 2 technologies (i.e., X.25, ISDN,

Frame Relay based, ATM based) in Chap. 2 and then we address layer 3 and above

technologies in Chap. 3 (i.e., IP routing, MPLS, transport-layer protocols, VoIP,

satellite networks).

In Part II of this book, queuing systems are studied with a special interest in

applying these analytical methods to the study of telecommunication systems.

In particular, queuing models are adopted at different levels in telecommunication

systems; they can be used to study the waiting time experienced by a given request

instanced to a processor or the time spent by a message or a packet waiting to be

transmitted on a given link or through a whole network. Note that the behavior of

every protocol in every node of a telecommunication network can be modeled by an

appropriate queuing process. Our analysis of queuing systems starts from Markov

chains, such as the classical M/M/1 queuing model for message-switched networks

and the M/M/S/S queue to study the call blocking probability in classical telephone

networks. Then, the interest is on more advanced concepts, such as imbedded

Markov chains (M/G/1 theory) with related models adopted to study the behavior

of ATM switches as well as of IP routers.

This second edition has been enriched and updated for what concerns both new

network technologies (Part I) and mathematical tools for queuing theory (Part II).

As for Part I, the main improvements are in Chaps. 2 and 3 as follows: (1) better

description of policers and shapers for ATM; (2) enriched contents on QoS support

in IP networks (e.g., deterministic queuing is introduced to deal with QoS guaran-

tees with IntServ); (3) detailed analysis of TCP congestion control behavior;

viii Preface to the Second Edition

(4) satellite IP-based networks; (5) VoIP. As for Part II, Chap. 6 on M/G/1 has been

substantially improved, detailing more general cases and the relations among

different imbedding options. Moreover, Chap. 7 now contains a better explanation

of the potential instability of Aloha protocols, updated details on Gigabit Ethernet,

and more details on three different approaches for the analysis of random access

schemes. Chapter 8 now provides a better description of the conditions for the

applicability of the Jackson theorem to real networks. Finally, new exercises

have been added to the first part of the book as well as to all the Chapters of the

second part of this book. The solution of all the exercises have been removed

from the book and provided in a separated solution manual, accessible online

www.extras.springer.com. Finally, a collection of slides has been made available

for downloading and represent a support and complementary tool for teaching

based on this book www.extras.springer.com.

QoS provision is a key element for both users who are happy of the telecommu-

nication services and network operators. The success of future telecommunication

services is heavily dependent on the appropriate modeling of the networks and the

application of analytical approaches for QoS support. This is the reason why the

analytical teletraffic methods are of crucial importance for the design of telecommu-

nication networks.

Siena, Italy Giovanni Giambene

Preface to the Second Edition ix

Preface to the First Edition

From the invention of the first telecommunication systems (i.e., telegraph and

telephone networks) the importance of these technologies has been clearly evident.

Humans need continuously to interact; the exchange of information of different

types at distance is today essential. Telecommunications favor the development of

countries and the diffusion of knowledge, and they are playing and will play a

pivotal role in the society.

Originally, telecommunications were simply conceived as links to transmit

information between two points. At present, telecommunication systems are char-

acterized by networks with nodes, where information is processed and properly

addressed (i.e., switching), and links that interconnect nodes.

The first telecommunication networks due to telegraphy were based on the

transmission of messages. Then, telephone networks have been based on the

establishment of a physical circuit at call setup in order to connect (for all the

duration of the conversation) the source and the destination. Today’s networks are

digital and based on the transmission of information organized in blocks, called

packets, that are either independently routed along the nodes or forwarded through

a virtual path connecting source and destination. Transmission media are distin-

guished according to a hierarchy in the network typology; in particular, twisted

pairs (copper) or wireless transmissions are used for the user access, whereas optic

fibers are employed for core network links.

Telecommunication systems have reached a worldwide diffusion on the basis of

the efforts of international and regional standardization bodies that have done a

significant work, allowing different pieces of hardware to interoperate on the basis

of well-defined rules.

Instead of having a specialized network for each traffic type, the digital repre-

sentation of the information has made possible to integrate efficiently in the same

network different traffic types, from voice, to video to data traffic, etc.

At present, the network of the networks, that is the Internet, has a tremendous

and ever increasing success. The outcome of this impressive process is that the

Internet protocol results as the glue that can unify different network technologies,

from mobile to fixed and from terrestrial to satellite.

xi

The crucial point for modern telecommunication networks is the provision of

multimedia services with global-scale connectivity (also including mobile users)

and guaranteeing several Quality of Service (QoS) requirements, differentiated

depending on the application the user is running (i.e., traffic classes). Moreover,

network resources are precious and costly and must be efficiently utilized.

The design of modern networks requires a deep knowledge of network charac-

teristics, transmission media types, traffic demand statistics, and so on. On the basis

of these data, analytical methods can be adopted to determine the appropriate

transmission capacity of links, the number of links, the management strategy for

sharing resources among traffic classes, and so on.

The interest of this book is in providing the basic characteristics of current

network technologies (i.e., X.25-based, ISDN, Frame Relay-based, ATM-based,

IP-based, MPLS, GMPLS, and NGN) as well as some important analytical methods

based on the queuing theory to be used to study the behavior of telecommunication

systems. The aim is to contribute to providing the basis of teletraffic analysis for

current telecommunication networks.

Queuing systems are studied in this book with a special interest in applying these

analytical methods to the study of telecommunication systems. In particular, queues

can be applied at different levels in telecommunication systems; they can

be adopted to study the waiting time experienced by a given request instanced to

a processor or the time spent by a message or a packet waiting to be transmitted on a

given link or through a whole network. In particular, every protocol in every node

of a telecommunication network can be modeled through an appropriate queuing

process.

Our analysis of queuing systems will start from Markov chains, such as

the typical M/M/1 queuing model to be used in message-switched networks and

the M/M/S/S queue employed to characterize the call loss behavior of local offices

in telephone networks. Then, the interest will be focused on more advanced

concepts, such as imbedded Markov chains (M/G/1 theory) with the related models

adopted to study the behavior of ATM switches.

QoS provision is a key element both for the users that are happy of

the telecommunication service they are adopting and for the network operators.

The success of future telecommunication services and networks is heavily depen-

dent on appropriate modeling and analysis in order to achieve an optimized network

design able to guarantee suitable QoS levels for different traffic classes. This is the

reason why the analytical methods of teletraffic analysis are of crucial importance

for telecommunication networks.

Siena, Italy Giovanni Giambene

xii Preface to the First Edition

Acknowledgments

The author wishes to thank Prof. Giuliano Benelli of the University of Siena for his

support and encouragement.

xiii

Contents

Part I Telecommunication Networks

1 Introduction to Telecommunication Networks . . . . . . . . . . . . . . . . . 3

1.1 Milestones in the Evolution of Telecommunications . . . . . . . . . . . 3

1.2 Standardization Bodies in Telecommunications . . . . . . . . . . . . . . 7

1.3 Telecommunication Networks: General Concepts . . . . . . . . . . . . . 9

1.3.1 Transmissions in Telecommunication Networks . . . . . . . . 11

1.3.2 Switching Techniques in Telecommunication

Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.3.3 The ISO/OSI Reference Model . . . . . . . . . . . . . . . . . . . . . 20

1.3.4 Traffic Engineering: General Concepts . . . . . . . . . . . . . . . 29

1.3.5 Queuing Theory in Telecommunications . . . . . . . . . . . . . . 30

1.4 Transmission Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

1.4.1 Copper Medium: The Twisted Pair . . . . . . . . . . . . . . . . . . 32

1.4.2 Copper Medium: The Coaxial Cable . . . . . . . . . . . . . . . . . 33

1.4.3 Wireless Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

1.4.4 Optical Fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

1.5 Multiplexing Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

1.5.1 FDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

1.5.2 TDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

1.5.3 The E1 Bearer Structure . . . . . . . . . . . . . . . . . . . . . . . . . 45

1.6 The Classical Telephone Network . . . . . . . . . . . . . . . . . . . . . . . . 46

1.6.1 Digital Transmissions Through POTS . . . . . . . . . . . . . . . . 50

1.6.2 Switching Elements in PSTN . . . . . . . . . . . . . . . . . . . . . . 52

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

2 Legacy Digital Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

2.1 Introduction to Digital Networks . . . . . . . . . . . . . . . . . . . . . . . . . 61

2.1.1 X.25-Based Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

2.1.2 ISDN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

2.1.3 Frame Relay-Based Networks . . . . . . . . . . . . . . . . . . . . . 74

xv

2.2 B-ISDN and ATM Technology . . . . . . . . . . . . . . . . . . . . . . . . . . 83

2.2.1 ATM Protocol Stack . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

2.2.2 Cell Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

2.2.3 ATM Protocol Stack . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

2.2.4 Traffic Classes and ALL Layer Protocols . . . . . . . . . . . . . 92

2.2.5 ATM Switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

2.2.6 ATM Switch Architectures . . . . . . . . . . . . . . . . . . . . . . . 96

2.2.7 Management of Traffic . . . . . . . . . . . . . . . . . . . . . . . . . . 102

2.2.8 ATM Physical Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

2.2.9 Internet Access Through ATM Over ADSL . . . . . . . . . . . 124

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

3 IP-Based Networks and Future Trends . . . . . . . . . . . . . . . . . . . . . . . 129

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

3.2 The Internet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

3.2.1 Introduction to the Internet Protocol Suite . . . . . . . . . . . . . 131

3.2.2 TCP/IP Protocol Architecture . . . . . . . . . . . . . . . . . . . . . . 131

3.3 IP (Version 4) Addressing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

3.3.1 IPv4 Datagram Format . . . . . . . . . . . . . . . . . . . . . . . . . . 136

3.3.2 IP Subnetting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

3.3.3 Public and Private IP Addresses . . . . . . . . . . . . . . . . . . . . 142

3.3.4 Static and Dynamic IP Addresses . . . . . . . . . . . . . . . . . . . 144

3.3.5 An Example of Local Area Network Architecture . . . . . . . 144

3.3.6 IP Version 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

3.4 Domain Structure and IP Routing . . . . . . . . . . . . . . . . . . . . . . . . 149

3.4.1 Routing Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

3.4.2 Routing Implementation Issues . . . . . . . . . . . . . . . . . . . . . 165

3.5 QoS Provision in IP Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

3.5.1 IntServ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

3.5.2 DiffServ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

3.6 IP Traffic Over ATM Networks . . . . . . . . . . . . . . . . . . . . . . . . . . 177

3.6.1 The LIS Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

3.6.2 The Next Hop Routing Protocol . . . . . . . . . . . . . . . . . . . . 180

3.6.3 The Integrated Approach for IP Over ATM . . . . . . . . . . . . 181

3.7 Multi-protocol Label Switching Technology . . . . . . . . . . . . . . . . 183

3.7.1 Comparison Between IP Routing

and Label Switching . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

3.7.2 Operations on Labels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

3.7.3 MPLS Header . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

3.7.4 MPLS Nested Domains . . . . . . . . . . . . . . . . . . . . . . . . . . 189

3.7.5 MPLS Forwarding Tables . . . . . . . . . . . . . . . . . . . . . . . . 190

3.7.6 Protocols for the Creation of an LSP . . . . . . . . . . . . . . . . 193

3.7.7 IP/MPLS Over ATM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

3.7.8 MPLS Traffic Management . . . . . . . . . . . . . . . . . . . . . . . 197

3.7.9 GMPLS Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

xvi Contents

3.8 Transport Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

3.8.1 TCP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

3.8.2 UDP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

3.8.3 Port Numbers and Sockets . . . . . . . . . . . . . . . . . . . . . . . 239

3.9 Next-Generation Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

3.9.1 NGN Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

3.9.2 Geographical Core/Transport Networks . . . . . . . . . . . . . 249

3.9.3 Current and Future Satellite Networks . . . . . . . . . . . . . . 251

3.10 Future Internet Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

Exercises on Part I of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

Part II Queuing Theory and Applications to Networks

4 Survey on Probability Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

4.1 The Notion of Probability and Basic Properties . . . . . . . . . . . . . 265

4.2 Random Variables: Basic Definitions and Properties . . . . . . . . . . 268

4.2.1 Sum of Independent Random Variables . . . . . . . . . . . . . 273

4.2.2 Minimum and Maximum of Random Variables . . . . . . . . 274

4.2.3 Comparisons of Random Variables . . . . . . . . . . . . . . . . . 275

4.2.4 Moments of Random Variables . . . . . . . . . . . . . . . . . . . 276

4.2.5 Random Variables in the Field

of Telecommunications . . . . . . . . . . . . . . . . . . . . . . . . . 279

4.3 Transforms of Random Variables . . . . . . . . . . . . . . . . . . . . . . . 297

4.3.1 The Probability Generating Function . . . . . . . . . . . . . . . 298

4.3.2 The Characteristic Function of a pdf . . . . . . . . . . . . . . . . 306

4.3.3 The Laplace Transform of a pdf . . . . . . . . . . . . . . . . . . . 311

4.4 Methods for the Generation of Random Variables . . . . . . . . . . . 313

4.4.1 Method of the Inverse of the Distribution Function . . . . . 313

4.4.2 Method of the Transform . . . . . . . . . . . . . . . . . . . . . . . . 314

4.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317

5 Markov Chains and Queuing Theory . . . . . . . . . . . . . . . . . . . . . . . . 319

5.1 Queues and Stochastic Processes . . . . . . . . . . . . . . . . . . . . . . . . 319

5.1.1 Compound Arrival Processes and Implications . . . . . . . . 322

5.2 Poisson Arrival Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

5.2.1 Sum of Independent Poisson Processes . . . . . . . . . . . . . . 326

5.2.2 Random Splitting of a Poisson Process . . . . . . . . . . . . . . 326

5.2.3 Compound Poisson Processes . . . . . . . . . . . . . . . . . . . . . 327

5.3 Birth-Death Markov Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

5.4 Notations for Queuing Systems . . . . . . . . . . . . . . . . . . . . . . . . . 330

5.5 Little Theorem and Insensitivity Property . . . . . . . . . . . . . . . . . 331

5.5.1 Proof of the Little Theorem . . . . . . . . . . . . . . . . . . . . . . 332

5.6 M/M/1 Queue Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

Contents xvii

5.7 M/M/1/K Queue Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336

5.7.1 PASTA Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338

5.8 M/M/S Queue Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339

5.9 M/M/S/S Queue Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340

5.10 The M/M/1 Queue Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 344

5.11 Distribution of the Queuing Delays in the FIFO Case . . . . . . . . . 345

5.11.1 M/M/1 Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

5.11.2 M/M/S Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

5.12 Erlang-B Generalization for Non-Poisson Arrivals . . . . . . . . . . . 349

5.12.1 The Traffic Types in the M/M/S/S Queue . . . . . . . . . . . 349

5.12.2 Blocking Probability for Non-Poisson Arrivals . . . . . . . 351

5.13 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364

6 M/G/1 Queuing Theory and Applications . . . . . . . . . . . . . . . . . . . . . 367

6.1 The M/G/1 Queuing Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 367

6.1.1 The M/D/1 Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

6.1.2 The M[comp]/G[b]/1 Queue with Bulk Arrivals

or Bulk Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375

6.2 M/G/1 System Delay Distribution in the FIFO Case . . . . . . . . . . 375

6.3 Numerical Inversion Method of the Laplace Transform . . . . . . . 377

6.4 Impact of the Service Time Distribution on M/G/1 Queue . . . . . 380

6.5 M/G/1 Theory with State-Dependent Arrival Process . . . . . . . . . 383

6.6 Applications of the M/G/1 Analysis to ATM . . . . . . . . . . . . . . . 385

6.7 A Survey of Advanced M/G/1 Cases . . . . . . . . . . . . . . . . . . . . . 389

6.8 Different Imbedding Options for the M/G/1 Theory . . . . . . . . . . 391

6.8.1 Imbedding at Slot End of the Output Line . . . . . . . . . . . 392

6.8.2 Imbedding at Transmission End

of Low-Priority Cells . . . . . . . . . . . . . . . . . . . . . . . . . . 393

6.8.3 Imbedding at Transmission End

of Low-Priority Messages . . . . . . . . . . . . . . . . . . . . . . . 396

6.9 Continuous-Time M/G/1 Queue with “Geometric”

Messages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397

6.9.1 Imbedding at Packet Transmission Completion . . . . . . . 398

6.9.2 Imbedding at Message Transmission Completion . . . . . . 400

6.10 M/G/1 Theory with Differentiated Service Times . . . . . . . . . . . . 402

6.10.1 The Differentiated Theory Applied to Compound

Arrivals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403

6.11 M/D[b]/1 Theory with Batched Service . . . . . . . . . . . . . . . . . . . . 404

6.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

7 Local Area Networks and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 415

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415

7.1.1 Standards for Local Area Networks . . . . . . . . . . . . . . . . 419

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7.2 Contention-Based MAC Protocols . . . . . . . . . . . . . . . . . . . . . . . 421

7.2.1 Aloha Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421

7.2.2 Slotted-Aloha Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . 427

7.2.3 The Aloha Protocol with Ideal Capture Effect . . . . . . . . . 430

7.2.4 Alternative Analytical Approaches

for Aloha Protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432

7.2.5 CSMA Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437

7.3 Demand-Assignment Protocols . . . . . . . . . . . . . . . . . . . . . . . . . 468

7.3.1 Polling Protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468

7.3.2 Token Passing Protocols . . . . . . . . . . . . . . . . . . . . . . . . 469

7.3.3 Analysis of Token and Polling Schemes . . . . . . . . . . . . . 471

7.3.4 Reservation-Aloha (R-Aloha) Protocol . . . . . . . . . . . . . . 475

7.3.5 Packet Reservation Multiple Access (PRMA)

Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480

7.3.6 Efficiency Comparison: CSMA/CD vs. Token

Protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481

7.4 Fixed Assignment Protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . 486

7.4.1 Frequency Division Multiple Access (FDMA) . . . . . . . . . 486

7.4.2 Time Division Multiple Access (TDMA) . . . . . . . . . . . . 486

7.4.3 Code Division Multiple Access (CDMA) . . . . . . . . . . . . 487

7.4.4 Orthogonal Frequency Division Multiple Access

(OFDMA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489

7.4.5 Resource Reuse in Cellular Systems . . . . . . . . . . . . . . . . 489

7.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494

8 Networks of Queues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497

8.1.1 Traffic Rate Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 500

8.1.2 The Little Theorem Applied to the Whole Network . . . . . 500

8.2 Tandem Queues and the Burke Theorem . . . . . . . . . . . . . . . . . . 501

8.3 The Jackson Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502

8.3.1 Analysis of a Queue with Feedback . . . . . . . . . . . . . . . . 504

8.4 Traffic Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506

8.5 Network Planning Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507

8.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

Contents xix

Author Biography

Giovanni Giambene (giambene@unisi.it) was born in Florence, Italy, in 1966.

He received the Dr. Ing. degree in Electronics in 1993 and the Ph.D. degree in

Telecommunications and Informatics in 1997, both from the University of

Florence, Italy. From 1994 to 1997, he was with the Electronic Engineering

Department of the University of Florence, Italy. He was Technical External Secre-

tary of the European Community COST 227 Action (“Integrated Space/Terrestrial

Mobile Networks”). From 1997 to 1998, he was with OTE of the Marconi Group,

Florence, Italy, where he was involved in a GSM development program. In 1999,

he joined the Department of Information Engineering and Mathematical Sciences

of the University of Siena, Italy, first as a research associate and then as an assistant

professor and aggregate professor. Since 2003, he teaches the master-level course

on Networking at the University of Siena. From 1999 to 2003 he participated in the

project “Multimedialita”, financed by the Italian National Research Council (CNR).

From 2000 to 2003, he contributed to the “Personalised Access to Local Informa-

tion and services for tourists” (PALIO) IST Project within the EU FP5 program.

He was vice-chair of the COST 290 Action for its whole duration 2004–2008,

entitled “Traffic and QoS Management in Wireless Multimedia Networks”

(Wi-QoST). He participated in the SatNEx I & II Network of Excellence

(EU FP6 program, 2004–2009) as work package leader of two groups on radio

access techniques and cross-layer air interface design for satellite communication

systems. He contributed to the EU FP7 Coordination Action “Road mapping

technology for enhancing security to protect medical and genetic data” (RADICAL)

as work package leader on security challenges for e-health applications. At present,

he is involved in the ESA SatNEX III research project (CoO3 on “Smart Gateway

Diversity”), in the COST Action IC0906 “Wireless Networking for Moving Objects”

(WiNeMO) and in the EU FP7 Coordination Action called “Responsibility”. He is the

author of more than 120 papers on internationally recognized journals or conferences.

Further details are available on the Web page with the following URL:

http://www.dii.unisi.it/~giambene/

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