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“Behold, I will send my angel who shallgo before thee, keep thee in the journey and bring thee into the place that I have prepared.” The Holy Bible, Exodus 23, 20 to Chiara Matteo, Luca,

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Switching Theory

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Switching Theory

Architectures and Performance

in Broadband ATM Networks

Achille Pattavina

Politecnico di Milano, Italy

JOHN WILEY & SONS

Chichester • New York • Weinheim • Brisbane • Singapore • Torontobook_title Page iii Tuesday, November 18, 1997 4:58 pm

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“Behold, I will send my angel who shall

go before thee, keep thee in the journey and bring thee into the place that I have prepared.”

(The Holy Bible, Exodus 23, 20)

to Chiara Matteo, Luca, Sara, Maria

book_acks Page 5 Tuesday, November 18, 1997 4:58 pm

Switching Theory: Architecture and Performance in Broadband ATM Networks

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fatti non foste a viver come bruti,

ma per seguir virtute e conoscenza.” (Dante, Inferno, Canto XXVI)

“

of your senses that remains, experience

of the unpeopled world behind the Sun Consider your origin: ye were not formed to live like brutes, but to follow virtue and knowledge.”

(Dante, Inferno, Canto XXVI)

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Preface xv

Chapter 1 Broadband Integrated Services Digital Network 1

1.1 Current Networking Scenario 1

1.1.1 Communication services 1

1.1.2 Networking issues 4

1.2 The Path to Broadband Networking 6

1.2.1 Network evolution through ISDN to B-ISDN 6

1.2.2 The protocol reference model 10

1.3 Transfer Mode and Control of the B-ISDN 14

1.3.1 Asynchronous time division multiplexing 14

1.3.2 Congestion control issues 16

1.4 Synchronous Digital Transmission 18

1.4.1 SDH basic features 19

1.4.2 SDH multiplexing structure 21

1.4.3 Synchronization by pointers 27

1.4.4 Mapping of SDH elements 31

1.5 The ATM Standard 33

1.5.1 Protocol reference model 34

1.5.2 The physical layer 39

1.5.3 The ATM layer 42

1.5.4 The ATM adaptation layer 45

1.5.4.1 AAL Type 1 47

1.5.4.2 AAL Type 2 48

1.5.4.3 AAL Type 3/4 48

1.5.4.4 AAL Type 5 49

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1.5.4.5 AAL payload capacity 50

1.6 References 51

1.7 Problems 52

Chapter 2 Interconnection Networks 53

2.1 Basic Network Concepts 53

2.1.1 Equivalence between networks 57

2.1.2 Crossbar network based on splitters and combiners 60

2.2 Full-connection Multistage Networks 63

2.3 Partial-connection Multistage Networks 64

2.3.1 Banyan networks 65

2.3.1.1 Banyan network topologies 66

2.3.1.2 Banyan network properties 70

2.3.2 Sorting networks 75

2.3.2.1 Merging networks 76

2.3.2.2 Sorting networks 80

2.4 Proof of Merging Schemes 86

2.4.1 Odd–even merge sorting 86

2.4.2 Bitonic merge sorting 87

2.5 References 89

2.6 Problems 90

Chapter 3 Rearrangeable Networks 91

3.2.1 Partially self-routing PC networks 96

3.2.1.1 Horizontal extension 97

3.2.1.2 Vertical replication 103

3.2.1.3 Vertical replication with horizontal extension 107

3.2.1.4 Bounds on PC rearrangeable networks 109

3.2.2 Fully self-routing PC networks 114

3.2.3 Fully self-routing PC networks with output multiplexing 118

3.3 Bounds on the Network Cost Function 123

3.4 References 124

3.5 Problems 126

Chapter 4 Non-blocking Networks 127

4.1.1 Two-stage network 127

4.1.2 Three-stage network 128

4.1.3 Recursive network construction 130

4.2.1 Vertical replication 134

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Contents xi

4.2.2 Vertical replication with horizontal extension 136

4.2.3 Link dilation 142

4.2.4 EGS networks 144

4.3 Comparison of Non-blocking Networks 150

4.4 Bounds on the Network Cost Function 152

4.6 Problems 155

Chapter 5 The ATM Switch Model 157

5.1 The Switch Model 159

5.2 ATM Switch Taxonomy 163

Chapter 6 ATM Switching with Minimum-Depth Blocking Networks 167

6.1 Unbuffered Networks 168

6.1.1 Crossbar and basic banyan networks 168

6.1.1.1 Basic structures 168

6.1.1.2 Performance 169

6.1.2 Enhanced banyan networks 172

6.1.2.1 Structures 172

6.2 Networks with a Single Plane and Internal Queueing 177

6.2.1 Input queueing 181

6.2.2 Output queueing 184

6.2.3 Shared queueing 192

6.2.4 Performance 197

6.3 Networks with Unbuffered Parallel Switching Planes 204

6.3.1 Basic architectures 204

6.3.2 Architectures with output queueing 205

6.3.2.1 Specific architectures 206

6.3.3 Architectures with combined input–output queueing 212

6.3.3.1 Models for performance analysis 213

6.3.3.2 Performance results 216

6.4 Additional Remarks 221

6.6 Problems 224

Chapter 7 ATM Switching with Non-Blocking Single-Queueing Networks 227

7.1 Input Queueing 229

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7.1.1.1 The Three-Phase switch 229

7.1.1.2 The Ring-Reservation switch 234

7.1.2 Performance analysis 236

7.1.2.1 Asymptotic throughput 237

7.1.2.2 Packet delay 239

7.1.2.3 Packet loss probability 240

7.1.3 Enhanced architectures 241

7.1.3.1 Architecture with channel grouping 242

7.1.3.2 Architecture with windowing 251

7.2 Output Queueing 259

7.3 Shared Queueing 267

7.4 Performance Comparison of Different Queueings 274

7.7 Problems 279

Chapter 8 ATM Switching with Non-Blocking Multiple-Queueing Networks 281

8.1 Combined Input–Output Queueing 284

8.1.1.1 Internal queue loss 284

8.1.1.2 Internal backpressure 288

8.1.2.1 Constrained output queue capacity 296

8.1.2.2 Arbitrary input and output queue capacities 299

8.1.3 Architectures with parallel switching planes 315

8.2 Combined Shared-Output Queueing 317

8.2.1 Basic architecture 318

8.3 Combined Input-Shared Queueing 324

8.4 Comparison of Switch Capacities in Non-blocking Switches 331

8.7 Problems 335

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Contents xiii

Chapter 9 ATM Switching with Arbitrary-Depth Blocking

Networks 337

9.1 Switch Architectures Based on Deflection Routing 338

9.1.1 The Shuffleout switch 339

9.1.2 The Shuffle Self-Routing switch 342

9.1.3 The Rerouting switch 343

9.1.4 The Dual Shuffle switch 345

9.2 Switch Architectures Based on Simpler SEs 350

9.2.1 Previous architectures with SEs 351

9.2.2 The Tandem Banyan switch 351

9.3 Architecture Enhancements 355

9.3.1 Extended routing 355

9.3.2 Interstage bridging 355

9.4 Performance Evaluation and Comparison 358

9.4.1 The Shuffleout switch 358

9.4.1.1 Network with 2 × 4 SEs 358

9.4.1.2 Network with 2 × 2 SEs 360

9.4.1.3 Network performance 361

9.4.2 The Shuffle Self-Routing switch 363

9.4.2.1 Basic network with 2 × 4 SEs 364

9.4.2.2 Basic network with 2 × 2 SEs 365

9.4.2.3 Basic network performance 365

9.4.2.4 Network with extended routing and 2 × 4 SEs 366

9.4.2.5 Network with extended routing and 2 × 2 SEs 368

9.4.2.6 Network performance with extended routing 369

9.4.3 The Rerouting switch 370

9.4.4 The Dual Shuffle switch 373

9.4.5 The Tandem Banyan switch 376

9.4.6 Interconnection network performance comparison 377

9.4.7 Overall switch performance 382

9.5 Switch Architectures with Parallel Switching Planes 384

9.8 Problems 390

Appendix Synchronous Queues 391

A.1 Synchronous Single-server Queues 392

A.1.1 The M/D/1 queue 392

A.1.1.1 The asynchronous M/G/1 queue 392

A.1.1.2 The asynchronous M/D/1 queue 394

A.1.1.3 The synchronous M/D/1 queue 395

A.1.2 The Geom(N)/D/1 queue 398

A.1.3 The Geom/G/1 queue 399

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A.1.4 The Geom/G/1/B queue 399

A.2 Synchronous Multiple-server Queues 401

A.2.1 The M/D/C queue 401

A.2.2 The Geom(N)/D/C/B queue 402

A.3 References 408

Index 409

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Broadband networks based on the Asynchronous Transfer Mode (ATM) standard are becomingmore and more popular worldwide for their flexibility in providing an integrated transport ofheterogeneous kinds of communication services The book is intended to provide the state ofthe art in the field of switching for broadband ATM networks by covering three different areas:the theory of switching in interconnection networks, the architectures of ATM switching fab-rics and the traffic performance of these switching fabrics

A full coverage of switching theory is provided starting from the very first steps taken inthis area about forty years ago to describe three-stage interconnection networks, either non-blocking or rearrangeable It is pointed out how this classical theory is no longer effective todescribe switching environments when hundreds of million packets per second must beswitched The brand new theory of multistage interconnection networks that has emergedfrom the studies of the last ten years is described and made homogeneous The key role played

by sorting and banyan networks of this new theory within the area of broadband ATM working is highlighted

net-The different types of ATM switching architectures are classified according to their mental parameters, related to the properties of their interconnection network and to the type

funda-of cell queueing adopted in the switching fabric ATM switching fabrics are characterized byenormous amounts of carried traffic if compared to the operations of classical circuit-switching

or packet-switching fabrics Thus the type of banyan network classes that can be effectivelyused in these switching fabrics is shown

Each class of switching architecture is evaluated in terms of its traffic performance, that isswitch capacity, packet delay and loss probability, when a random traffic is offered to theswitch Analytical models, as well as computer simulation, are used for the numerical evalua-tion of the traffic parameters by studying the effect of the different network parameters

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Putting together the material for this book has required roughly ten years of studies andresearch The active contribution across these years of many students of the Engineering Fac-ulty of the Politecnico di Milano, who have prepared their theses, has made possible thecollection of the material used here Therefore I am grateful to all of them I am deeplyindebted to Professor Maurizio Decina for inspiring interest and passion in the study ofswitching theory and for his continual confidence in me Without him this book could neverhave been completed Last but not least, my family deserves the same gratitude, since writingthis book has been possible only by stealing a lot of free time that I should have spent with mywife and children.

Achille PattavinaMilan, 1997

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Chapter 1 Broadband Integrated Services

Digital Network

A broad overview on the Broadband Integrated Services Digital Network (B-ISDN) is heregiven The key issues of the communication environment are first outlined (Section 1.1) Thenthe main steps leading to the evolution to the B-ISDN are described (Section 1.2), by also dis-cussing issues related to the transfer mode and to the congestion control of the B-ISDN(Section 1.3) The main features of the B-ISDN in terms of transmission systems that are based

on the SDH standard (Section 1.4) and of communication protocols that are based on theATM standard (Section 1.5) are also presented

1.1 Current Networking Scenario

The key features of the current communication environment are now briefly discussed,namely the characterization of the communication services to be provided as well as the fea-tures and properties of the underlying communication network that is supposed to support theprevious services

1.1.1 Communication servicesThe key parameters of a telecommunication service cannot be easily identified, owing to thevery different nature of the various services that can be envisioned The reason is the rapidlychanging technological environment taking place in the eighties In fact, a person living in thesixties, who faced the only provision of the basic telephone service and the first low-speed dataservices, could rather easily classify the basic parameters of these two services The tremendouspush in the potential provision of telecommunication services enabled by the current network-ing capability makes such classification harder year after year In fact, not only are new servicesbeing thought and network-engineered in a span of a few years, but also the tremendous

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progress in VLSI technology makes it very difficult to foresee the new network capabilities thatthe end-users will be able to exploit even in the very near future

A feature that can be always defined for a communication service provided within a set of

n end-users irrespective of the supporting network is the service direction A service is tional if only one of the n end-users is the source of information, the others being the sink; atypical example of unidirectional service is broadcast television A service is multidirectional if atleast one of the n end-users is both a source and a sink of information For decades a multidi-rectional telecommunication service involved only two end-users, thus configuring abidirectional communication service Only in the seventies and eighties did the interest in pro-viding communication service within a set of more than two users grow; consider, e.g., theelectronic-mail service, videoconferencing, etc Apparently, multidirectional communicationservices, much more than unidirectional services, raise the most complete set of issues related

unidirec-to the engineering of a telecommunication network

It is widely agreed that telecommunications services can be divided into three broadclasses, that is sound, data and image services These three classes have been developed and grad-ually enriched during the years as more powerful telecommunication and computing deviceswere made available Sound services, such as the basic telephone service (today referred to as

plain old telephone service - POTS), have been provided first with basically unchanged servicecharacteristics for decades Data services have started to be provided in the sixties with theearly development of computers, with tremendous service upgrades in the seventies and eight-ies in terms of amounts of information transported per second and features of the data service.For about three decades the image services, such as broadcast television, have been providedonly as unidirectional Only in the last decade have the multidirectional services, such as video

on demand, videotelephony, been made affordable to the potential users

Communication services could be initially classified based on their information capacity,which corresponds to the typical rate (bit/s) at which the information is required to be carried

by the network from the source to the destination(s) This parameter depends on technicalissues such as the recommendations from the international standard bodies, the features of thecommunication network, the required network performance, etc A rough indication of theinformation capacity characterizing some of the communication services is given in Table 1.1,where three classes have been identified: low-speed services with rates up to 100 kbit/s, medium- speed services with rates between 0.1 and 10 Mbit/s, and high-speed services with rates above 10Mbit/s Examples of low-speed services are voice (PCM or compressed), telemetry, terminal-to-host interaction, slow-scan video surveillance, videotelephony, credit-card authorization atpoint of sales (POS) HI-FI sound, host-to-host interaction in a LAN and videoconferencingrepresent samples of medium-speed services Among data applications characterized by a highspeed we can mention high-speed LANs or MANs, data exchange in an environment ofsupercomputers However, most of the applications in the area of high speed are image ser-vices These services range from compressed television to conventional uncompressedtelevision, with bit rates in the range 1–500 Mbit/s Nevertheless, note that these indicative bitrates change significantly when we take into account that coding techniques are progressing sorapidly that the above rates about video services can be reduced by one order of magnitude oreven more

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4 Broadband Integrated Services Digital Network

unidirectional broadcasting TV (either conventional or high quality) However the mentionedprogress in coding techniques can significantly modify the burstiness factor of an image infor-mation source for a given channel rate enabling its reduction by more than one order ofmagnitude

Two features of a communication service are felt as becoming more and more important tothe user, that is the multipoint and multimedia capability of a communication service A multi-point service, representing the evolution of the basic point-to-point service, enables more thantwo users to be involved in the same communication Also a multimedia service can be seen asthe evolution of the “single-medium” service; a multimedia service consists in transportingdifferent types of information between the end-users by keeping a time relation in the trans-port of the different information types, for example voice and data, or images coupled withsounds and texts Both multipoint and multimedia communication services are likely to play avery important role in the social and business community In fact a business meeting to bejoined by people from different cities or even different countries can be accomplished bymeans of videoconferencing by keeping each partner in his own office University lecturescould be delivered from a central university to distributed faculty locations spread over thecountry by means of a multipoint multimedia channel conveying not only the speaker's imageand voice, as well as the students' questions, but also texts and other information

1.1.2 Networking issues

A parallel evolution of two different network types has taken place in the last decades: works for the provision of the basic voice service on the one hand, and networks for thesupport of data services on the other hand Voice signals were the first type of information to

net-be transported by a communication network several decades ago based on the circuit-switching

transfer mode: a physical channel crossing one or more switching nodes was made availableexclusively to two end-users to be used for the information transfer between them The set-up

Figure 1.1 Service burstiness factor

Packet Switching

Voice

Video Uncompressed

Compressed Low

Speed Data

Terminal

To Host

Super Computer

Low Speed LAN High Speed LAN/MAN Image

Peak Service Bit-Rate (bit/s)

Audio Video Conference

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