SWITCHING AND TRAFFIC THEORY FOR INTEGRATED BROADBAND NETWORKS THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE COMMUNICATIONS AND INFORMATION THEORY Consulting Editor Robert Gallager Other books in the series: Digital Communications. Edward A. Lee, David G. Messer Schmitt ISBN 0-89838-274-2 An Introduction to Cryptology. Henk C.A. van Tilborg ISBN 0-89838-271-8 Finite Fields for Computer Scientists and Engineers. Robert J. McEliece ISBN 0-89838-191-6 An Introduction to Error Correcting Codes With Applications. Scott A. Vanstone and Paul C. van Oorschot, ISBN 0-7923-9017-2 Source Coding Theory. Robert M. Gray ISBN 0-7923-9048-2 SWITCHING AND TRAFFIC THEORY FOR INTEGRATED BROADBAND NETWORKS by Joseph Y. Hui Rutgers University foreword by Robert G. Gallager SPRINGER SCIENCE+BUSINESS MEDIA, LLC Library of Congress Cataloging-in-Publication Data Hui, Joseph yu Ngai. Switching and traffic theory for integrated broadband networks / by Joseph Y. Hui. p. cm. — (The Kluwer international series in engineering and computer science. Communications and information theory) Includes bibliographical references. ISBN 978-1-4613-6436-8 ISBN 978-1-4615-3264-4 (eBook) DOI 10.1007/978-1-4615-3264-4 1. Telecommunication switching systems. 2. Broadband communication systems. I Titi* n. Series. TK5103.8H85 1990 621.382—dc20 89-26704 CIP Copyright © 1990 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 1990 Tenth Printing 2001. Softcover reprint of the hardcover 1st edition 1990 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media, LLC. This printing is a digital duplication of the original edition. CONTENTS FOREWORD ix PREFACE xi Chapter 1. Integrated Broadband Services and Networks­ An Introduction 1.1 Communication Networking 2 1.2 Broadband Technologies 4 1.3 Broadband Services 9 1.4 To Integrate or Not to Integrate 11 1.5 Outline of the Book 14 1.6 Exercises 16 1.7 References 21 PART I: SWITCHING THEORY Chapter 2. Broadband Integrated Access and Multiplexing 25 2.1 Time Division Multiplexing for Multi-Rate Services 26 2.2 The Synchronous Transfer Mode 27 2.3 The Asynchronous Transfer Mode 31 2.4 Time Division Multiplexing Techniques for Bursty Services 35 2.5 Switching Mechanisms by Time or Space Division 38 2.6 Time Multiplexed Space Division Switching 42 2.7 Appendix-What is in a Label? 47 2.8 Exercises 48 2.9 References 50 Chapter 3. Point-to-Point Multi-Stage Circuit Switching 53 3.1 Point-to-Point Circuit Switching 53 3.2 Cost Criteria for Switching 56 3.3 Multi-Stage Switching Networks 60 vi Contents 3.4 Representing Connections by Paull's Matrix 61 3.5 Strict-Sense Non-Blocking Clos Networks 64 3.6 Rearrangeable Networks 66 3.7 Recursive Construction of Switching Networks 70 3.8 The Cantor Network 74 3.9 Control Algorithms 77 3.10 Exercises 80 3.11 References 82 Chapter 4. Multi-Point and Generalized Circuit Switching 85 4.1 Generalized Circuit Switching 85 4.2 Combinatorial Bounds on Crosspoint Complexity 89 4.3 Two Stage Factorization of Compact Superconcentrators 94 4.4 Superconcentrators and Distribution Networks-A Dual 99 4.5 Construction of Copy Networks 101 4.6 Construction of Multi-Point Networks 104 4.7 Alternative Multi-Point Networks 106 4.8 Exercises 108 4.9 References 111 Chapter 5. From Multi-Rate Circuit Switching to Fast Packet Switching 113 5.1 Depth-First-Search Circuit Hunting 114 5.2 Point-to-Point Interconnection of Multi-Slot TOM 117 5.3 Fast Packet Switching 119 5.4 Self-Routing Banyan Networks 126 5.5 Combinatorial Limitations of Banyan Networks 131 5.6 Appendix-Non-Blocking Conditions for Banyan Networks 134 5.7 Exercises 135 5.8 References 136 Chapter 6. Applying Sorting for Self-Routing and Non-Blocking Switches 139 6.1 Types of Blocking for a Packet Switch 140 Contents vii 6.2 Sorting Networks for Removing Internal Blocking 144 6.3 Resolving Output Conflicts for Packet Switching 152 6.4 Easing Head of Line Blocking 159 6.5 A Postlude-Integrated Circuit and Packet Switching 161 6.6 Appendix-Self-Routing Multi-Point Switching 164 6.7 Exercises 170 6.8 References 173 PART II: TRAFFIC THEORY Chapter 7. Terminal and Aggregate Traffic 177 7.1 Finite State Models for Terminals 178 7.2 Modeling of State Transitions 182 7.3 Steady State Probabilities 184 7.4 Superposition of Traffic 186 7.5 Traffic Distribution for Alternating State Processes 191 7.6 Traffic Distribution for Poisson Processes 193 7.7 Broadband Limits and The Law of Large Numbers 199 7.8 Estimating the Traffic Tail Distribution 201 7.9 Appendix-Improved Large Deviation Approximation 203 7.10 Exercises 207 7.11 References 208 Chapter 8. Blocking for Single-Stage Resource Sharing 211 8.1 Sharing of Finite Resources 212 8.2 Truncated Markov Chains and Blocking Probabilities 215 8.3 Insensitivity of Blocking Probabilities 221 8.4 The Equivalent Random Method 227 8.5 Traffic Engineering for Multi-Rate Terminals 230 8.6 Bandwidth Allocation for Bursty Calls 236 8.7 Exercises 238 8.8 References 242 Chapter 9. Blocking for Multi-Stage Resource Sharing 245 9.1 The Multi-Commodity Resource Sharing Problem 246 viii Contents 9.2 Blocking for Unique Path Routing 247 9.3 Alternative Path Routing-The Lee Method 248 9.4 Assumptions for Approximating Blocking Probabilities 254 9.5 Alternative Path Routing-The lacobaeus Method 256 9.6 Complexity of Asymptotically Non-Blocking Networks 262 9.7 Exercises 267 9.8 References 269 Chapter 10. Queueing for Single-Stage Packet Networks 271 10.1 The MIMlm Queue 274 10.2 The MIGII Queue-Mean Value Analysis 276 10.3 The MIGII Queue-Transform Method 280 10.4 Decomposing the Multi-Queue/Multi-Server System 284 10.5 HOL Effect for Packet Multiplexers 290 10.6 HOL Effect for Packet Switches 291 10.7 Load Imbalance for Single-Stage Packet Switches 298 10.8 Queueing for Multi-Cast Packet Switches 301 10.9 Exercises 304 10.10 References 310 Chapter II. Queueing for Multi-Stage Packet Networks 313 11.1 Multi-Stages of MIMII Queues 314 11.2 Open and Closed Queueing Networks 322 11.3 Application to Multi-Stage Packet Switching 326 11.4 Analysis of Banyan Network with Limited Buffering 331 11.5 Local Congestion in Banyan Network 334 11.6 Appendix-Traffic Distribution for Permutations 336 11.7 Exercises 338 11.8 References 340 INDEX 343 Foreword The rapid development of optical fiber transmission technology has created the possibility for constructing digital networks that are as ubiquitous as the current voice network but which can carry video, voice, and data in massive qlJantities. How and when such networks will evolve, who will pay for them, and what new applications will use them is anyone's guess. There appears to be no doubt, however, that the trend in telecommunication networks is toward far greater transmission speeds and toward greater heterogeneity in the requirements of different applications. This book treats some of the central problems involved in these networks of the future. First, how does one switch data at speeds orders of magnitude faster than that of existing networks? This problem has roots in both classical switching for telephony and in switching for packet networks. There are a number of new twists here, however. The first is that the high speeds necessitate the use of highly parallel processing and place a high premium on computational simplicity. The second is that the required data speeds and allowable delays of different applications differ by many orders of magnitude. The third is that it might be desirable to support both point to point applications and also applications involving broadcast from one source to a large set of destinations. The second major problem is that of traffic analysis or performance analysis for future networks. The roots for this problem again go back to telephony and to data networks, both of which are rooted in queueing theory. The new twists here are, first, that studying traffic flowing through various stages of the switches is more important than studying the traffic on the network links. Next, the heterogeneity of required speeds and allowable delays for different applications is important, and also the possibility of broadcast applications is x Foreword important. The reader will be pleasantly surprised to find that most of the topics here are quite accessible. An undergraduate senior in electrical engineering or computer science certainly has the background (although not necessarily the maturity) to understand switching for future networks as developed in the first half of the book. The traffic analysis in the second half requires quite a bit of facility with probability, but given this facility, the material is again surprisingly accessible. Many of the results here are not found elsewhere in book form and have only appeared relatively recently in journals. Professor Hui, however, has managed to pull all these results together into an integrated whole. There is quite a bit of discussion about engineering constraints and practical aspects of the subject, but it is placed within a conceptual framework that helps the reader develop an overall understanding and intuition for the issues involved in designing high speed networks. There will probably be a large number of books coming out in this area in the next few years, and one hopes that this book will set a standard that these other books will follow.