Computer Networks and Systems

Transcription

1 Computer Networks and Systems Queueing Theory and Performance Evaluation Third Edition

2 Springer Science+Business Media, LLC

3 Thomas G. Robertazzi Computer Networks and Systems Queueing Theory and Performance Evaluation Third Edition With 116 Figures Springer

4 Thomas G. Robertazzi Department of Electrical Engineering SUNY Stony Brook Stony Brook, NY USA CIP data available. Printed on acid-free paper. 2000, 1994, 1990 Springer Science+Business Media New York Originally published by Springer-Veriag New York, Inc. in 2000 Softcover reprint of the hardcover 3rd edition 2000 All rights reserved. This work may not be translated or copied in whole or in part without the written pennission of the publisher Springer Science+Business Media, LLC, except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any fonn of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the fonner are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely byanyone. Production managed by Jenny Wolkowicki; manufacturing supervised by Joseph Quatela. Camera-ready copy prepared using the author' s Troff files SPIN ISBN ISBN (ebook) DOI /

5 To Marsha, Rachel, and Deanna

6 Preface Statistical performance evaluation has assumed an increasing amount of importance as we seek to design more and more sophisticated communication and information processing systems. The ability to predict a proposed system's performance before one constructs it is an extremely cost effective design tool. This book is meant to be a first-year graduate level introduction to the field of statistical performance evaluation. It is intended for people who work with statistical performance evaluation including engineers, computer scientists and applied mathematicians. As such, it covers continuous time queueing theory (chapters 1-4), stochastic Petri networks (chapter 5), discrete time queueing theory (chapter 6) and recent network traffic modeling work (chapter 7). There is a short appendix at the end of the book that reviews basic probability theory. This material can be taught as a complete semester long course in performance evaluation or queueing theory. Alternatively, one may teach only chapters 2 and 6 in the first half of an introductory computer networking course, as is done at Stony Brook. The second half of the course could use a more protocol oriented text such as ones by Saadawi [SAAD] or Stallings [STALl What is new in the third edition of this book? In addition to the well received material of the second edition, this edition has three major new features. First of all, solutions to all of the chapter 2 through 6 problems are being published in a separate volume by Springer-Verlag. I believe this will be a great aid to students and engineers, computer scientists and applied mathematicians seeking to learn this subject. The second feature is a new chapter 7 on network traffic models that have been the subject of much interest since the publication of the second edition. Chapter 7 includes discussions of continuous and discrete time models, burstiness, self-similar traffic modeling and solution techniques. Lastly, I have added sixteen new problems to chapter 6 on discrete time queueing systems. Many of these involve switching. I am grateful to B. L. Bodnar, J. Blake, X. Chao, J. S. Emer, M. Garrett, R. Guerin, W. Hagen, M. Haviv, H. Huang, Y. C. Jenq, M. Karol, J. F. Kurose, S.-Q. Li, A. C. Liu, J. McKenna, H. T. Mouftah, W. G. Nichols, M. Pinedo, I. Y. Wang, the IEEE, Digital Equipment Corporation and International Business Machines Corporation for allowing material, most of it previously published, to appear in this book. My appreciation of this material has been enhanced by interaction with my students in Stony Brook's computer networks and performance evaluation courses. I am grateful to S. Rappaport for encouraging me to teach the performance evaluation course. Thanks are due for editorial assistance for this edition to Springer-Vedag's T. von Foerster and J. Mallozzi and to 1. Wolkowicki for the production of this book and the solutions volume. Thanks are due to M. Gerla for reviewing the manuscript of the first edition. Thanks are also due to H. Badr, M.

7 VllI Preface Crovella, and S. Rappaport for looking over a draft of chapter 7 and providing valuable feedback. This book benefited from the drawing ability of L. Koh. Certain graphs and tables were made by J.-W. Jeng, K. Ko and J. Shor. Thanks are due to J. Eimer for typing new material for this edition. This book would not have been possible without the use of computer facilities supervised by A. Levochkin and M. Dorojevets. Finally, I would like to dedicate this book to my wife, Marsha and my two daughters, Rachel and Deanna, who made writing this book worthwhile. T.G.R. Stony Brook, N.Y.

8 Contents Preface vii Chapter 1: The Queueing Paradigm 1.1 Introduction Queueing Theory Queueing Models Case Study I: Performance Model of a Distributed File Service By W.G. Nichols and 1.S. Emer Case Study II: Single-bus Multiprocessor Modeling By B.L. Bodnar and A.C. Liu Case Study III: TeraNet, A Lightwave Network Case Study IV: Performance Model of a Shared Medium Packet Switch By R. Guerin Chapter 2: Single Queueing Systems 2.1 Introduction The MIMII Queueing System The Poisson Process Foundations of the Poisson Process Poisson Distribution Mean and Variance The Inter-Arrival Times The Markov Property Exponential Service Times Foundation of the MIMII Queueing System Flows and Balancing The MIMII Queueing System in Detail Little's Law Reversibility and Burke's Theorem Introduction Reversibility Burke's Theorem The State Dependent MIMII Queueing System The General Solution Performance Measures The MIMI lin Queueing System: The Finite Buffer Case The MIMloo Queueing System: Infinite Number of Servers... 59

9 x Contents 2.8 The M/M/m Queueing System: m Parallel Servers with a Queue The M/M/m/m Queue: A Loss System Central Server CPU Model Transient Solution ofthe MIMI Queueing System The Technique The Solution Speeding Up the Computation The M/G/1 Queueing System Introduction Mean Number in the Queueing System Why We Use Departure Instants Probability Distribution of the Number in the Queueing System Priority Systems for Multiclass Traffic To Look Further Problems Chapter 3: Networks of Queues 3.1 Introduction The Product Form Solution Introduction Open Networks The Global Balance The Traffic Equations The Product Form Solution Local Balance Closed Queueing Networks The BCMP Generalization Algebraic Topological Interpretation of the Product Form Solution Introduction A First Look at Building Blocks Building Block Circulatory Structure The Consistency Condition Recursive Solution of Nonproduct Form Networks Introduction Recursive Examples Numerical Implementation of the Equations Queueing Networks with Negative Customers Introduction Product Form Solutions The Chao/Pinedo Model Introduction The Model By X. Chao and M. Pinedo

10 Contents xi To Look Further Problems Chapter 4: Numerical Solution of Models 4.1 Introduction Closed Queueing Networks: Convolution Algorithm Lost in the State Space Convolution Algorithm: Single Customer Class Performance Measures from Normalization Constants Mean Value Analysis State (Load) Independent Servers A Closer Look at the Arrival Theorem State (Load) Independent Servers (Random Routing) PANACEA: Approach for Large Markovian Queueing Networks Introduction The Product Form Solution Conversion to Integral Representation Performance Measures "Normal Usage" Some Transformations Asymptotic Expansions The Pseudonetworks Error Analysis Norton's Equivalent for Queueing Networks Introduction Equivalence Simulation of Communication Networks By J.F. Kurose and H.T. Mouftah Introduction The Statistical Nature of a Simulation Sensitivity Analysis of Simulation Results Speeding up a Simulation To Look Further Problems Chapter 5: Stochastic Petri Nets 5.1 Introduction Bus-oriented Multiprocessor Model Toroidal MPN Lattices The Dining Philosophers Problem A Station-oriented CSMA/CD Protocol Model The Alternating Bit Protocol

11 XII Contents 5.7 SPN's without Product FOTIn Solutions Introduction Nonsafe Resource Sharing Models Synchronization Models Conclusion To Look Further Problems Chapter 6: Discrete Time Queueing Systems 6.1 Introduction Discrete Time Queueing Systems Discrete Time Arrival Processes The Bernoulli Process The Geometric Distribution The Binomial Distribution Poisson Approximation to Binomial Distribution The GeomlGeomlmIN Queueing System The GeomlGeomll1N and GeomlGeomll Queueing Systems Case Study I: Queueing on a Space Division Packet Switch Introduction Output Queueing Input Queueing Case Study II: Queueing on a Single-buffered Banyan Network Introduction The Model Assumptions The Model and Solution Case Study III: DQDB Erasure Station Location Introduction Optimal Location of Erasure Nodes By M.W. Garrett and S.-Q. Li To Look Further Problems Chapter 7: Network Traffic Modeling 7.1 Introduction Continuous Time Models Poisson Process (PP or M) Generally Modulated Poisson Process (GMPP) Markov Modulated Poisson Process (MMPP) Switched Poisson Process (SPP) Interrupted Poisson Process (IPP) Markovian Arrival Process (MAP) Autoregressive Moving Average Model (ARMA) Fluid Flow Approximation Model (FFA) Self-Similarity Source Model (SSS) Renewal Process (RP, GI)

12 Contents xiii Semi-Markov Processes (SMP) Discrete Time Models Deterministic Process (DP) Bernoulli Process (BP) Generally Modulated Deterministic Process (GMDP) Markov Modulated Deterministic Process (MMDP) Switched Deterministic Process (SDP) Interrupted Deterministic Process (ldp) Discrete Time Markovian Arrival Process (DMAP) Discrete Renewal Process (DRP) Solution Methods Simulation Linear Equation Solution Probability Generating Function Fluid Flow Approximation Transient Effect Models Burstiness Ratio of Peak Rate to Mean Rate Coefficient of Variation of Traffic Load Index of Dispersion Spectral Characteristics Some Other Techniques Queueing Performance under Burstiness Self-Similar Traffic Some Basics Self-Similarity The Hurst Effect Roots of Self-Similarity Detecting Self-Similarity Network Performance To Look Further Appendix: Probability Theory Review A.I Probability A.2 Densities and Distribution Functions A.3 Joint Densities and Distributions A.4 Expectations A.5 Convolution A.6 Combinatorics A.7 Some Useful Summations A.8 Useful Moment-generating Function Identities References., About the Author Index