Performance of computer communication systems : a model-based approach

499 Pages·1998·31.823 MB·English

by  Boudewijn R Haverkort

Performance of Computer Communication Systems: A Model-Based Approach.
Boudewijn R. Haverkort
Copyright © 1998 John Wiley & Sons, Ltd
Print ISBN 0-471-197228-2 Electronic ISBN 0-470-84192-3
PERFO~CI~ 0E;
CoMPUTER
COMMUNICA~ON
SYSTEMS
PERFORMAN~E~F
COMPUTER
COMMUNICATION
SYSTEMS
A Model-Based Approach
BOUDEWIJN R. HAVERKORT
Rheinisch- Westfalische Technische
Hochschule Aachen, Germany
John Wiley & Sons, Ltd
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Reprinted June 1999
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Library of Congress Cataloguing in Publication Data
Haverkort, Boudewijn R.
Performance of computer communication systems : a model-based
approach / Boudewijn R. Haverkort.
p. cm.
Includes bibliographical references and index.
ISBN O-471-97228-2 (alk. paper)
1. Computer networks-Evaluation. 2. Electronic digital
computers-Evaluation. 3. Queuing theory. 4. Telecommunication
systems-Evaluation, 5. Stochastic processes. I. Title.
TK5 105.5.H375 1998
004.6-dc2 1 98-27222
CIP
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
ISBN 0 471 97228 2
Produced from Postcript files supplied by the author.
Printed and bound in Great Britain by Biddles Ltd, Guildford and King’s Lynn.
This book is printed on acid-free paper responsibly manufactured from sustainable
forestry, in which at least two trees are planted for each one used in paper production.
In memory of my father
Johannes Hermannus Hendrikus Haverkort
Contents
Preface xvii
I Performance modelling with stochastic processes 1
1 Introduction 3
1.1 Performance evaluation: aim and approach .................. 3
1.2 Model solution techniques ........................... 8
1.3 Stochastic models ................................ 9
1.4 Queueing models ................................ 11
1.4.1 The principle of queueing ....................... 11
1.4.2 Single queues: the Kendall notation .................. 13
1.5 Tool support. .................................. 15
1.5.1 Model construction ........................... 15
1.5.2 Model solution ............................. 18
1.6 Further reading ................................. 19
1.7 Exercises ..................................... 19
2 Little’s law and the MIMI1 queue 21
2.1 Little’s law ................................... 21
2.1.1 Understanding Little’s law ....................... 21
2.1.2 Proof of Little’s law ........................... 24
2.2 The simplest queueing model: the MI M 11 queue ............... 25
2.3 Further reading ................................. 28
2.4 Exercises ..................................... 28
3 Stochastic processes 31
31
3.1 Overview of stochastic processes . . . . . . . . . . . . . . . . . . . . . . . .
. . .
Contents
Vlll
3.2 Renewal processes ................................ 34
3.3 Discrete-time Markov chains .......................... 37
3.4 Convergence properties of Markov chains ................... 41
3.5 Continuous-time Markov chains ........................ 43
3.5.1 From DTMC to CTMC ........................ 43
3.5.2 Evaluating the steady-state and transient behaviour ......... 45
3.6 Semi-Markov chains ............................... 51
3.7 The birth-death process ............................ 53
3.8 The Poisson process. .............................. 53
3.9 Renewal processes as arrival processes ..................... 54
3.9.1 Phase-type distributions ........................ 55
3.9.2 Phase-type renewal processes ..................... 58
3.10 Summary of Markov chains .......................... 62
3.11 Further reading ................................. 63
3.12 Exercises. .................................... 63
II Single-server queueing models 67
4 MIMI1 queueing models 69
4.1 General solution of the MIMI1 queue ..................... 70
4.2 The MIMI1 queue with constant rates ..................... 73
4.3 The PASTA property .............................. 74
4.4 Response time distribution in the MIMI1 queue ............... 76
4.5 The MIMI m multi-server queue ........................ 77
4.6 The MIMI 00 infinite-server queue ....................... 79
4.7 Job allocation in heterogeneous multi-processors ............... 80
4.8 The MIMI11 m single-server queue with bounded buffer ........... 83
4.9 The MIMI m Im multi-server queue without buffer ............... 85
4.10 The MIM(l((K queue or the terminal model ................. 86
4.11 Mean values for the terminal model ...................... 88
4.12 Further reading ................................. 92
4.13 Exercises. .................................... 92
5 MIGjl-FCFS queueing models 95
5.1 The M/Gil result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.2 An intuitive proof of the M/G/l result . . . . . . . . . . . . . . . . . . . . . 99
Contents iX
5.2.1 Residual lifetime ............................ 100
5.2,2 Intuitive proof .............................. 103
5.3 A formal proof of the MlGll result ...................... 104
5.4 The MlGll model with batch arrivals ..................... 107
5.5 MI G/ 1 queueing systems with server breakdowns ............... 109
5.5.1 Single arrivals .............................. 110
5.5.2 Batch arrivals .............................. 111
5.6 Further reading ................................. 112
5.7 Exercises ..................................... 112
6 M/G/ 1 queueing models with various scheduling disciplines 115
6.1 Non-preemptive priority scheduling ...................... 115
6.2 Preemptive priority scheduling ......................... 121
6.3 Shortest job next scheduling .......................... 123
6.4 Round robin scheduling ............................. 126
6.5 Processor sharing scheduling .......................... 128
6.6 Scheduling based on elapsed processing time ................. 129
6.7 Further reading ................................. 131
6.8 Exercises ..................................... 131
7 G)Mll-FCFS and GIGIl-FCFS queueing models 133
7.1 The GlMll queue ................................ 133
7.2 The GIG11 queue ................................ 139
7.3 Approximate results for the G(GI 1 queue ................... 143
7.4 Further reading ................................. 143
7.5 Exercises ..................................... 144
8 PHIPHIl queueing models 145
8.1 The MIMI1 queue ................................ 145
8.2 The PHIPHIl queue .............................. 148
8.2.1 A structured description of the CTMC ................ 148
8.2.2 Matrix-geometric solution ....................... 152
8.2.3 Stability issues ............................. 153
8.2.4 Performance measures ......................... 154
8.3 Numerical aspects ................................ 155
8.3.1 Solving the boundary equations .................... 155
Contents
X
8.3.2 A successive substitution algorithm .................. 156
8.3.3 The logarithmic reduction algorithm ................. 158
8.4 A few special cases ............................... 162
8.4.1 The M/PHI1 q ueue: an explicit expression for R ........... 162
8.4.2 The PHlMlm queue ........................... 163
8.5 The caudal curve ................................ 164
8.6 Other models with matrix-geometric solution ................. 167
8.7 Further reading ................................. 169
8.8 Exercises ..................................... 169
9 Polling models 173
9.1 Characterisation of polling models ....................... 173
9.1.1 Basic terminology ............................ 174
9.1.2 The visit order ............................. 174
9.1.3 The scheduling strategy ........................ 176
9.2 Cyclic polling: cycle time and conservation law ............... 177
9.3 Count-based symmetric cyclic polling models ................. 180
9.4 Count-based asymmetric cyclic polling models ................ 183
9.4.1 Exhaustive service: exact analysis ................... 183
9.4.2 Some approximate results ....................... 184
9.5 Performance evaluation of the IBM token ring ................ 186
9.5.1 Timed-token access mechanisms .................... 186
9.5.2 Approximating the timed-token access mechanism .......... 187
9.5.3 The influence of the token holding timer ............... 189
9.6 Local and global time-based polling models .................. 191
9.7 Further reading ................................. 194
9.8 Exercises ..................................... 194
III Queueing network models 197
10 Open queueing networks 199
10.1 Basic terminology ................................ 200
10.2 Feed-forward queueing networks ........................ 200
10.2.1 The MIMI1 queue ............................ 200
10.2.2 Series of MIMI1 queues ......................... 201
10.2.3 Feed-forward queueing networks .................... 204