Performability Modelling Techniques and Tools

Computer scientists and engineers will find this excellent overview compulsive reading as will postgraduates and researchers in computer science and related fields.

Boudewijn R. Haverkort is the editor of Performability Modelling : Techniques and Tools, published by Wiley. Raymond Marie is the editor of Performability Modelling : Techniques and Tools, published by Wiley.

Contributing authors

v

Foreword

xiii

Preface

xvii

Introduction

1

(10)

The performability concept

1

(2)

Mathematical framework

3

(4)

Overview of the book

7

(4)

Queues with Breakdowns

11

(20)

Introduction

11

(1)

The multiprocessor queue with independent interruptions

12

(9)

Generating functions

14

(1)

Matrix-geometric solution

15

(1)

Spectral expansion

16

(1)

Comparison

17

(2)

Asymptotics

19

(2)

Generalizations

21

(4)

Several queues coupled by breakdowns

25

(5)

Conclusion

30

(1)

The Uniformization Method in Performability Analysis

31

(28)

Introduction

31

(2)

The uniformization technique

33

(9)

The basic approach

33

(4)

Extensions to the basic approach

37

(5)

Expected values

42

(5)

Basic results

43

(2)

Additional results

45

(2)

Probability distributions

47

(10)

Conclusions

57

(2)

Closed-Form Solutions for Performability

59

(24)

Introduction

59

(3)

Reward models

62

(1)

Properties of reward model solutions

63

(4)

Definition and genesis of closed-form solutions

67

(7)

Analytical-probabilistic approaches

68

(3)

Direct probabilistic approaches

71

(2)

Computational complexity

73

(1)

Alternative solution of reward models

74

(3)

Conclusions

77

(1)

Appendices

78

(5)

Proof of equation (4.3)

78

(3)

Proof of theorem 4.1

81

(1)

Proof of equation (4.13)

82

(1)

Markov-Reward Models and Hyperbolic Systems

83

(24)

Introduction

84

(4)

Motivation

84

(1)

Markov-reward process

85

(1)

Scope and organization

86

(2)

Duality in Markov-reward models

88

(5)

Dual systems of hyperbolic PDEs

88

(2)

Duality in the transform domain

90

(1)

Dual systems of moment recursions

91

(2)

Method of characteristics and uniformization

93

(9)

Uniformized renewal equation and the MOC

93

(2)

Uniformization as the analytic solution of an infinite set of scalar PDEs

95

(3)

Successive approximation (Picard's method)

98

(2)

Asymptotic properties

100

(2)

Conclusions and future directions

102

(2)

Appendix: Distribution of cumulative operational time

104

(3)

Monotonicity and Error Bound Results

107

(32)

Introduction

107

(3)

Preliminaries and a motivating example

110

(8)

Marginal expectations

111

(1)

Cumulative measures

112

(1)

A performability example

113

(5)

Monotonicity in time

118

(6)

A performability model

119

(1)

Time monotonicity results

119

(4)

A performability application

123

(1)

Comparison results

124

(8)

Introduction

124

(1)

General comparison lemma

125

(2)

A special performability application

127

(5)

Error bound results

132

(6)

General error bound theorem

132

(2)

Two special performability applications

134

(4)

Summary

138

(1)

The Task Completion Time in Degradable Systems

139

(24)

Introduction

139

(2)

The barrier hitting problem

141

(4)

The distribution of the completion time

145

(4)

Applications and extensions

149

(2)

Completion time and Petri nets

151

(9)

Generally Distributed Transitions SPN

152

(2)

Deterministic SPN

154

(1)

Markov Regenerative SPN

155

(1)

Modelling completion time

156

(1)

Petri nets

Numerical examples

157

(3)

Conclusion

160

(3)

Rare Event Simulation

163

(16)

Introduction

164

(2)

Problem statement

166

(1)

Rare event simulation

167

(1)

Importance sampling

167

(3)

Applications of importance sampling

170

(6)

Reliability models

170

(3)

Queueing models

173

(3)

Other models

176

(1)

The splitting method

176

(2)

Acknowledgements

178

(1)

Specification and Construction of Performability Models

179

(44)

Introduction

180

(4)

Performability model specification

184

(17)

Measure specification

186

(4)

Base model specification

190

(8)

Reward structure specification

198

(3)

Performability model construction

201

(20)

Marking-transition algorithms

202

(3)

Detailed base model construction

205

(6)

Reduced base model construction

211

(10)

Summary

221

(2)

A Survey of Performability Modelling Tools

223

(40)

Introduction

223

(2)

A general modelling tool framework

225

(5)

Classifying performability measures

230

(1)

Performability modelling tool survey

231

(28)

DSPN Express

232

(2)

DyQNtool+

234

(2)

Metaphor

236

(1)

Metasan

237

(1)

Metfac

238

(2)

Numas

240

(1)

Panda

241

(1)

Penelope and COSTPN

242

(2)

Penpet

244

(2)

Save

246

(1)

Sharpe and GISharpe

247

(2)

SPNP

249

(2)

Surf-2

251

(1)

Tangram-II

251

(2)

TimeNET

253

(2)

TIPPtool

255

(2)

UltraSAN

257

(2)

Summary and outlook

259

(4)

Bibliography

263

(50)

Concise glossary

313

(2)

Index

315

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Performability Modelling Techniques and Tools

Summary

Author Biography

Table of Contents

Supplemental Materials