- 作 者：Robin A.Sahner ; Kishor S. Trivedi ; Antonio Puliafito
- 出 版 社：Kluwer Academic Publishers
- 出版年份：1996
- ISBN：0792396502
- 标注页数：404 页
- PDF页数：419 页
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Part Ⅰ MODELING THEORY 1
1 DISTRIBUTION FUNCTIONS 5
1.1 Basic Definitions 5
1.2 The Exponential Distribution 9
1.3 Operations on Random Variables 10
1.4 Exponential Polynomial Distributions 17
1.5 Mixture Distributions 18
1.6 EP and Other Classes of Distributions 21
1.7 Approximating non-EP Distributions with EP Distributions 22
1.8 Operations on Exponential Polynomials 23
2 RELIABILITY AND AVAILABILITY MODELS 27
2.1 Reliability 27
2.2 Availability 30
2.3 Series-Parallel Reliability Block Diagrams 35
2.4 Fault Trees 39
2.5 Reliability Graphs 42
2.6 Analysis of Network Reliability Models 45
3 SERIES-PARALLEL ACYCLIC DIRECTED GRAPHS 47
3.1 A Simple Task Graph Example 48
3.2 Running Example: Performance from a Program's Point of View 49
3.3 Definition of a Series-Parallel Acyclic Directed Graph Model 50
3.4 Series-Parallel Acyclic Directed Graph Analysis 53
4 MARKOV MODELS 55
4.1 Stochastic Processes 55
4.2 Markov Chains 57
4.3 Basic Equations 58
4.4 Classification of States and Chains 61
4.5 Examples of Markov Chain Analysis 63
4.6 Steady-state Solution Techniques 72
4.7 Transient Analysis Methods 73
4.8 Examples 80
5 PRODUCT-FORM QUEUEING NETWORKS 85
5.1 Queueing Terminology 85
5.2 Queueing Network Analysis 89
5.3 Examples 100
6 PERFORMABILITY MODELS 103
6.1 Introduction 104
6.2 Degradable Systems 106
6.3 Largeness and stiffness: the decomposition approach 108
6.4 The Markov Reward Model 109
6.5 Measures of interest 110
6.6 Reward Assignment and Reward Computation 116
7 STOCHASTIC PETRI NET MODELS 119
7.1 Introduction to Petri Net Models 120
7.2 Petri Net Model Definitions 123
7.3 Petri Net Extensions 126
7.4 SPN and GSPN Analysis 133
7.5 GSPN EXAMPLES 137
7.6 Non-Markovian SPN Model Extensions 141
8 SEMI-MARKOV CHAINS 143
8.1 Describing Semi-Markov chains 143
8.2 Analysis of Irreducible Semi-Markov Chains 145
8.3 A Semi-Symbolic Analysis for Acyclic Semi-Markov Chains 147
Part Ⅱ MODELING EXAMPLES 151
9 RELIABILITY AND AVAILABILITY MODELING 155
9.1 Modeling with Block Diagrams 155
9.2 Modeling Reliability and Availability with Fault Trees 172
9.3 Modeling With A Reliability Graph 180
9.4 Modeling Using Markov Chains 183
9.5 Ring Network Reliability Models 193
10 PERFORMANCE MODELING 203
10.1 Program Performance Analysis Using Task Graphs 204
10.2 System Performance Analysis 222
11 HIERARCHICAL MODELS 261
11.1 A Non-Series-Parallel Block Diagram 262
11.2 A Non-Series-Parallel Task Precedence Graph 271
11.3 A Task Graph Containing a Cycle 274
11.4 A Queueing Model with Resource Constraints 277
11.5 A Queueing Model with Simultaneous Resource Possession 280
11.6 A Queueing Model with Job Priorities 284
11.7 Parallel Processing of Task Systems with Resource Con-straints 288
11.8 A Queue Subject to Failure and Repair 294
11.9 Modeling Repair Dependence 295
11.10 Intermittent and Near-coincident Faults 301
12 PERFORMABILITY MODELS 313
12.1 An Acyclic Markov Reward Model 313
12.2 An Irreducible Markov Reward Model 318
12.3 A Hierarchical Markov Reward Model 320
12.4 A Multiprocessor Performability Model 324
13 HANDLING ALGORITHMIC AND NUMERICAL LIMITATIONS 329
13.1 Distributions with Very Large Coefficients 330
13.2 A Phase-type Markov Chain 334
13.3 An Irreducible Markov Chain 337
13.4 An Example Where the Order of States Matters 339
Part Ⅲ APPENDICES 343
A SHARPE COMMAND LINE SYNTAX 345
B SHARPE LANGUAGE DESCRIPTION 347
B.1 Conventions 347
B.2 Basic Language Components 347
B.3 Specification of Exponential Polynomial Functions 352
B.4 Specification of Models 354
B.5 Asking for Results 367
B.6 Built-in Functions 371
B.7 Controlling the Analysis Process 375
B.8 Program Constants 377
B.9 Summary of Top-level Input Statements 378
C USING SHARPE INTERACTIVELY 381
D ALGORITHM CHOICES FOR PHASE-TYPE MARKOV CHAINS 387
REFERENCES 389
INDEX 401