《Performance and reliability analysis of computer systems an example-based approach using the SHARPE》

Part Ⅰ MODELING THEORY1

1DISTRIBUTION FUNCTIONS5

1.1 Basic Definitions5

1.2 The Exponential Distribution9

1.3 Operations on Random Variables10

1.4 Exponential Polynomial Distributions17

1.5 Mixture Distributions18

1.6 EP and Other Classes of Distributions21

1.7 Approximating non-EP Distributions with EP Distributions22

1.8 Operations on Exponential Polynomials23

2RELIABILITY AND AVAILABILITY MODELS27

2.1 Reliability27

2.2 Availability30

2.3 Series-Parallel Reliability Block Diagrams35

2.4 Fault Trees39

2.5 Reliability Graphs42

2.6 Analysis of Network Reliability Models45

3SERIES-PARALLEL ACYCLIC DIRECTED GRAPHS47

3.1 A Simple Task Graph Example48

3.2 Running Example: Performance from a Program's Point of View49

3.3 Definition of a Series-Parallel Acyclic Directed Graph Model50

3.4 Series-Parallel Acyclic Directed Graph Analysis53

4MARKOV MODELS55

4.1 Stochastic Processes55

4.2 Markov Chains57

4.3 Basic Equations58

4.4 Classification of States and Chains61

4.5 Examples of Markov Chain Analysis63

4.6 Steady-state Solution Techniques72

4.7 Transient Analysis Methods73

4.8 Examples80

5PRODUCT-FORM QUEUEING NETWORKS85

5.1 Queueing Terminology85

5.2 Queueing Network Analysis89

5.3 Examples100

6PERFORMABILITY MODELS103

6.1 Introduction104

6.2 Degradable Systems106

6.3 Largeness and stiffness: the decomposition approach108

6.4 The Markov Reward Model109

6.5 Measures of interest110

6.6 Reward Assignment and Reward Computation116

7STOCHASTIC PETRI NET MODELS119

7.1 Introduction to Petri Net Models120

7.2 Petri Net Model Definitions123

7.3 Petri Net Extensions126

7.4 SPN and GSPN Analysis133

7.5 GSPN EXAMPLES137

7.6 Non-Markovian SPN Model Extensions141

8SEMI-MARKOV CHAINS143

8.1 Describing Semi-Markov chains143

8.2 Analysis of Irreducible Semi-Markov Chains145

8.3 A Semi-Symbolic Analysis for Acyclic Semi-Markov Chains147

Part ⅡMODELING EXAMPLES151

9RELIABILITY AND AVAILABILITY MODELING155

9.1 Modeling with Block Diagrams155

9.2 Modeling Reliability and Availability with Fault Trees172

9.3 Modeling With A Reliability Graph180

9.4 Modeling Using Markov Chains183

9.5 Ring Network Reliability Models193

10 PERFORMANCE MODELING203

10.1 Program Performance Analysis Using Task Graphs204

10.2 System Performance Analysis222

11HIERARCHICAL MODELS261

11.1 A Non-Series-Parallel Block Diagram262

11.2 A Non-Series-Parallel Task Precedence Graph271

11.3 A Task Graph Containing a Cycle274

11.4 A Queueing Model with Resource Constraints277

11.5 A Queueing Model with Simultaneous Resource Possession280

11.6 A Queueing Model with Job Priorities284

11.7 Parallel Processing of Task Systems with Resource Con-straints288

11.8 A Queue Subject to Failure and Repair294

11.9 Modeling Repair Dependence295

11.10 Intermittent and Near-coincident Faults301

12PERFORMABILITY MODELS313

12.1 An Acyclic Markov Reward Model313

12.2 An Irreducible Markov Reward Model318

12.3 A Hierarchical Markov Reward Model320

12.4 A Multiprocessor Performability Model324

13 HANDLING ALGORITHMIC AND NUMERICAL LIMITATIONS329

13.1 Distributions with Very Large Coefficients330

13.2 A Phase-type Markov Chain334

13.3 An Irreducible Markov Chain337

13.4 An Example Where the Order of States Matters339

Part ⅢAPPENDICES343

A SHARPE COMMAND LINE SYNTAX345

BSHARPE LANGUAGE DESCRIPTION347

B.1 Conventions347

B.2 Basic Language Components347

B.3 Specification of Exponential Polynomial Functions352

B.4 Specification of Models354

B.5 Asking for Results367

B.6 Built-in Functions371

B.7 Controlling the Analysis Process375

B.8 Program Constants377

B.9 Summary of Top-level Input Statements378

C USING SHARPE INTERACTIVELY381

D ALGORITHM CHOICES FOR PHASE-TYPE MARKOV CHAINS387

REFERENCES389

INDEX401