Reliability of Computer Systems and Networks

546 Pages·2002·3.684 MB·English

by  Martin L. Shooman

Reliability of Computer Systems and Networks: Fault Tolerance, Analysis, and Design
Martin L. Shooman
Copyright2002John Wiley & Sons, Inc.
ISBNs:0-471-29342-3(Hardback);0-471-22460-X (Electronic)
RELIABILITY OF
COMPUTER SYSTEMS
AND NETWORKS
RELIABILITY OF
COMPUTER SYSTEMS
AND NETWORKS
Fault Tolerance, Analysis, and
Design
MARTIN L. SHOOMAN
Polytechnic University
and
Martin L. Shooman & Associates
A Wiley-Interscience Publication
JOHN WILEY & SONS, INC.
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To Danielle Leah and Aviva Zissel
CONTENTS
Preface xix
1 Introduction 1
1.1 What is Fault-Tolerant Computing?, 1
1.2 The Rise of Microelectronics and the Computer, 4
1.2.1 A Technology Timeline, 4
1.2.2 Moore’s Law of Microprocessor Growth, 5
1.2.3 Memory Growth, 7
1.2.4 Digital Electronics in Unexpected Places, 9
1.3 Reliability and Availability, 10
1.3.1 Reliability Is Often an Afterthought, 10
1.3.2 Concepts of Reliability, 11
1.3.3 Elementary Fault-Tolerant Calculations, 12
1.3.4 The Meaning of Availability, 14
1.3.5 Need for High Reliability and Safety in Fault-
Tolerant Systems, 15
1.4 Organization of the Book, 18
1.4.1 Introduction, 18
1.4.2 Coding Techniques, 19
1.4.3 Redundancy, Spares, and Repairs, 19
1.4.4 N-Modular Redundancy, 20
1.4.5 Software Reliability and Recovery Techniques, 20
1.4.6 Networked Systems Reliability, 21
1.4.7 Reliability Optimization, 22
1.4.8 Appendices, 22
vii
viii CONTENTS
General References, 23
References, 25
Problems, 27
2 Coding Techniques 30
2.1 Introduction, 30
2.2 Basic Principles, 34
2.2.1 Code Distance, 34
2.2.2 Check-Bit Generation and Error Detection, 35
2.3 Parity-Bit Codes, 37
2.3.1 Applications, 37
2.3.2 Use of Exclusive OR Gates, 37
2.3.3 Reduction in Undetected Errors, 39
2.3.4 Effect of Coder–Decoder Failures, 43
2.4 Hamming Codes, 44
2.4.1 Introduction, 44
2.4.2 Error-Detection and -Correction Capabilities, 45
2.4.3 The Hamming SECSED Code, 47
2.4.4 The Hamming SECDED Code, 51
2.4.5 Reduction in Undetected Errors, 52
2.4.6 Effect of Coder–Decoder Failures, 53
2.4.7 How Coder–Decoder Failures Effect SECSED
Codes, 56
2.5 Error-Detection and Retransmission Codes, 59
2.5.1 Introduction, 59
2.5.2 Reliability of a SECSED Code, 59
2.5.3 Reliability of a Retransmitted Code, 60
2.6 Burst Error-Correction Codes, 62
2.6.1 Introduction, 62
2.6.2 Error Detection, 63
2.6.3 Error Correction, 66
2.7 Reed–Solomon Codes, 72
2.7.1 Introduction, 72
2.7.2 Block Structure, 72
2.7.3 Interleaving, 73
2.7.4 Improvement from the RS Code, 73
2.7.5 Effect of RS Coder–Decoder Failures, 73
2.8 Other Codes, 75
References, 76
Problems, 78
3 Redundancy, Spares, and Repairs 83
3.1 Introduction, 85
3.2 Apportionment, 85
CONTENTS ix
3.3 System Versus Component Redundancy, 86
3.4 Approximate Reliability Functions, 92
3.4.1 Exponential Expansions, 92
3.4.2 System Hazard Function, 94
3.4.3 Mean Time to Failure, 95
3.5 Parallel Redundancy, 97
3.5.1 Independent Failures, 97
3.5.2 Dependent and Common Mode Effects, 99
3.6 An r-out-of-n Structure, 101
3.7 Standby Systems, 104
3.7.1 Introduction, 104
3.7.2 Success Probabilities for a Standby System, 105
3.7.3 Comparison of Parallel and Standby Systems, 108
3.8 Repairable Systems, 111
3.8.1 Introduction, 111
3.8.2 Reliability of a Two-Element System with
Repair, 112
3.8.3 MTTF for Various Systems with Repair, 114
3.8.4 The Effect of Coverage on System
Reliability, 115
3.8.5 Availability Models, 117
3.9 RAID Systems Reliability, 119
3.9.1 Introduction, 119
3.9.2 RAID Level 0, 122
3.9.3 RAID Level 1, 122
3.9.4 RAID Level 2, 122
3.9.5 RAID Levels 3, 4, and 5, 123
3.9.6 RAID Level 6, 126
3.10 Typical Commercial Fault-Tolerant Systems: Tandem
and Stratus, 126
3.10.1 Tandem Systems, 126
3.10.2 Stratus Systems, 131
3.10.3 Clusters, 135
References, 137
Problems, 139
4 N-Modular Redundancy 145
4.1 Introduction, 145
4.2 The History of N-Modular Redundancy, 146
4.3 Triple Modular Redundancy, 147
4.3.1 Introduction, 147
4.3.2 System Reliability, 148
4.3.3 System Error Rate, 148
4.3.4 TMR Options, 150
x CONTENTS
4.4 N-Modular Redundancy, 153
4.4.1 Introduction, 153
4.4.2 System Voting, 154
4.4.3 Subsystem Level Voting, 154
4.5 Imperfect Voters, 156
4.5.1 Limitations on Voter Reliability, 156
4.5.2 Use of Redundant Voters, 158
4.5.3 Modeling Limitations, 160
4.6 Voter Logic, 161
4.6.1 Voting, 161
4.6.2 Voting and Error Detection, 163
4.7 N-Modular Redundancy with Repair, 165
4.7.1 Introduction, 165
4.7.2 Reliability Computations, 165
4.7.3 TMR Reliability, 166
4.7.4 N-Modular Reliability, 170
4.8 N-Modular Redundancy with Repair and Imperfect
Voters, 176
4.8.1 Introduction, 176
4.8.2 Voter Reliability, 176
4.8.3 Comparison of TMR, Parallel, and Standby
Systems, 178
4.9 Availability of N-Modular Redundancy with
Repair and Imperfect Voters, 179
4.9.1 Introduction, 179
4.9.2 Markov Availability Models, 180
4.9.3 Decoupled Availability Models, 183
4.10 Microcode-Level Redundancy, 186
4.11 Advanced Voting Techniques, 186
4.11.1 Voting with Lockout, 186
4.11.2 Adjudicator Algorithms, 189
4.11.3 Consensus Voting, 190
4.11.4 Test and Switch Techniques, 191
4.11.5 Pairwise Comparison, 191
4.11.6 Adaptive Voting, 194
References, 195
Problems, 196
5 Software Reliability and Recovery Techniques 202
5.1 Introduction, 202
5.1.1 Definition of Software Reliability, 203
5.1.2 Probabilistic Nature of Software
Reliability, 203
5.2 The Magnitude of the Problem, 205
CONTENTS xi
5.3 Software Development Life Cycle, 207
5.3.1 Beginning and End, 207
5.3.2 Requirements, 209
5.3.3 Specifications, 209
5.3.4 Prototypes, 210
5.3.5 Design, 211
5.3.6 Coding, 214
5.3.7 Testing, 215
5.3.8 Diagrams Depicting the Development Process, 218
5.4 Reliability Theory, 218
5.4.1 Introduction, 218
5.4.2 Reliability as a Probability of Success, 219
5.4.3 Failure-Rate (Hazard) Function, 222
5.4.4 Mean Time To Failure, 224
5.4.5 Constant-Failure Rate, 224
5.5 Software Error Models, 225
5.5.1 Introduction, 225
5.5.2 An Error-Removal Model, 227
5.5.3 Error-Generation Models, 229
5.5.4 Error-Removal Models, 229
5.6 Reliability Models, 237
5.6.1 Introduction, 237
5.6.2 Reliability Model for Constant Error-Removal
Rate, 238
5.6.3 Reliability Model for Linearly Decreasing Error-
Removal Rate, 242
5.6.4 Reliability Model for an Exponentially Decreasing
Error-Removal Rate, 246
5.7 Estimating the Model Constants, 250
5.7.1 Introduction, 250
5.7.2 Handbook Estimation, 250
5.7.3 Moment Estimates, 252
5.7.4 Least-Squares Estimates, 256
5.7.5 Maximum-Likelihood Estimates, 257
5.8 Other Software Reliability Models, 258
5.8.1 Introduction, 258
5.8.2 Recommended Software Reliability Models, 258
5.8.3 Use of Development Test Data, 260
5.8.4 Software Reliability Models for Other Development
Stages, 260
5.8.5 Macro Software Reliability Models, 262
5.9 Software Redundancy, 262
5.9.1 Introduction, 262
5.9.2 N-Version Programming, 263
5.9.3 Space Shuttle Example, 266
xii CONTENTS
5.10 Rollback and Recovery, 268
5.10.1 Introduction, 268
5.10.2 Rebooting, 270
5.10.3 Recovery Techniques, 271
5.10.4 Journaling Techniques, 272
5.10.5 Retry Techniques, 273
5.10.6 Checkpointing, 274
5.10.7 Distributed Storage and Processing, 275
References, 276
Problems, 280
6 Networked Systems Reliability 283
6.1 Introduction, 283
6.2 Graph Models, 284
6.3 Definition of Network Reliability, 285
6.4 Two-Terminal Reliability, 288
6.4.1 State-Space Enumeration, 288
6.4.2 Cut-Set and Tie-Set Methods, 292
6.4.3 Truncation Approximations, 294
6.4.4 Subset Approximations, 296
6.4.5 Graph Transformations, 297
6.5 Node Pair Resilience, 301
6.6 All-Terminal Reliability, 302
6.6.1 Event-Space Enumeration, 302
6.6.2 Cut-Set and Tie-Set Methods, 303
6.6.3 Cut-Set and Tie-Set Approximations, 305
6.6.4 Graph Transformations, 305
6.6.5 k-Terminal Reliability, 308
6.6.6 Computer Solutions, 308
6.7 Design Approaches, 309
6.7.1 Introduction, 310
6.7.2 Design of a Backbone Network Spanning-Tree
Phase, 310
6.7.3 Use of Prim’s and Kruskal’s Algorithms, 314
6.7.4 Design of a Backbone Network: Enhancement
Phase, 318
6.7.5 Other Design Approaches, 319
References, 321
Problems, 324
7 Reliability Optimization 331
7.1 Introduction, 331
7.2 Optimum Versus Good Solutions, 332