Introduction To Computer System Performance Evaluation

634 Pages·1992·48.529 MB·English

by  Krishna Kant

INTRODUCTION TO
COMPUTER SYSTEM
PERFORMANCE EVALUATION
CONTENTS
Preface xv
Part 1 Basic Concepts
1 Performance Measures and Evaluation Techniques
3
1.1 Evaluation Metrics 3
1.2 Techniques of Performance Evaluation 6
1.2.1 Measurement 6
1.2.2 Simulation Modeling 7
1.2.3 Analytic Modeling 8
1.2.4 Hybrid Modeling 8
1.3 Applications of Performance Evaluation 9
1.4 Workload Characterization 11
1.5 Benchmarking Computer Systems 13
1.5.1 Traditional Computer Systems 13
1.5.2 Highly Parallel Architectures 18
l.6 Exercises 22
Bibliographic Notes 23
2 Measurement Techniques 24
2.1 Classification of Measurement Techniques 24
2.2 Hardware Monitoring 27
2.3 Software Monitoring 34
2.3.1 Trace Monitoring 34
2.3.2 Sampled Monitoring 37
2.4 Hybrid Monitoring 39
2.5 Other Issues in Measurement 43
2.5.1 Real-Time Control of Performance 43
2.5.2 Measurability Limitations 47
2.5.3 Monitoring Parallel and Distributed Systems 48
2.6 Exercises 51
Bibliographic Notes 53
VII
viii CONTENTS
3 Experiment Design and Data Analysis
3.1 Simulation Techniques
3.2 Fundamentals of Data Analysis
3.3 Organizing Simulation Runs
3.4 Selection ofInputs
3.5 Comparison ofAlternate Designs
3.5.1 Selection Procedures
3.5.2 Validity of Selection Procedures
3.6 Regression Analysis
3.6.1 General Treatment
3.6.2 Linear Regression 73
3.6.3 Other Issues in Regression Analysis 74
3.7 Variance Reduction Techniques 77
3.7.1 Common Random Numbers 77
3.7.2 Antithetic Variable Method 78
3.7.3 Control Variate Method 79
3.8 Exercises 81
Bibliographic Notes 83
4 Fundamentals of Queuing Models 84
4.1 Structure and Performance Parameters 84
4.1.1 Open and Closed Models 85
4.1.2 Performance Parameters 87
4.2 Operational Analysis ofQueuing Models 88
4.2.1 Behavioral Properties 88
4.2.2 Operational Definitions of Performance Measures 90
4.2.3 Forced Flows a~d Visit Ratios 92
4.2.4 Some Fundamental Results 93
4.2.5 Properties of Queue Length Distributions 96
4.2.6 Comparison of Operational and Stochastic Analysis 99
4.3 General Features of Queuing Models 101
4.3.1 Classes and Chains 101
4.3.2 Load-Dependent Stations 101
4.3.3 Other Features and Limitations 104
4.4 Analysis of Multiple-Class Networks 105
4.4.1 Characterization of Classes and Chains 106
4.4.2 Characteristics of Multiple-Class Networks 109
4.4.3 Operational Analysis of Multiple-Chain Networks III
4.5 Calibration of Queuing Models l16
4.5.1 Number of Chains or Classes 117
4.5.2 Queuing Discipline l18
4.5.3 Chain Population 119
4.5.4 Mean Service Times 120
4.5.5 Service=Time Distribution 122
4.5.6 Passive Resource Demands 123
4.5.7 Routing Probabilities and Visit Ratios 123
4.5.8 Overhead and Load Dependence 124
4.5.9 Output Parameters and Model Validation 125
4.6 Exercises 127
Bibliographic Notes 130
be
CONTENTS
5 Elementary Stochastic Analysis 131
5.1 RandomProcesses 131
ed
5.1.1 ClassificationofRandomProcesses 132
5.1.2 MarkovProcesses 133
5.1.3 IndependentProcesses 135
5.2 AnalysisofMarkovChains 137
5.2.1 DiscreteParameter Case 138
5.2.2 ContinuousParameter Case 140
5.3 Long-TermBehaviorofMarkovChains 144
5.3.1 Limitingand StationaryDistributions 144
5.3.2 State ClassificationandErgodicity 145
5.3.3 Analysis.ofReducibleChains 149
5.3.4 ErgodicityofGeneralRandomProcesses 151
5.4 Birth and Death Processes 153
5.5 Steady-StateAnalysisofM/M Systems 156
5.5.1 SimpleM/M/1/SI/oo/ooQueue 156
5.5.2 M/M/c/SI/oo/ooQueue 157
5.5.3 SimpleM/G/oo/SI/oo/ooQueue 159
5.5.4 SimpleM/M/c/SI/K/oo Queue 159
5.5.5 Finite PopulationSystems 161
5.5.6 Output Processin M/M/c Queues 162
5.5.7 Response-TimeDistributions 165
5.6 BatchSystemsand MethodofStages 167
5.6.1 AnalysisofBatchSystems 197
5.6.2 StagedServicewithFCFSScheduling 171
5.6.3 StagedServicewithPS Scheduling 175
5.7 Exercises 177
BibliographicNotes 180
6 Product-Form Queuing Network Models 181
6.1 CharacterizationofProduct-FormSolution 181c
6.1.1 LocalBalanceandProduct-FormSolution 182
6.1.2 ReversibleMarkovProcesses 186
6.1.3 Quasi-ReversibleQueuingSystems 190
6.2 OpenQueuingNetworkModels 192
6.2.1 StabilityConditions 193
6.2.2 Single-ChainProduct-FormNetworks 194
6.2.3 Multiple-ChainProduct-FormNetworks 199
6.3 ClosedProduct-FormNetworks 203
6.3.1 Sing.l!e~Chai.nNetworks 204
6.3.2 Brute-ForceAlgorithm 206
6.3.3 Multiple-ChainNetworks 208
6.4 Multiple-ClassModels tg~;
211
6.5 AlgorithmsforClosedPF Networks
212
6.5.1 Exact Algorithms . in
6.5.2 ApproximateAlgorithms
6.5.3 PerformanceBounds "i15
6.6 ConditionsforProduct-FormSolution 216
6.7 Exercises···
BibliographicNotes
X CONTENTS
7 Basic Algorithms for Product-Form Networks 223
7.1 Single-Chain Convolution 223
7.1.1 Fundamental Relationships 224
7.1.2 Algorithmic Considerations 227
7.2 Single-Chain Mean Value Analysis 231
7.3 Multiple-Chain Convolution 235
7.4 Multiple-Chain Mean Value Analysis 241
7.5 The LBANC Algorithm 246
7.6 Algorithms for Mixed Networks 247
7.7 Approximate Mean Value Analysis 252
7.7.1 Multiple-Chain Linearizer 253
7.7.2 Extensions for Load-Dependent Stations 254
7.7.3 Cost and Accuracy 255
7.8 Exercises 258
Bibliographic Notes 261
8 Aggregation and Approximate Modeling 263
8.1 Flow-Equivalent Aggregation 263
8.1.1 Characterization of Aggregate Station 264
8.1.2 Analysis of the Aggregate Station 266
8.1.3 Aggregation in Multiple-Chain Networks 267
8.2 Applications of Aggregation 268
8.2.1 Resource Constraints in Single-Chain Networks 269
8.2.2 Swapping and Partial Allocation 273
8.2.3 Multiple-Resource Types 275
8.2.4 Resource Constraints in Multiple-Chain Models 276
8.2.5 Modeling Channel Contention 279
8.3 Modeling Non-PF Scheduling Disciplines 283
8.3.1 FCFS Scheduling Discipline 283
8.3.2 Priority Scheduling Discipline 286
8.3.3 Biased Processor Sharing Discipline 288
8.3.4 Shortest Job Next Scheduling 289
8.3.5 Comparison of Scheduling Disciplines 291
8.3.6 Load-Dependent Stations 293
8.4 Decomposition Approximation 294
8.4.1 Physical and Logical Decomposition 294
8.4.2 Nearly Completely Decomposable Systems 295
8.4.3 Decomposability Criteria and Error Estimation 300
8.4.4 Lumpable and Other Special Matrices 301
8.4.5 Modeling Degradable Multiserver Systems 305
8.5 Exercises 308
Bibliographic Notes 311
Part II Advanced Topics
9 Advanced Stochastic Analysis 317
9.1 Solution Using Generating Functions 317
9.2 Some Results on General Queuing Systems 323
9.2.1 Properties of Systems with Poisson Arrivals 323
9.2.2 Virtual Load and Conservation Laws 326
xi
CONTENTS
9.2.3 Properties ofRenewalProcesses 329
9.2.4 SolutionUsingEmbeddedMarkovChains 333
9.3 The M/G/1 QueuingSystem 338
9.3.1 Queue-LengthMoments 339
9.3.2 Response-Timeand Busy-PeriodDistribution 341
9.4 Phase-Type Distributions 344
9.4.1 ContinuousPhase-TypeDistributions 344
9.4.2 DiscretePhase-TypeDistributions 347
9.5 Matrix-AnalyticMethods 348
9.5.1 AnalysisofM/PH/1 Queue 348
9.5.2 Matrix-GeometricSolutions 351
9.5.3 Queuesina RandomEnvironment 357
9.5.4 QueuesofM/G/1 Type 359
9.6 AdditionalTopics 360
9.6.1 Representation ofArrivalProcesses 360
9.6.2 Direct SolutionofGlobalBalanceEquations 363
9.7 Exercises 365
BibliographicNotes 366
10 Algorithims for Networks with Specialized Features 368
10.1 Networkswith AdvancedFeatures 368
10.1.1 Chain-DependentCapacities 369
10.1.2 Networkswith VariablePopulations 370
10.1.3 State-Dependent Routing 374
10.1.4 RejectionBlocking 378
10.1.5 Mutual Blocking 380
10.2 Chain-BasedRecursionAlgorithms 381
10.2.1 Recursion-By-ChainAlgorithm 382
10.2.2 MeanValueAnalysisbyChain 385
10.2.3 The DACAlgorithm 387
10.3 AlgorithmsExploitingSparsity 390
10.3.1 Tree-Convolution 390
10.3.2 TreeMeanValueAnalysis 394
10.4 AsymptoticExpansions 396
10.5 Exercises 400
BibliographicNotes 401
11 Bounds on Performance 403
11.1 BoundsonSingle-ChainNetworks 404
11.1.1 AsymptoticBoundAnalysis 404
11.1.2 BalancedJob Bounds 405
11.1.3 PerformanceBoundHierarchies 407
11.1.4 SuccessivelyImprovingBounds 409
11.2 Networkswith Load-DependentStations 411
11.3 BoundsonMeanQueueLengths 413
{nit
11.4 BoundsforMultiple-ChainNetworks
11.4.1 Asymptoticand BalancedJob Bounds 414
11.4.2 PerformanceBoundHierarchies 415
11.5 Exercises
BibliographicNotes 419
xii CONTENTS
12 Petri Net-Based Performance Modeling 420
12.1 Classical Petri Nets 420
12.1.1 Basic Definitions and Motivation 421
12.1.2 Properties and Analysis Problems 425
12.1.3 Structural Analysis of Petri Nets 429
12.2 Timed Petri Nets 434
12.2.1 Timing Semantics 435
12.2.2 Issues in Analysis 437
12.3 Generalized Stochastic Petri Nets 439
12.3.1 Analysis Details 439
12.3.2 Refinements to the GSPN Model 445
12.4 Discrete Time Petri Nets 448
12.4.1 Geometric Firing Times 448
12.4.2 Deterministic Firing Times 450
12.5 Modeling Multiprocessor Systems 452
12.6 Extensions to Stochastic Petri Nets 455
12.7 Product-Form Solutions 455
12.8 Exercises 462
Bibliographic Notes 463
13 Selected Applications 466
13.1 Analysis of Polling Systems 467
13.1.1 Polling Disciplines 468
13.1.2 The M/G/1 Vacation Model 468
13.1.3 Mean Cycle and Waiting Times 469
13.1.4 Markovian Analysis and Conservation Laws 471
13.1.5 Approximations for Mean Waiting Times 475
13.2 Problems in Performance Optimization 480
13.2.1 File-Allocation Problem 480
13.2.2 Optimal Routing in Computer Networks 483
13.3 Analysis of Jobs with Internal Concurrency 487
13.3.1 Generalized Task Graphs 487
13.3.2 Multiserver with I-Level Task Graphs 492
13.3.3 Multiserver with 2-Level Task Graphs 495
13.3.4 Analysis of Queuing Networks 498
13.4 Modeling Fault-Tolerant Systems 502
13.4.1 Reliability Modeling 502
13.4.2 Performability Measures 505
13.4.3 Evaluation of Performability Measures 507
13.4.4 Transient Analysis of Markov Chains 513
13.5 Exercises 517
Bibliographic Notes 519
Part III Appendices
A Notation 525
CONTENTS xiii
B Introduction to Probability Theory 529
B.l BasicConcepts 529
B.l.l Events and the Probability Measure 529
B.1.2 Random Variablesand Distributions 530
B.1.3 Functionsofa RandomVariable 533
B.1.4 Expectation and Moments 534
B.1.5 SomeInequalities 536
B.2 SummaryofSelectedDistributions 538
B.2.! DiscreteDistributions 538
B.2.2 ContinuousDistributions 540
B.3 Characteristic Functions 545
B.3.! The Z-Transform 545
B.3.2 LaplaceTransform 548
B.3.3 GeneralCharacteristic Function 550
BA Exercises 552
BibliographicNotes 553
C A Suggested Modeling Project 554
C.! Project Overview 554
C.2 Operational DetailsofSYS-A 556
C.2.l HardwareConfiguration 556
C.2.2 SystemOperation 557
C.3 ModelConstruction 560
C.3.! ModelDescription 560
C.3.2 ModelingofMinorOverheads 564
C.3.3 ModelCalibration and Validation 564
CA ModelingEnhancements 568
D Performance Tuning Using Solver 570
D.l OverviewofSolver 570
D.2 Tuninga Paging System 572
D.2.! The SolverProgram 573
D.2.2 Interpretation ofResults 574
D.2.3 IssuesforFurther Study 577
D.3 Program Listingand Output 578
E Selected Tables 583
E.! Critical Points oft Distribution 583
E.2 SelectionamongAlternate Designs 584
E.3 SelectedLaplaceTransformPairs 587
EA Selectedz-TransformPairs 588
References 589
Index 603