Performance, Reliability, and Availability Evaluation of Computational Systems, Volume I: Performance and Background

Description

This textbook intends to be a comprehensive and substantially self-contained two-volume book covering performance, reliability, and availability evaluation subjects. The volumes focus on computing systems, although the methods may also be applied to other systems. The first volume covers Chapter 1 to Chapter 14, whose subtitle is ``Performance Modeling and Background". The second volume encompasses Chapter 15 to Chapter 25 and has the subtitle ``Reliability and Availability Modeling, Measuring and Workload, and Lifetime Data Analysis". This text is helpful for computer performance professionals for supporting planning, design, configuring, and tuning the performance, reliability, and availability of computing systems. Such professionals may use these volumes to get acquainted with specific subjects by looking at the particular chapters. Many examples in the textbook on computing systems will help them understand the concepts covered in each chapter. The text may also be helpful for the instructor who teaches performance, reliability, and availability evaluation subjects. Many possible threads could be configured according to the interest of the audience and the duration of the course. Chapter 1 presents a good number of possible courses programs that could be organized using this text. Volume I is composed of the first two parts, besides Chapter 1. Part I gives the knowledge required for the subsequent parts of the text. This part includes six chapters. It covers an introduction to probability, descriptive statistics and exploratory data analysis, random variables, moments, covariance, some helpful discrete and continuous random variables, Taylor series, inference methods, distribution fitting, regression, interpolation, data scaling, distance measures, and some clustering methods. Part II presents methods for performance evaluation modeling, such as operational analysis, Discrete-Time Markov Chains (DTMC), and Continuous Time Markov Chains (CTMC), Markovian queues, Stochastic Petri nets (SPN), and discrete event simulation. Cover Half Title Title Page Copyright Page Dedication Contents Preface Acknowledgement Chapter 1: Introduction 1.1. An Overview 1.2. A Glance at Evaluation Planning PART I: Fundamental Concepts Chapter 2: Introduction to Probability 2.1. Sets and Algebra of Sets 2.2. Probability 2.3. Conditional Probability 2.4. Independence 2.5. Bayes’ Rule and the Law of Total Probability 2.6. Counting 2.6.1. N-Permutation 2.6.2. K out of N Permutation with Replacement 2.6.3. K out of N Permutation without Replacement 2.6.4. K out of N Combination without Replacement 2.6.5. K out of N Combination with Replacement Chapter 3: Exploratory Data Analysis 3.1. Diagrams and Plots 3.2. Statistics of Central Tendency 3.3. Measures of Dispersion 3.4. Statistics of Shape (Asymmetry and Kurtosis) 3.5. Outliers Chapter 4: Introduction to Random Variables 4.1. Discrete Random Variables 4.2. Continuous Random Variables 4.3. Moments 4.4. Joint Distributions 4.4.1. Joint Discrete Random Variables 4.4.2. Joint Continuous Random Variables 4.4.3. Convolution 4.4.4. Expect. and Var. of Prod. of Rand. Variab. 4.4.5. Expect. and Var. of Sums of Rand. Variab. 4.5. Summary of Properties of Expectation and Variance 4.6. Covariance, Correlation, and Independence Chapter 5: Some Important Random Variables 5.1. Some Discrete Random Variables 5.1.1. Bernoulli 5.1.2. Geometric 5.1.3. Binomial 5.1.4. Negative Binomial 5.1.5. Hypergeometric 5.1.6. Poisson 5.2. Some Continuous Random Variables 5.2.1. Uniform 5.2.2. Triangular 5.2.3. Normal 5.2.4. Chi-Square 5.2.5. Student’s t 5.2.6. F Distributions 5.2.7. Exponential 5.2.8. Gamma 5.2.9. Phase-Type 5.2.10. Erlang 5.2.11. Hypoexponential 5.2.12. Hyperexponential 5.2.13. Cox 5.2.14. Weibull 5.3. Functions of a Random Variable 5.4. Taylor Series Chapter 6: Statistical Inference and Data Fitting 6.1. Parametric Confidence Interval for Mean 6.1.1. Confidence Interval when Variance is Known 6.1.2. Confidence Interval when Variance is Unknown 6.2. Parametric Confidence Interval for SD2 and SD 6.3. Parametric Confidence Interval for Proportion 6.3.1. Parametric Confid. Interv. for p based on b(n,k) 6.3.2. Parametric Confid. Interv. for p based on N(µ,σ) 6.4. Parametric Confidence Interval for Difference 6.4.1. Confidence Interval for Paired Comparison 6.4.2. Conf. Interv. for Non-Corresp. Measurements 6.5. Bootstrap 6.5.1. Basic Bootstrap 6.5.2. Bootstrap-t 6.5.3. Semi-Parametric Bootstrap 6.6. Goodness of Fit 6.6.1. Probability–Probability Plot Method 6.6.2. χ2 Method 6.6.3. Kolmogorov-Smirnov Method 6.7. Data Fitting 6.7.1. Linear Regression 6.7.2. Polynomial Regression 6.7.3. Exponential Regression 6.7.4. Lagrange’s Polynomial Chapter 7: Data Scaling, Distances, and Clustering 7.1. Data Scaling 7.2. Distance and Similarity Measures 7.3. Cluster Distances 7.4. Clustering: an introduction 7.5. K-Means 7.6. K-Medoid and K-Median 7.7. Hierarchical Clustering PART II: Performance Modeling Chapter 8: Operational Analysis 8.1. Utilization Law 8.2. Forced Flow Law 8.3. Demand Law 8.4. Little’s Law 8.5. General Response Time Law 8.6. Interactive Response Time Law 8.7. Bottleneck Analysis and Bounds Chapter 9: Discrete Time Markov Chain 9.1. Stochastic Processes 9.2. Chapman-Kolmogorov Equation 9.3. Transient Distribution 9.4. Steady State Distribution 9.5. Classification of States, MRT and MFPT 9.6. Holding Time (Sojourn Time or Residence Time) 9.7. Mean Time to Absorption 9.8. Some Applications Chapter 10: Continuous Time Markov Chain 10.1. Rate Matrix 10.2. Chapman-Kolmogorov Equation 10.3. Holding Times 10.4. Stationary Analysis 10.4.1. Gauss Elimination 10.4.2. Gauss-Seidel Method 10.5. Transient Analysis 10.5.1. Interval Subdivision 10.5.2. First Order Differential Linear Equation 10.5.3. Solution through Laplace Transform 10.5.4. Uniformization Method 10.6. Time to Absorption 10.6.1. Method Based on Moments 10.7. Semi-Markov Chain 10.8. Additional Modeling Examples 10.8.1. Online Processing Request Control 10.8.2. Tiny Private Cloud System 10.8.3. Two Servers with Different Processing Rates 10.8.4. M/E/1/4 Queue System 10.8.5. Mobile Application Offloading 10.8.6. Queue System with MMPP Arrival 10.8.7. Poisson Process and Two Queues 10.8.8. Two Stage Tandem System 10.8.9. Event Recommendation Mashup Chapter 11: Basic Queueing Models 11.1. The Birth and Death Process 11.2. M/M/1 Queue 11.3. M/M/m Queue 11.4. M/M/∞ Queue 11.5. M/M/1/k Queue 11.6. M/M/m/k Queue 11.7. M/M/m/m Queue Chapter 12: Petri Nets 12.1. A Glance at History 12.2. Basic Definitions 12.3. Basic Models 12.4. Conflict, Concurrency, and Confusion 12.5. Petri Nets Subclasses 12.6. Modeling Classical Problems 12.7. Behavioral Properties 12.7.1. Boundedness 12.7.2. Reachability 12.7.3. Reversibility 12.7.4. Conservation 12.7.5. Deadlock Freedom 12.7.6. Liveness 12.7.7. Coverability 12.8. Behavioral Property Analysis 12.8.1. Coverability Tree 12.8.2. State Equation 12.8.3. Reductions 12.9. Structural Properties and Analysis 12.9.1. Transition Invariants 12.9.2. Place Invariants Chapter 13: Stochastic Petri Nets 13.1. Definition and Basic Concepts 13.1.1. A Comment about the Model Presented 13.2. Mapping SPN to CTMC 13.3. Performance Modeling with SPN 13.3.1. M/M/1/k Queue System 13.3.2. Modulated Traffic 13.3.3. M/M/m/k Queue System 13.3.4. Queue System with Distinct Classes of Stations 13.3.5. Queue System with Breakdown 13.3.6. Queue System with Priority 13.3.7. Open Tandem Queue System with Blocking 13.3.8. Modeling Phase-Type Distributions 13.3.9. Memory Policies and Phase-Type Distributions 13.3.10. Probability Distribution of SPNs Chapter 14: Stochastic Simulation 14.1. Introduction 14.1.1. Monte Carlo Simulation 14.2. Discrete Event Simulation: an Overview 14.3. Random Variate Generation 14.3.1. Pseudo-Random Number Generation 14.3.2. Inverse Transform Method 14.3.3. Convolution Method 14.3.4. Composition Method 14.3.5. Acceptance-Rejection Method 14.3.6. Characterization 14.4. Output Analysis 14.4.1. Transient Simulation 14.4.2. Steady-State Simulation 14.5. Additional Modeling Examples 14.5.1. G/G/m Queue System 14.5.2. G/G/m Queue System with Breakdown 14.5.3. Planning Mobile Cloud Infrastructures Bibliography