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.
Author(s): Paulo Romero, Martins Maciel
Publisher: CRC Press
Year: 2023
Language: English
Pages: 841
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
