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

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