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| Preface to the Second Edition | |
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| Preface to the First Edition | |
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| Acronyms | |
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| Introduction | |
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| Motivation | |
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| Probability Models | |
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| Sample Space | |
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| Events | |
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| Algebra of Events | |
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| Graphical Methods of Representing Events | |
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| Probability Axioms | |
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| Combinatorial Problems | |
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| Conditional Probability | |
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| Independence of Events | |
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| Bayes' Rule | |
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| Bernoulli Trials | |
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| Discrete Random Variables | |
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| Introduction | |
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| Random Variables and Their Event Spaces | |
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| The Probability Mass Function | |
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| Distribution Functions | |
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| Special Discrete Distributions | |
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| Analysis of Program MAX | |
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| The Probability Generating Function | |
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| Discrete Random Vectors | |
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| Independent Random Variables | |
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| Continuous Random Variables | |
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| Introduction | |
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| The Exponential Distribution | |
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| The Reliability and Failure Rate | |
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| Some Important Distributions | |
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| Functions of a Random Variable | |
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| Jointly Distributed Random Variables | |
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| Order Statistics | |
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| Distribution of Sums | |
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| Functions of Normal Random Variables | |
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| Expectation | |
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| Introduction | |
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| Moments | |
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| Expectation Based on Multiple Random Variables | |
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| Transform Methods | |
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| Moments and Transforms of Some Distributions | |
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| Computation of Mean Time to Failure | |
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| Inequalities and Limit Theorems | |
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| Conditional Distribution and Expectation | |
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| Introduction | |
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| Mixture Distributions | |
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| Conditional Expectation | |
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| Impefect Fault Coverage and Reliability | |
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| Random Sums | |
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| Stochastic Processes | |
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| Introduction | |
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| Classification of Stochastic Processes | |
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| The Bernoulli Process | |
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| The Poisson Process | |
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| Renewal Processes | |
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| Availability Analysis | |
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| Random Incidence | |
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| Renewal Model of Program Behavior | |
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| Discrete-Time Markov Chains | |
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| Introduction | |
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| Computation of n-step Transition Probabilities | |
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| State Classification and Limiting Probabilities | |
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| Distribution of Times Between State Changes | |
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| Markov Modulated Bernoulli Process | |
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| Irreducible Finite Chains with Aperiodic States | |
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| * The M/G/1 Queuing System | |
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| Discrete-Time Birth-Death Processes | |
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| Finite Markov Chains with Absorbing States | |
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| Continuous-Time Markov Chains | |
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| Introduction | |
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| The Birth-Death Process | |
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| Other Special Cases of the Birth-Death Model | |
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| Non-Birth-Death Processes | |
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| Markov Chains with Absorbing States | |
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| Solution Techniques | |
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| Automated Generation | |
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| Networks of Queues | |
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| Introduction | |
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| Open Queuing Networks | |
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| Closed Queuing Networks | |
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| General Service Distribution and Multiple Job Types | |
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| Non-product-form Networks | |
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| Computing Response Time Distribution | |
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| Summary | |
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| Statistical Inference | |
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| Introduction | |
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| Parameter Estimation | |
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| Hypothesis Testing | |
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| Regression and Analysis of Variance | |
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| Introduction | |
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| Least-squares Curve Fitting | |
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| The Coefficients of Determination | |
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| Confidence Intervals in Linear Regression | |
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| Trend Detection and Slope Estimation | |
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| Correlation Analysis | |
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| Simple Nonlinear Regression | |
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| Higher-dimensional Least-squares Fit | |
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| Analysis of Variance | |
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| Bibliography | |
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| Theory | |
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| Applications | |
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| Properties of Distributions | |
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| Statistical Tables | |
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| Laplace Transforms | |
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| Program Performance Analysis | |
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| Author Index | |
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| Subject Index | |