Difference and differential equations with applications in queueing theory /
"This book features a collection of topics that are used in stochastic processes and, particularly, in queueing theory. Differential equations, difference equations, and Markovian queues (as they relate to systems of linear differential difference equations) are presented, and the relationship...
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Format:  eBook 
Language:  English 
Published: 
Hoboken, New Jersey :
John Wiley & Sons, Inc.,
[2013]

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Online Access:  Connect to the full text of this electronic book 
Table of Contents:
 Cover; Title page; Copyright page; Contents; Preface; CHAPTER ONE: Probability and Statistics; 1.1. Basic Definitions and Concepts of Probability; 1.2. Discrete Random Variables and Probability Distribution Functions; 1.3. Moments of a Discrete Random Variable; 1.4. Continuous Random Variables; 1.5. Moments of a Continuous Random Variable; 1.6. Continuous Probability Distribution Functions; 1.7. Random Vector; 1.8. Continuous Random Vector; 1.9. Functions of a Random Variable; 1.10. Basic Elements of Statistics; 1.10.1. Measures of Central Tendency; 1.10.2. Measure of Dispersion.
 1.10.3. Properties of Sample Statistics1.11. Inferential Statistics; 1.11.1. Point Estimation; 1.11.2. Interval Estimation; 1.12. Hypothesis Testing; 1.13. Reliability; Exercises; CHAPTER TWO: Transforms; 2.1. Fourier Transform; 2.2. Laplace Transform; 2.3. ZTransform; 2.4. Probability Generating Function; 2.4.1. Some Properties of a Probability Generating Function; Exercises; CHAPTER THREE: Differential Equations; 3.1. Basic Concepts and Definitions; 3.2. Existence and Uniqueness; 3.3. Separable Equations; 3.3.1. Method of Solving Separable Differential Equations.
 3.4. Linear Differential Equations3.4.1. Method of Solving a Linear FirstOrder Differential Equation; 3.5. Exact Differential Equations; 3.6. Solution of the First ODE by Substitution Method; 3.6.1. Substitution Method; 3.6.2. Reduction to Separation of Variables; 3.7. Applications of the FirstOrder ODEs; 3.8. SecondOrder Homogeneous ODE; 3.8.1. Solving a Linear Homogeneous SecondOrder Differential Equation; 3.9. The SecondOrder Nonhomogeneous Linear ODE with Constant Coefficients; 3.9.1. Method of Undetermined Coefficients; 3.9.2. Variation of Parameters Method.
 3.10. Miscellaneous Methods for Solving ODE3.10.1. CauchyEuler Equation; 3.10.2. Elimination Method to Solve Differential Equations; 3.10.3. Application of Laplace Transform to Solve ODE; 3.10.4. Solution of Linear ODE Using Power Series; 3.11. Applications of the SecondOrder ODE; 3.11.1. SpringMass System: Free Undamped Motion; 3.11.2. DampedFree Vibration; 3.12. Introduction to PDE: Basic Concepts; 3.12.1. FirstOrder Partial Differential Equations; 3.12.2. SecondOrder Partial Differential Equations; Exercises; CHAPTER FOUR: Difference Equations; 4.1. Basic Terms.
 4.2. Linear Homogeneous Difference Equations with Constant Coefficients4.3. Linear Nonhomogeneous Difference Equations with Constant Coefficients; 4.3.1. Characteristic Equation Method; 4.3.2. Recursive Method; 4.4. System of Linear Difference Equations; 4.4.1. Generating Functions Method; 4.5. DifferentialDifference Equations; 4.6. Nonlinear Difference Equations; Exercises; CHAPTER FIVE: Queueing Theory; 5.1. Introduction; 5.2. Markov Chain and Markov Process; 5.3. Birth and Death (BD) Process; 5.4. Introduction to Queueing Theory; 5.5. SingleServer Markovian Queue, M/M/1.
 5.5.1. Transient Queue Length Distribution for M/M/1.