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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Bibliographic Details
Main Author: Haghighi, Aliakbar Montazer
Other Authors: Mishev, D. P. (Dimiter P.)
Format: eBook
Published: Hoboken, New Jersey : John Wiley & Sons, Inc., [2013]
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. Z-Transform; 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 First-Order 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 First-Order ODEs; 3.8. Second-Order Homogeneous ODE; 3.8.1. Solving a Linear Homogeneous Second-Order Differential Equation; 3.9. The Second-Order 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. Cauchy-Euler 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 Second-Order ODE; 3.11.1. Spring-Mass System: Free Undamped Motion; 3.11.2. Damped-Free Vibration; 3.12. Introduction to PDE: Basic Concepts; 3.12.1. First-Order Partial Differential Equations; 3.12.2. Second-Order 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. Differential-Difference 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 (B-D) Process; 5.4. Introduction to Queueing Theory; 5.5. Single-Server Markovian Queue, M/M/1.
  • 5.5.1. Transient Queue Length Distribution for M/M/1.