Differential and Difference Equations with Applications in Queueing Theory.

Format:

Book

Author/Creator:

Haghighi, Aliakbar Montazer.

Language:

English

Subjects (All):

Queuing theory.

Differential equations.

Physical Description:

1 online resource (513 pages)

Edition:

2nd ed.

Place of Publication:

Newark : John Wiley & Sons, Incorporated, 2026.

Summary:

A newly updated and authoritative exploration of differential and difference equations used in queueing theory In the newly revised second edition of Differential and Difference Equations with Applications in Queueing Theory , a team of distinguished researchers delivers an up-to-date discussion of the unique connections between the methods and.

Contents:

Cover

Title Page

Copyright

Contents

About the Authors

Preface to the Second Edition

Chapter 1 Introduction

1.1 Introduction

1.2 Functions of a Real Variable

1.3 Some Properties of Differentiable Functions

1.4 Functions of More Than One Real Variable

1.4.1 The Chain Rule for Real Multivariable Functions

1.5 Function of a Complex Variable

1.5.1 Complex Numbers and Their Properties

1.5.2 Properties of a Complex Variable z

1.5.3 Complex Variables and Functions of Complex Variables

1.5.4 Some Particular Functions of Complex Variables

1.6 Differentiation of Functions of Complex Variables

1.6.1 Partial Differentiation of Functions of Complex Variables

1.7 Vectors

1.7.1 Dot (or Scalar or Inner) Product of Vectors and Some of Its Properties

1.7.2 The Cross Product (or Vector Product) of Vectors and Some of Its Properties

1.7.3 Directional Derivatives and Gradient Vectors

1.7.4 Eigenvalues and Eigenvectors

Exercises

Chapter 2 Transforms

2.1 Introduction

2.2 Fourier Series

2.3 Convergence of Fourier Series

2.4 Fourier Transform

2.4.1 Continuous Fourier Transform

2.4.2 Discrete Fourier Transform

2.4.3 Some Properties of a Fourier Transform

2.4.4 Fast Fourier Transform

2.5 Laplace Transform

2.5.1 Properties of Laplace Transform

2.5.1.1 Linearity

2.5.1.2 Existence of Laplace Transform

2.5.1.3 Uniqueness of the Laplace Transforms

2.5.1.4 The First Shifting or s‐Shifting

2.5.1.5 Time Delay

2.5.1.6 Laplace Transform of Derivatives

2.5.1.7 Laplace Transform of Integral

2.5.1.8 The Second Shifting or t‐Shifting Theorem

2.5.1.9 Laplace Transform of Convolution of Two Functions

2.5.2 Partial Fraction and Inverse Laplace Transform

2.6 Integral Transform

2.7 Ƶ‐Transform

Notes

Exercises.

Chapter 3 Ordinary Differential Equations

3.1 Introduction and History of Ordinary Differential Educations

3.2 Basics Concepts and Definitions

3.3 Existence and Uniqueness

3.4 Separable Equations

3.4.1 Method of Solving Separable Ordinary Differential Equations

3.5 Linear Ordinary Differential Equations

3.5.1 Method of Solving a Linear First‐Order Differential Equation

3.6 Exact Ordinary Differential Equations

3.7 Solution of the First ODE by Substitution Method

3.7.1 Substitution Method

3.7.2 Reduction to Separation of Variables

3.8 Applications of the First‐Order ODEs

3.9 Second‐Order Homogeneous Ordinary Differential Equation

3.9.1 Solution of the Homogenous Second‐Order Homogeneous Ordinary Differential Equation with Constant Coefficients, Equation (3.9.3)

3.10 The Second‐Order Nonhomogeneous Linear Ordinary Differential Equation with Constant Coefficients

3.10.1 Method of Undetermined Coefficients

3.10.2 Variation of Parameters Method

3.11 Laplace Transform Method

3.12 Cauchy-Euler Equation Differential Equation

3.12.1 The Second‐Order Homogenous Cauchy-Euler Equation

3.12.2 Solving the Second‐Order Homogeneous Cauchy-Euler Equation Using x &amp

equals

et or t &amp

ln |x|

3.13 Elimination Method to Solve Differential Equations

3.14 Solution of Linear ODE Using Power Series

Chapter 4 Partial Differential Equations

4.1 Introduction

4.2 Basic Terminologies for Partial Differential Equations

4.3 Some Particular Functions Used in Partial Differential Equations

4.4 Types of Boundary Conditions for a Partial Differential Equation

4.5 Solution for a Partial Differential Equation

4.5.1 Methods of Finding Solution for a Partial Differential Equation

4.6 Linear, Semi‐linear, and Quasi‐linear Partial Differential Equations.

4.6.1 Examples and Solutions of One‐ and Two‐Dimensional Linear and Quasi‐linear Partial Differential Equations of the First, Second, and Third Order

4.6.2 Characteristics Equation Method with Steps

4.7 Solution of Wave Partial Differential Equation, First and Second Orders, with Different Methods

4.8 A One‐Dimensional, Second‐Order Heat (or Parabolic) Equations

Chapter 5 Differential Difference Equations

5.1 Introduction

5.2 Basic Terms

5.3 Linear Homogeneous Difference Equations with Constant Coefficients

5.3.1 Recursive Method

5.3.2 Characteristic Equation Method

5.4 Linear Nonhomogeneous Difference Equations with Constant Coefficients

5.4.1 Characteristic Equation Method

5.4.1.1 Case 1: a &amp

1

5.4.1.2 Case 2: a ≠ 1

5.4.1.3 Case 3: a &amp

−1

5.4.1.4 Case 4: a &gt

5.4.1.5 Case 5: 0 &lt

a &lt

5.4.1.6 Case 6: −1 &lt

0

5.4.1.7 Case 7: a &lt

5.4.1.8 Case 8: a ≠ 1, c &amp

b/(1 − a)

5.4.2 Recursive Method

5.4.2 Proof:

5.4.3 Solving Differential Equations by Difference Equations

5.5 System of Linear Difference Equations

5.5.1 Recursive Method

5.5.2 Generating Functions Method

5.6 Differential‐Difference Equations

5.6.1 Recursive Method

5.6.2 Generating Function Method

5.7 Nonlinear Difference Equations

Chapter 6 Probability and Statistics

6.1 Introduction and Basic Definitions and Concepts of Probability

6.1.1 Axioms of Probabilities of Events

6.2 Discrete Random Variables and Probability Distribution Functions

6.3 Moments of a Discrete Random Variable

6.4 Continuous Random Variables

6.5 Moments of a Continuous Random Variable

6.6 Continuous Probability Distribution Functions

6.7 Random Vector

6.8 Continuous Random Vector.

6.9 Functions of a Random Variable

6.10 Basic Elements of Statistics

6.10.1 Measures of Central Tendency

6.10.2 Measure of Dispersion

6.10.3 Properties of Sample Statistics

6.11 Inferential Statistics

6.11.1 Point Estimation

6.11.2 Interval Estimation

6.12 Hypothesis Testing

6.13 Reliability

Chapter 7 Queueing Theory

7.1 Introduction

7.2 Markov Chain and Markov Process

7.3 Birth and Death Process

7.4 Introduction to Queueing Theory

7.5 Single‐Server Markovian Queue, M/M/1

7.5.1 Transient Queue Length Distribution for M/M/1

7.5.2 Stationary Queue Length Distribution for M/M/1

7.5.3 Stationary Waiting Time of a Task in M/M/1 Queue

7.5.4 Distribution of a Busy Period for M/M/1 Queue

7.6 Finite Buffer Single‐Server Markovian Queue: M/M/1/N

7.7 M/M/1 Queue with Feedback

7.8 Single‐Server Markovian Queue with State‐Dependent Balking

7.9 Multiserver Parallel Queue

7.9.1 Transient Queue Length Distribution for M/M/m

7.9.2 Stationary Queue Length Distribution for M/M/m

7.9.3 Stationary Waiting Time of a Task in M/M/m Queue

7.10 Many‐Server Parallel Queues with Feedback

7.10.1 Introduction

7.10.2 Stationary Distribution of the Queue Length

7.10.3 Stationary Waiting Time of a Task in Many‐Server Queue with Feedback

7.11 Many‐Server Queues with Balking and Reneging

7.11.1 Priority M/M/2 with Constant Balking and Exponential Reneging

7.11.2 M/M/m with Constant Balking and Exponential Reneging

7.11.3 Distribution of the Queue Length for M/M/m System with Constant Balking and Exponential Reneging

7.12 Single‐Server Markovian Queueing System with Splitting and Delayed Feedback

7.12.1 Description of the Model

7.12.2 Analysis

7.12.3 Computation of Expected Values of the Queue Length and Waiting Time at Each Station, Algorithmically.

7.12.4 Numerical Example

7.12.5 Discussion and Conclusion

Appendix

The Poisson Probability Distribution

The Chi-Square Distribution

The Standard Normal Probability Distribution

The (Student) t Probability Distribution

Bibliography

Answers/Solutions to Selected Exercises

Index

EULA.

Notes:

Description based on publisher supplied metadata and other sources.

Part of the metadata in this record was created by AI, based on the text of the resource.

ISBN:

1-394-29407-7

1-394-29406-9

9781394294060

OCLC:

1577547929