Buch, Englisch, 512 Seiten, Format (B × H): 155 mm x 231 mm, Gewicht: 1383 g
Buch, Englisch, 512 Seiten, Format (B × H): 155 mm x 231 mm, Gewicht: 1383 g
ISBN: 978-1-394-29404-6
Verlag: Wiley
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 applications of differential equations, difference equations, and Markovian queues. The authors provide a deep exploration of first principles and a wide variety of examples in applied mathematics and engineering and stochastic processes.
This book demonstrates the wide applicability of queuing theory in a range of fields, including telecommunications, traffic engineering, computing, and facility design. It contains brand-new information on partial differential equations as a prerequisite for solving queueing models, as well as sample MATLAB code for addressing these models.
Readers will also find: - A large collection of new examples and enhanced end-of-chapter problems with included solutions
- Comprehensive explorations of single-server, multiple-server, parallel, and series queue models
- Practical discussions of splitting, delayed-service, and delayed feedback
- Enhanced treatments of concepts queueing theory, accessible across engineering and mathematics
Perfect for junior and up undergraduate, as well as graduate students in electrical and mechanical engineering, Differential and Difference Equations with Applications in Queueing Theory will also benefit students of computer science, mathematics, and applied mathematics.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
About the Authors xiii
Preface to the Second Edition xv
1 Introduction 1
1.1 Introduction 1
1.2 Functions of a Real Variable 1
1.3 Some Properties of Differentiable Functions 3
1.4 Functions of More Than One Real Variable 3
1.4.1 The Chain Rule for Real Multivariable Functions 4
1.5 Function of a Complex Variable 7
1.5.1 Complex Numbers and Their Properties 7
1.5.2 Properties of a Complex Variable z 9
1.5.3 Complex Variables and Functions of Complex Variables 10
1.5.4 Some Particular Functions of Complex Variables 12
1.6 Differentiation of Functions of Complex Variables 12
1.6.1 Partial Differentiation of Functions of Complex Variables 13
1.7 Vectors 15
1.7.1 Dot (or Scalar or Inner) Product of Vectors and Some of Its Properties 17
1.7.2 The Cross Product (or Vector Product) of Vectors and Some of Its Properties 18
1.7.3 Directional Derivatives and Gradient Vectors 19
1.7.4 Eigenvalues and Eigenvectors 24
Exercises 25
2 Transforms 31
2.1 Introduction 31
2.2 Fourier Series 32
2.3 Convergence of Fourier Series 39
2.4 Fourier Transform 40
2.4.1 Continuous Fourier Transform 44
2.4.2 Discrete Fourier Transform 48
2.4.3 Some Properties of a Fourier Transform 48
2.4.4 Fast Fourier Transform 49
2.5 Laplace Transform 50
2.5.1 Properties of Laplace Transform 51
2.5.1.1 Linearity 51
2.5.1.2 Existence of Laplace Transform 52
2.5.1.3 Uniqueness of the Laplace Transforms 53
2.5.1.4 The First Shifting or s-Shifting 54
2.5.1.5 Time Delay 54
2.5.1.6 Laplace Transform of Derivatives 56
2.5.1.7 Laplace Transform of Integral 56
2.5.1.8 The Second Shifting or t-Shifting Theorem 57
2.5.1.9 Laplace Transform of Convolution of Two Functions 59
2.5.2 Partial Fraction and Inverse Laplace Transform 63
2.6 Integral Transform 68
