Differential and Difference Equations with Applications in Queueing Theory

• Autore: Haghighi Aliakbar Montazer
• Pubblicazione: Newark : , : John Wiley & Sons, Incorporated, , 2026; ©2026
• Edizione: 2nd ed.
• Descrizione fisica: 1 online resource (513 pages)
• Disciplina: 515.35
• Soggetto topico: Queuing theory; Differential equations
• Nota di contenuto: 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 & -- equals -- et or t & -- equals -- ln |x| -- 3.13 Elimination Method to Solve Differential Equations -- 3.14 Solution of Linear ODE Using Power Series -- Exercises -- 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 -- Exercises -- 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 & -- equals -- 1 -- 5.4.1.2 Case 2: a ≠ 1 -- 5.4.1.3 Case 3: a & -- equals -- −1 -- 5.4.1.4 Case 4: a > -- 1 -- 5.4.1.5 Case 5: 0 < -- a < -- 1 -- 5.4.1.6 Case 6: −1 < -- a < -- 0 -- 5.4.1.7 Case 7: a < -- −1 -- 5.4.1.8 Case 8: a ≠ 1, c & -- equals -- 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 -- Exercises -- 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 -- Exercises -- 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 -- Exercises -- 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Differential and Difference Equations with Applications in Queueing Theory
• ISBN: 1-394-29407-7; 1-394-29406-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9911069825503321
• Lo trovi qui: Univ. Federico II