Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Haghighi, Aliakbar Montazer
Titre(s) : Difference and differential equations with applications in queueing theory [Texte électronique] / Aliakbar M. Haghighi Department of Mathematics, Prairie View A & M University, Prairie View, Texas, Dimitar P. Mishev Department of Mathematics, Prairie View A & M University, Prairie View, Texas
Publication : Hoboken, New Jersey : John Wiley & Sons, Inc., [2013]
Description matérielle : 1 online resource
Note(s) : Includes bibliographical references and index. - Print version record and CIP data provided by publisher.
"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 between the methods and applications are thoroughly
addressed"
Autre(s) auteur(s) : Mishev, Dimitr P. (1952-....). Fonction indéterminée
Sujet(s) : Files d'attente, Théorie des
Équations aux différences
Équations différentielles
Mathématiques
Indice(s) Dewey :
519.82 (23e éd.) = Théorie des files d'attente
Identifiants, prix et caractéristiques : ISBN 9781118400678
Identifiant de la notice : ark:/12148/cb44653621f
Notice n° :
FRBNF44653621
(notice reprise d'un réservoir extérieur)
Table des matières : 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.
