Difference and Differential Equations with Applications in Queueing Theory.
Title:
Difference and Differential Equations with Applications in Queueing Theory.
Author:
Haghighi, Aliakar M.
ISBN:
9781118400654
Personal Author:
Edition:
1st ed.
Physical Description:
1 online resource (396 pages)
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 Statistics -- 1.11. 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 Equations -- 3.4.1. 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 ODE -- 3.10.1. 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 Coefficients -- 4.3. 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 -- 5.5.2. Stationary Queue Length Distribution for M/M/1 -- 5.5.3. Stationary Waiting Time of a Task in M/M/1 Queue -- 5.5.4. Distribution of a Busy Period for M/M/1 Queue -- 5.6. Finite Buffer Single-Server Markovian Queue: M/M/1/N -- 5.7. M/M/1 Queue with Feedback -- 5.8. Single-Server Markovian Queue with State-Dependent Balking -- 5.9. Multiserver Parallel Queue -- 5.9.1. Transient Queue Length Distribution for M/M/m -- 5.9.2. Stationary Queue Length Distribution for M/M/m -- 5.9.3. Stationary Waiting Time of a Task in M/M/m Queue -- 5.10. Many-Server Parallel Queues with Feedback.
5.10.1. Introduction -- 5.10.2. Stationary Distribution of the Queue Length -- 5.10.3. Stationary Waiting Time of a Task in Many-Server Queue with Feedback -- 5.11. Many-Server Queues with Balking and Reneging -- 5.11.1. Priority M/M/2 with Constant Balking and Exponential Reneging -- 5.11.2. M/M/m with Constant Balking and Exponential Reneging -- 5.11.3. Distribution of the Queue Length for M/M/m System with Constant Balking and Exponential Reneging -- 5.12. Single-Server Markovian Queueing System with Splitting and DELAYED Feedback -- 5.12.1. Description of the Model -- 5.12.2. Analysis -- 5.12.3. Computation of Expected Values of the Queue Length and Waiting Time at each Station, Algorithmically -- 5.12.4. Numerical Example -- 5.12.5. Discussion and Conclusion -- Exercises -- Appendix -- The Poisson Probability Distribution -- The Chi-Square Distribution -- The Chi-Square Distribution (continued) -- The Standard Normal Probability Distribution -- The Standard Normal Probability Distribution (continued) -- The (Student's) t Probability Distribution -- References and Further Readings -- Answers/Solutions to Selected Exercises -- Index.
Abstract:
A Useful Guide to the Interrelated Areas of Differential Equations, Difference Equations, and Queueing Models Difference and Differential Equations with Applications in Queueing Theory presents the unique connections between the methods and applications of differential equations, difference equations, and Markovian queues. Featuring a comprehensive collection of topics that are used in stochastic processes, particularly in queueing theory, the book thoroughly discusses the relationship to systems of linear differential difference equations. The book demonstrates the applicability that queueing theory has in a variety of fields including telecommunications, traffic engineering, computing, and the design of factories, shops, offices, and hospitals. Along with the needed prerequisite fundamentals in probability, statistics, and Laplace transform, Difference and Differential Equations with Applications in Queueing Theory provides: A discussion on splitting, delayed-service, and delayed feedback for single-server, multiple-server, parallel, and series queue models Applications in queue models whose solutions require differential difference equations and generating function methods Exercises at the end of each chapter along with select answers The book is an excellent resource for researchers and practitioners in applied mathematics, operations research, engineering, and industrial engineering, as well as a useful text for upper-undergraduate and graduate-level courses in applied mathematics, differential and difference equations, queueing theory, probability, and stochastic processes.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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