05362nam 2200709Ia 450 991081579070332120240313230602.01-118-40067-41-118-40065-81-118-40064-X(CKB)2560000000103317(EBL)1207568(OCoLC)830837653(SSID)ssj0000885958(PQKBManifestationID)11499250(PQKBTitleCode)TC0000885958(PQKBWorkID)10816517(PQKB)11313624(MiAaPQ)EBC1207568(DLC) 2013011634(Au-PeEL)EBL1207568(CaPaEBR)ebr10716702(CaONFJC)MIL496087(PPN)191455539(EXLCZ)99256000000010331720130320d2013 uy 0engur|n|---|||||txtccrDifference and differential equations with applications in queueing theory /Aliakbar M. Haghighi, Dimitar P. Mishev1st ed.Hoboken, NJ John Wiley & Sons, Inc.c20131 online resource (420 p.)Description based upon print version of record.1-118-39324-4 Includes bibliographical references and index.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 Dispersion1.10.3. 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 Equations3.4. 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 Method3.10. 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 Terms4.2. 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/15.5.1. Transient Queue Length Distribution for M/M/1"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"--Provided by publisher.Difference equationsDifferential equationsQueuing theoryDifference equations.Differential equations.Queuing theory.519.8/2MAT029000bisacshHaghighi Aliakbar Montazer1597410Mishev D. P(Dimiter P.)1597412MiAaPQMiAaPQMiAaPQBOOK9910815790703321Difference and differential equations with applications in queueing theory4049666UNINA