Difference and Differential Equations with Applications in Queueing Theory

Inbunden, Engelska, 2013

Av Aliakbar Montazer Haghighi, Dimitar P. Mishev, TX) Haghighi, Aliakbar Montazer (Prairie View A&M University, TX) Mishev, Dimitar P. (Prairie View A&M University, Dimitar P Mishev

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A Useful Guide to the Interrelated Areas of Differential Equations, Difference Equations, and Queueing ModelsDifference 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 modelsApplications in queue models whose solutions require differential difference equations and generating function methodsExercises at the end of each chapter along with select answersThe 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.

Produktinformation

Utgivningsdatum2013-08-23
Mått160 x 242 x 26 mm
Vikt699 g
FormatInbunden
SpråkEngelska
Antal sidor424
FörlagJohn Wiley & Sons Inc
ISBN9781118393246

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ALIAKBAR MONTAZER HAGHIGHI, PhD, is Professor and Head of the Department of Mathematics at Prairie View A&M University, as well as founder and Editor-in-Chief of Applications and Applied Mathematics: An International Journal (AAM). Dr. Haghighi's research interests and publications are in the areas of probability, statistics, stochastic processes, and queueing theory.DIMITAR P. MISHEV, PhD, is Professor in the Department of Mathematics at Prairie View A&M University. The author of numerous research papers and three books coauthored with Dr. Haghighi, Dr. Mishev's areas of research interest include differential and difference equations and queueing theory.

Preface xi1. Probability and Statistics 11.1. Basic Definitions and Concepts of Probability 11.2. Discrete Random Variables and Probability Distribution Functions 71.3. Moments of a Discrete Random Variable 161.4. Continuous Random Variables 201.5. Moments of a Continuous Random Variable 251.6. Continuous Probability Distribution Functions 261.7. Random Vector 411.8. Continuous Random Vector 481.9. Functions of a Random Variable 491.10. Basic Elements of Statistics 531.10.1. Measures of Central Tendency 581.10.2. Measure of Dispersion 591.10.3. Properties of Sample Statistics 611.11. Inferential Statistics 671.11.1. Point Estimation 681.11.2. Interval Estimation 721.12. Hypothesis Testing 751.13. Reliability 78Exercises 812. Transforms 902.1. Fourier Transform 902.2. Laplace Transform 942.3. Z-Transform 1042.4. Probability Generating Function 1112.4.1. Some Properties of a Probability Generating Function 112Exercises 1163. Differential Equations 1213.1. Basic Concepts and Definitions 1213.2. Existence and Uniqueness 1303.3. Separable Equations 1323.3.1. Method of Solving Separable Differential Equations 1333.4. Linear Differential Equations 1403.4.1. Method of Solving a Linear First-Order Differential Equation 1413.5. Exact Differential Equations 1443.6. Solution of the First ODE by Substitution Method 1533.6.1. Substitution Method 1543.6.2. Reduction to Separation of Variables 1583.7. Applications of the First-Order ODEs 1593.8. Second-Order Homogeneous ODE 1643.8.1. Solving a Linear Homogeneous Second-Order Differential Equation 1653.9. The Second-Order Nonhomogeneous Linear ODE with Constant Coefficients 1753.9.1. Method of Undetermined Coefficients 1783.9.2. Variation of Parameters Method 1843.10. Miscellaneous Methods for Solving ODE 1883.10.1. Cauchy–Euler Equation 1883.10.2. Elimination Method to Solve Differential Equations 1903.10.3. Application of Laplace Transform to Solve ODE 1933.10.4. Solution of Linear ODE Using Power Series 1953.11. Applications of the Second-Order ODE 1993.11.1. Spring–Mass System: Free Undamped Motion 1993.11.2. Damped-Free Vibration 2003.12. Introduction to PDE: Basic Concepts 2033.12.1. First-Order Partial Differential Equations 2053.12.2. Second-Order Partial Differential Equations 208Exercises 2134. Difference Equations 2184.1. Basic Terms 2204.2. Linear Homogeneous Difference Equations with Constant Coefficients 2244.3. Linear Nonhomogeneous Difference Equations with Constant Coefficients 2314.3.1. Characteristic Equation Method 2314.3.2. Recursive Method 2374.4. System of Linear Difference Equations 2444.4.1. Generating Functions Method 2454.5. Differential–Difference Equations 2534.6. Nonlinear Difference Equations 259Exercises 2645. Queueing Theory 2675.1. Introduction 2675.2. Markov Chain and Markov Process 2685.3. Birth and Death (B-D) Process 2815.4. Introduction to Queueing Theory 2845.5. Single-Server Markovian Queue, M/M/ 1 2865.5.1. Transient Queue Length Distribution for M/M/ 1 2915.5.2. Stationary Queue Length Distribution for M/M/ 1 2945.5.3. Stationary Waiting Time of a Task in M/M/1 Queue 3005.5.4. Distribution of a Busy Period for M/M/1 Queue 3005.6. Finite Buffer Single-Server Markovian Queue: M/M/1/N 3035.7. M/M/1 Queue with Feedback 3075.8. Single-Server Markovian Queue with State-Dependent Balking 3085.9. Multiserver Parallel Queue 3115.9.1. Transient Queue Length Distribution for M/M/m 3125.9.2. Stationary Queue Length Distribution for M/M/m 3205.9.3. Stationary Waiting Time of a Task in M/M/m Queue 3235.10. Many-Server Parallel Queues with Feedback 3265.10.1. Introduction 3265.10.2. Stationary Distribution of the Queue Length 3265.10.3. Stationary Waiting Time of a Task in Many-Server Queue with Feedback 3275.11. Many-Server Queues with Balking and Reneging 3285.11.1. Priority M/M/2 with Constant Balking and Exponential Reneging 3285.11.2. M/M/m with Constant Balking and Exponential Reneging 3325.11.3. Distribution of the Queue Length for M/M/m System with Constant Balking and Exponential Reneging 3335.12. Single-Server Markovian Queueing System with Splitting and Delayed Feedback 3345.12.1. Description of the Model 3345.12.2. Analysis 3365.12.3. Computation of Expected Values of the Queue Length and Waiting Time at each Station, Algorithmically 3415.12.4. Numerical Example 3495.12.5. Discussion and Conclusion 350Exercises 353Appendix 358The Poisson Probability Distribution 358The Chi-Square Distribution 361The Chi-Square Distribution (continued) 362The Standard Normal Probability Distribution 363The Standard Normal Probability Distribution (continued) 364The (Student’s) t Probability Distribution 365References and Further Readings 366Answers/Solutions to Selected Exercises 372Index 379