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Informationen zum Autor 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. Klappentext 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 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 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. Zusammenfassung 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. Inhaltsverzeichnis Preface xi 1. Probability and Statistics 1 1.1. Basic Definitions and Concepts of Probability 1 1.2. Discrete Random Variables and Probability Distribution Functions 7 1.3. Moments of a Discrete Random Variable 16 1.4. Continuous Random Variables 20 1.5. Moments of a Continuous Random Variable 25 1.6. Continuous Probability Distribution Functions 26 1.7. Random Vector 41 1.8. Continuous Random Vector 48 1.9. Functions of a Random Variable 49 1.10. Basic Elements of Statistics 53 1.10.1. Measures of Central Tendency 58 1.10.2. Measure of Dispersion 59 1.10.3. Properties of Sample Statistics 61 1.11. Inferential Statistics 67 1.11.1. Point Estimation 68 1.11.2. Interval Estimation 72 1.12. Hypothesis Testing 75 1.13. Reliability 78 Exercises 81 2. Transforms 90 2.1. Fourier Transform 90 2.2. Laplace Transform 94 2.3. Z-Transform 104 2.4. Probability Generating Function 111 2.4.1. Some Properties of a Probability Generating Function 112 Exercises 116 3. Differential Equations 121 3.1. Basic Concepts and D...
