{"product_id":"difference-and-differential-equations-with-applications-in-queueing-theory-isbn-9781118393246","title":"Difference and Differential Equations with Applications in Queueing Theory","description":"\u003cp\u003e\u003cb\u003eA Useful Guide to the Interrelated Areas of Differential Equations, Difference Equations, and Queueing Models\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eDifference and Differential Equations with Applications in Queueing Theory\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003eThe 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, \u003ci\u003eDifference and Differential Equations with Applications in Queueing Theory\u003c\/i\u003e provides:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eA discussion on splitting, delayed-service, and delayed feedback for single-server, multiple-server, parallel, and series queue models\u003c\/li\u003e \u003cli\u003eApplications in queue models whose solutions require differential difference equations and generating function methods\u003c\/li\u003e \u003cli\u003eExercises at the end of each chapter along with select answers\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe 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.\u003c\/p\u003e \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1. Probability and Statistics 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1. Basic Definitions and Concepts of Probability 1\u003c\/p\u003e \u003cp\u003e1.2. Discrete Random Variables and Probability Distribution Functions 7\u003c\/p\u003e \u003cp\u003e1.3. Moments of a Discrete Random Variable 16\u003c\/p\u003e \u003cp\u003e1.4. Continuous Random Variables 20\u003c\/p\u003e \u003cp\u003e1.5. Moments of a Continuous Random Variable 25\u003c\/p\u003e \u003cp\u003e1.6. Continuous Probability Distribution Functions 26\u003c\/p\u003e \u003cp\u003e1.7. Random Vector 41\u003c\/p\u003e \u003cp\u003e1.8. Continuous Random Vector 48\u003c\/p\u003e \u003cp\u003e1.9. Functions of a Random Variable 49\u003c\/p\u003e \u003cp\u003e1.10. Basic Elements of Statistics 53\u003c\/p\u003e \u003cp\u003e1.10.1. Measures of Central Tendency 58\u003c\/p\u003e \u003cp\u003e1.10.2. Measure of Dispersion 59\u003c\/p\u003e \u003cp\u003e1.10.3. Properties of Sample Statistics 61\u003c\/p\u003e \u003cp\u003e1.11. Inferential Statistics 67\u003c\/p\u003e \u003cp\u003e1.11.1. Point Estimation 68\u003c\/p\u003e \u003cp\u003e1.11.2. Interval Estimation 72\u003c\/p\u003e \u003cp\u003e1.12. Hypothesis Testing 75\u003c\/p\u003e \u003cp\u003e1.13. Reliability 78\u003c\/p\u003e \u003cp\u003eExercises 81\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2. Transforms 90\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1. Fourier Transform 90\u003c\/p\u003e \u003cp\u003e2.2. Laplace Transform 94\u003c\/p\u003e \u003cp\u003e2.3. Z-Transform 104\u003c\/p\u003e \u003cp\u003e2.4. Probability Generating Function 111\u003c\/p\u003e \u003cp\u003e2.4.1. Some Properties of a Probability Generating Function 112\u003c\/p\u003e \u003cp\u003eExercises 116\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Differential Equations 121\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1. Basic Concepts and Definitions 121\u003c\/p\u003e \u003cp\u003e3.2. Existence and Uniqueness 130\u003c\/p\u003e \u003cp\u003e3.3. Separable Equations 132\u003c\/p\u003e \u003cp\u003e3.3.1. Method of Solving Separable Differential Equations 133\u003c\/p\u003e \u003cp\u003e3.4. Linear Differential Equations 140\u003c\/p\u003e \u003cp\u003e3.4.1. Method of Solving a Linear First-Order Differential Equation 141\u003c\/p\u003e \u003cp\u003e3.5. Exact Differential Equations 144\u003c\/p\u003e \u003cp\u003e3.6. Solution of the First ODE by Substitution Method 153\u003c\/p\u003e \u003cp\u003e3.6.1. Substitution Method 154\u003c\/p\u003e \u003cp\u003e3.6.2. Reduction to Separation of Variables 158\u003c\/p\u003e \u003cp\u003e3.7. Applications of the First-Order ODEs 159\u003c\/p\u003e \u003cp\u003e3.8. Second-Order Homogeneous ODE 164\u003c\/p\u003e \u003cp\u003e3.8.1. Solving a Linear Homogeneous Second-Order Differential Equation 165\u003c\/p\u003e \u003cp\u003e3.9. The Second-Order Nonhomogeneous Linear ODE with Constant Coefficients 175\u003c\/p\u003e \u003cp\u003e3.9.1. Method of Undetermined Coefficients 178\u003c\/p\u003e \u003cp\u003e3.9.2. Variation of Parameters Method 184\u003c\/p\u003e \u003cp\u003e3.10. Miscellaneous Methods for Solving ODE 188\u003c\/p\u003e \u003cp\u003e3.10.1. Cauchy–Euler Equation 188\u003c\/p\u003e \u003cp\u003e3.10.2. Elimination Method to Solve Differential Equations 190\u003c\/p\u003e \u003cp\u003e3.10.3. Application of Laplace Transform to Solve ODE 193\u003c\/p\u003e \u003cp\u003e3.10.4. Solution of Linear ODE Using Power Series 195\u003c\/p\u003e \u003cp\u003e3.11. Applications of the Second-Order ODE 199\u003c\/p\u003e \u003cp\u003e3.11.1. Spring–Mass System: Free Undamped Motion 199\u003c\/p\u003e \u003cp\u003e3.11.2. Damped-Free Vibration 200\u003c\/p\u003e \u003cp\u003e3.12. Introduction to PDE: Basic Concepts 203\u003c\/p\u003e \u003cp\u003e3.12.1. First-Order Partial Differential Equations 205\u003c\/p\u003e \u003cp\u003e3.12.2. Second-Order Partial Differential Equations 208\u003c\/p\u003e \u003cp\u003eExercises 213\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4. Difference Equations 218\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1. Basic Terms 220\u003c\/p\u003e \u003cp\u003e4.2. Linear Homogeneous Difference Equations with Constant Coefficients 224\u003c\/p\u003e \u003cp\u003e4.3. Linear Nonhomogeneous Difference Equations with Constant Coefficients 231\u003c\/p\u003e \u003cp\u003e4.3.1. Characteristic Equation Method 231\u003c\/p\u003e \u003cp\u003e4.3.2. Recursive Method 237\u003c\/p\u003e \u003cp\u003e4.4. System of Linear Difference Equations 244\u003c\/p\u003e \u003cp\u003e4.4.1. Generating Functions Method 245\u003c\/p\u003e \u003cp\u003e4.5. Differential–Difference Equations 253\u003c\/p\u003e \u003cp\u003e4.6. Nonlinear Difference Equations 259\u003c\/p\u003e \u003cp\u003eExercises 264\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5. Queueing Theory 267\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1. Introduction 267\u003c\/p\u003e \u003cp\u003e5.2. Markov Chain and Markov Process 268\u003c\/p\u003e \u003cp\u003e5.3. Birth and Death (B-D) Process 281\u003c\/p\u003e \u003cp\u003e5.4. Introduction to Queueing Theory 284\u003c\/p\u003e \u003cp\u003e5.5. Single-Server Markovian Queue, M\/M\/ 1 286\u003c\/p\u003e \u003cp\u003e5.5.1. Transient Queue Length Distribution for M\/M\/ 1 291\u003c\/p\u003e \u003cp\u003e5.5.2. Stationary Queue Length Distribution for M\/M\/ 1 294\u003c\/p\u003e \u003cp\u003e5.5.3. Stationary Waiting Time of a Task in M\/M\/1 Queue 300\u003c\/p\u003e \u003cp\u003e5.5.4. Distribution of a Busy Period for M\/M\/1 Queue 300\u003c\/p\u003e \u003cp\u003e5.6. Finite Buffer Single-Server Markovian Queue: M\/M\/1\/N 303\u003c\/p\u003e \u003cp\u003e5.7. M\/M\/1 Queue with Feedback 307\u003c\/p\u003e \u003cp\u003e5.8. Single-Server Markovian Queue with State-Dependent Balking 308\u003c\/p\u003e \u003cp\u003e5.9. Multiserver Parallel Queue 311\u003c\/p\u003e \u003cp\u003e5.9.1. Transient Queue Length Distribution for M\/M\/m 312\u003c\/p\u003e \u003cp\u003e5.9.2. Stationary Queue Length Distribution for M\/M\/m 320\u003c\/p\u003e \u003cp\u003e5.9.3. Stationary Waiting Time of a Task in M\/M\/m Queue 323\u003c\/p\u003e \u003cp\u003e5.10. Many-Server Parallel Queues with Feedback 326\u003c\/p\u003e \u003cp\u003e5.10.1. Introduction 326\u003c\/p\u003e \u003cp\u003e5.10.2. Stationary Distribution of the Queue Length 326\u003c\/p\u003e \u003cp\u003e5.10.3. Stationary Waiting Time of a Task in Many-Server Queue with Feedback 327\u003c\/p\u003e \u003cp\u003e5.11. Many-Server Queues with Balking and Reneging 328\u003c\/p\u003e \u003cp\u003e5.11.1. Priority M\/M\/2 with Constant Balking and Exponential Reneging 328\u003c\/p\u003e \u003cp\u003e5.11.2. M\/M\/m with Constant Balking and Exponential Reneging 332\u003c\/p\u003e \u003cp\u003e5.11.3. Distribution of the Queue Length for M\/M\/m System with Constant Balking and Exponential Reneging 333\u003c\/p\u003e \u003cp\u003e5.12. Single-Server Markovian Queueing System with Splitting and Delayed Feedback 334\u003c\/p\u003e \u003cp\u003e5.12.1. Description of the Model 334\u003c\/p\u003e \u003cp\u003e5.12.2. Analysis 336\u003c\/p\u003e \u003cp\u003e5.12.3. Computation of Expected Values of the Queue Length and Waiting Time at each Station, Algorithmically 341\u003c\/p\u003e \u003cp\u003e5.12.4. Numerical Example 349\u003c\/p\u003e \u003cp\u003e5.12.5. Discussion and Conclusion 350\u003c\/p\u003e \u003cp\u003eExercises 353\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix 358\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Poisson Probability Distribution 358\u003c\/p\u003e \u003cp\u003eThe Chi-Square Distribution 361\u003c\/p\u003e \u003cp\u003eThe Chi-Square Distribution (continued) 362\u003c\/p\u003e \u003cp\u003eThe Standard Normal Probability Distribution 363\u003c\/p\u003e \u003cp\u003eThe Standard Normal Probability Distribution (continued) 364\u003c\/p\u003e \u003cp\u003eThe (Student’s) t Probability Distribution 365\u003c\/p\u003e \u003cp\u003eReferences and Further Readings 366\u003c\/p\u003e \u003cp\u003eAnswers\/Solutions to Selected Exercises 372\u003c\/p\u003e \u003cp\u003eIndex 379\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eALIAKBAR MONTAZER HAGHIGHI, PhD,\u003c\/b\u003e is Professor and Head of the Department of Mathematics at Prairie View A\u0026amp;M University, as well as founder and Editor-in-Chief of \u003ci\u003eApplications and Applied Mathematics: An International Journal (AAM)\u003c\/i\u003e. Dr. Haghighi's research interests and publications are in the areas of probability, statistics, stochastic processes, and queueing theory.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eDIMITAR P. MISHEV, PhD,\u003c\/b\u003e is Professor in the Department of Mathematics at Prairie View A\u0026amp;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.\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eA Useful Guide to the Interrelated Areas of Differential Equations, Difference Equations, and Queueing Models\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eDifference and Differential Equations with Applications in Queueing Theory\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003eThe 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, \u003ci\u003eDifference and Differential Equations with Applications in Queueing Theory\u003c\/i\u003e provides:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eA discussion on splitting, delayed-service, and delayed feedback for single-server, multiple-server, parallel, and series queue models\u003c\/li\u003e \u003cli\u003eApplications in queue models whose solutions require differential difference equations and generating function methods\u003c\/li\u003e \u003cli\u003eExercises at the end of each chapter along with select answers\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe 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.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989061943525,"sku":"NP9781118393246","price":137.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118393246.jpg?v=1761782636","url":"https:\/\/k12savings.com\/es\/products\/difference-and-differential-equations-with-applications-in-queueing-theory-isbn-9781118393246","provider":"K12savings","version":"1.0","type":"link"}