{"product_id":"a-first-course-in-stochastic-models-isbn-9780471498803","title":"A First Course in Stochastic Models","description":"The field of applied probability has changed profoundly in the past twenty years. The development of computational methods has greatly contributed to a better understanding of the theory. \u003ci\u003eA First Course in Stochastic Models\u003c\/i\u003e provides a self-contained introduction to the theory and applications of stochastic models. Emphasis is placed on establishing the theoretical foundations of the subject, thereby providing a framework in which the applications can be understood. Without this solid basis in theory no applications can be solved.  \u003cul\u003e \u003cli\u003eProvides an introduction to the use of stochastic models through an integrated presentation of theory, algorithms and applications.\u003c\/li\u003e \u003cli\u003eIncorporates recent developments in computational probability.\u003c\/li\u003e \u003cli\u003eIncludes a wide range of examples that illustrate the models and make the methods of solution clear.\u003c\/li\u003e \u003cli\u003eFeatures an abundance of motivating exercises that help the student learn how to apply the theory.\u003c\/li\u003e \u003cli\u003eAccessible to anyone with a basic knowledge of probability.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eA First Course in Stochastic Models\u003c\/i\u003e is suitable for senior undergraduate and graduate students from computer science, engineering, statistics, operations resear ch, and any other discipline where stochastic modelling takes place. It stands out amongst other textbooks on the subject because of its integrated presentation of theory, algorithms and applications.\u003c\/p\u003e \u003cp\u003ePreface ix\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 The Poisson Process and Related Processes 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.0 Introduction 1\u003c\/p\u003e \u003cp\u003e1.1 The Poisson Process 1\u003c\/p\u003e \u003cp\u003e1.1.1 The Memoryless Property 2\u003c\/p\u003e \u003cp\u003e1.1.2 Merging and Splitting of Poisson Processes 6\u003c\/p\u003e \u003cp\u003e1.1.3 The M\/G\/∞ Queue 9\u003c\/p\u003e \u003cp\u003e1.1.4 The Poisson Process and the Uniform Distribution 15\u003c\/p\u003e \u003cp\u003e1.2 Compound Poisson Processes 18\u003c\/p\u003e \u003cp\u003e1.3 Non-Stationary Poisson Processes 22\u003c\/p\u003e \u003cp\u003e1.4 Markov Modulated Batch Poisson Processes 24\u003c\/p\u003e \u003cp\u003eExercises 28\u003c\/p\u003e \u003cp\u003eBibliographic Notes 32\u003c\/p\u003e \u003cp\u003eReferences 32\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Renewal-Reward Processes 33\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.0 Introduction 33\u003c\/p\u003e \u003cp\u003e2.1 Renewal Theory 34\u003c\/p\u003e \u003cp\u003e2.1.1 The Renewal Function 35\u003c\/p\u003e \u003cp\u003e2.1.2 The Excess Variable 37\u003c\/p\u003e \u003cp\u003e2.2 Renewal-Reward Processes 39\u003c\/p\u003e \u003cp\u003e2.3 The Formula of Little 50\u003c\/p\u003e \u003cp\u003e2.4 Poisson Arrivals See Time Averages 53\u003c\/p\u003e \u003cp\u003e2.5 The Pollaczek–Khintchine Formula 58\u003c\/p\u003e \u003cp\u003e2.6 A Controlled Queue with Removable Server 66\u003c\/p\u003e \u003cp\u003e2.7 An Up- And Downcrossing Technique 69\u003c\/p\u003e \u003cp\u003eExercises 71\u003c\/p\u003e \u003cp\u003eBibliographic Notes 78\u003c\/p\u003e \u003cp\u003eReferences 78\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Discrete-Time Markov Chains 81\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.0 Introduction 81\u003c\/p\u003e \u003cp\u003e3.1 The Model 82\u003c\/p\u003e \u003cp\u003e3.2 Transient Analysis 87\u003c\/p\u003e \u003cp\u003e3.2.1 Absorbing States 89\u003c\/p\u003e \u003cp\u003e3.2.2 Mean First-Passage Times 92\u003c\/p\u003e \u003cp\u003e3.2.3 Transient and Recurrent States 93\u003c\/p\u003e \u003cp\u003e3.3 The Equilibrium Probabilities 96\u003c\/p\u003e \u003cp\u003e3.3.1 Preliminaries 96\u003c\/p\u003e \u003cp\u003e3.3.2 The Equilibrium Equations 98\u003c\/p\u003e \u003cp\u003e3.3.3 The Long-run Average Reward per Time Unit 103\u003c\/p\u003e \u003cp\u003e3.4 Computation of the Equilibrium Probabilities 106\u003c\/p\u003e \u003cp\u003e3.4.1 Methods for a Finite-State Markov Chain 107\u003c\/p\u003e \u003cp\u003e3.4.2 Geometric Tail Approach for an Infinite State Space 111\u003c\/p\u003e \u003cp\u003e3.4.3 Metropolis—Hastings Algorithm 116\u003c\/p\u003e \u003cp\u003e3.5 Theoretical Considerations 119\u003c\/p\u003e \u003cp\u003e3.5.1 State Classification 119\u003c\/p\u003e \u003cp\u003e3.5.2 Ergodic Theorems 126\u003c\/p\u003e \u003cp\u003eExercises 134\u003c\/p\u003e \u003cp\u003eBibliographic Notes 139\u003c\/p\u003e \u003cp\u003eReferences 139\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Continuous-Time Markov Chains 141\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.0 Introduction 141\u003c\/p\u003e \u003cp\u003e4.1 The Model 142\u003c\/p\u003e \u003cp\u003e4.2 The Flow Rate Equation Method 147\u003c\/p\u003e \u003cp\u003e4.3 Ergodic Theorems 154\u003c\/p\u003e \u003cp\u003e4.4 Markov Processes on a Semi-Infinite Strip 157\u003c\/p\u003e \u003cp\u003e4.5 Transient State Probabilities 162\u003c\/p\u003e \u003cp\u003e4.5.1 The Method of Linear Differential Equations 163\u003c\/p\u003e \u003cp\u003e4.5.2 The Uniformization Method 166\u003c\/p\u003e \u003cp\u003e4.5.3 First Passage Time Probabilities 170\u003c\/p\u003e \u003cp\u003e4.6 Transient Distribution of Cumulative Rewards 172\u003c\/p\u003e \u003cp\u003e4.6.1 Transient Distribution of Cumulative Sojourn Times 173\u003c\/p\u003e \u003cp\u003e4.6.2 Transient Reward Distribution for the General Case 176\u003c\/p\u003e \u003cp\u003eExercises 179\u003c\/p\u003e \u003cp\u003eBibliographic Notes 185\u003c\/p\u003e \u003cp\u003eReferences 185\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Markov Chains and Queues 187\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.0 Introduction 187\u003c\/p\u003e \u003cp\u003e5.1 The Erlang Delay Model 187\u003c\/p\u003e \u003cp\u003e5.1.1 The M\/M\/1 Queue 188\u003c\/p\u003e \u003cp\u003e5.1.2 The M\/M\/c Queue 190\u003c\/p\u003e \u003cp\u003e5.1.3 The Output Process and Time Reversibility 192\u003c\/p\u003e \u003cp\u003e5.2 Loss Models 194\u003c\/p\u003e \u003cp\u003e5.2.1 The Erlang Loss Model 194\u003c\/p\u003e \u003cp\u003e5.2.2 The Engset Model 196\u003c\/p\u003e \u003cp\u003e5.3 Service-System Design 198\u003c\/p\u003e \u003cp\u003e5.4 Insensitivity 202\u003c\/p\u003e \u003cp\u003e5.4.1 A Closed Two-node Network with Blocking 203\u003c\/p\u003e \u003cp\u003e5.4.2 The M\/G\/1 Queue with Processor Sharing 208\u003c\/p\u003e \u003cp\u003e5.5 A Phase Method 209\u003c\/p\u003e \u003cp\u003e5.6 Queueing Networks 214\u003c\/p\u003e \u003cp\u003e5.6.1 Open Network Model 215\u003c\/p\u003e \u003cp\u003e5.6.2 Closed Network Model 219\u003c\/p\u003e \u003cp\u003eExercises 224\u003c\/p\u003e \u003cp\u003eBibliographic Notes 230\u003c\/p\u003e \u003cp\u003eReferences 231\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Discrete-Time Markov Decision Processes 233\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.0 Introduction 233\u003c\/p\u003e \u003cp\u003e6.1 The Model 234\u003c\/p\u003e \u003cp\u003e6.2 The Policy-Improvement Idea 237\u003c\/p\u003e \u003cp\u003e6.3 The Relative Value Function 243\u003c\/p\u003e \u003cp\u003e6.4 Policy-Iteration Algorithm 247\u003c\/p\u003e \u003cp\u003e6.5 Linear Programming Approach 252\u003c\/p\u003e \u003cp\u003e6.6 Value-Iteration Algorithm 259\u003c\/p\u003e \u003cp\u003e6.7 Convergence Proofs 267\u003c\/p\u003e \u003cp\u003eExercises 272\u003c\/p\u003e \u003cp\u003eBibliographic Notes 275\u003c\/p\u003e \u003cp\u003eReferences 276\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Semi-Markov Decision Processes 279\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.0 Introduction 279\u003c\/p\u003e \u003cp\u003e7.1 The Semi-Markov Decision Model 280\u003c\/p\u003e \u003cp\u003e7.2 Algorithms for an Optimal Policy 284\u003c\/p\u003e \u003cp\u003e7.3 Value Iteration and Fictitious Decisions 287\u003c\/p\u003e \u003cp\u003e7.4 Optimization of Queues 290\u003c\/p\u003e \u003cp\u003e7.5 One-Step Policy Improvement 295\u003c\/p\u003e \u003cp\u003eExercises 300\u003c\/p\u003e \u003cp\u003eBibliographic Notes 304\u003c\/p\u003e \u003cp\u003eReferences 305\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Advanced Renewal Theory 307\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.0 Introduction 307\u003c\/p\u003e \u003cp\u003e8.1 The Renewal Function 307\u003c\/p\u003e \u003cp\u003e8.1.1 The Renewal Equation 308\u003c\/p\u003e \u003cp\u003e8.1.2 Computation of the Renewal Function 310\u003c\/p\u003e \u003cp\u003e8.2 Asymptotic Expansions 313\u003c\/p\u003e \u003cp\u003e8.3 Alternating Renewal Processes 321\u003c\/p\u003e \u003cp\u003e8.4 Ruin Probabilities 326\u003c\/p\u003e \u003cp\u003eExercises 334\u003c\/p\u003e \u003cp\u003eBibliographic Notes 337\u003c\/p\u003e \u003cp\u003eReferences 338\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Algorithmic Analysis of Queueing Models 339\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.0 Introduction 339\u003c\/p\u003e \u003cp\u003e9.1 Basic Concepts 341\u003c\/p\u003e \u003cp\u003e9.2 The M\/G\/1 Queue 345\u003c\/p\u003e \u003cp\u003e9.2.1 The State Probabilities 346\u003c\/p\u003e \u003cp\u003e9.2.2 The Waiting-Time Probabilities 349\u003c\/p\u003e \u003cp\u003e9.2.3 Busy Period Analysis 353\u003c\/p\u003e \u003cp\u003e9.2.4 Work in System 358\u003c\/p\u003e \u003cp\u003e9.3 The MX\/G\/1 Queue 360\u003c\/p\u003e \u003cp\u003e9.3.1 The State Probabilities 361\u003c\/p\u003e \u003cp\u003e9.3.2 The Waiting-Time Probabilities 363\u003c\/p\u003e \u003cp\u003e9.4 M\/G\/1 Queues with Bounded Waiting Times 366\u003c\/p\u003e \u003cp\u003e9.4.1 The Finite-Buffer M\/G\/1 Queue 366\u003c\/p\u003e \u003cp\u003e9.4.2 An M\/G\/1 Queue with Impatient Customers 369\u003c\/p\u003e \u003cp\u003e9.5 The GI\/G\/1 Queue 371\u003c\/p\u003e \u003cp\u003e9.5.1 Generalized Erlangian Services 371\u003c\/p\u003e \u003cp\u003e9.5.2 Coxian-2 Services 372\u003c\/p\u003e \u003cp\u003e9.5.3 The GI \/P h\/1 Queue 373\u003c\/p\u003e \u003cp\u003e9.5.4 The Ph\/G\/1 Queue 374\u003c\/p\u003e \u003cp\u003e9.5.5 Two-moment Approximations 375\u003c\/p\u003e \u003cp\u003e9.6 Multi-Server Queues with Poisson Input 377\u003c\/p\u003e \u003cp\u003e9.6.1 The M\/D\/c Queue 378\u003c\/p\u003e \u003cp\u003e9.6.2 The M\/G\/c Queue 384\u003c\/p\u003e \u003cp\u003e9.6.3 The MX\/G\/c Queue 392\u003c\/p\u003e \u003cp\u003e9.7 The GI\/G\/c Queue 398\u003c\/p\u003e \u003cp\u003e9.7.1 The GI\/M\/c Queue 400\u003c\/p\u003e \u003cp\u003e9.7.2 The GI\/D\/c Queue 406\u003c\/p\u003e \u003cp\u003e9.8 Finite-Capacity Queues 408\u003c\/p\u003e \u003cp\u003e9.8.1 The M\/G\/c\/c + N Queue 408\u003c\/p\u003e \u003cp\u003e9.8.2 A Basic Relation for the Rejection Probability 410\u003c\/p\u003e \u003cp\u003e9.8.3 The MX\/G\/c\/c + N Queue with Batch Arrivals 413\u003c\/p\u003e \u003cp\u003e9.8.4 Discrete-Time Queueing Systems 417\u003c\/p\u003e \u003cp\u003eExercises 420\u003c\/p\u003e \u003cp\u003eBibliographic Notes 428\u003c\/p\u003e \u003cp\u003eReferences 428\u003c\/p\u003e \u003cp\u003eAppendices 431\u003c\/p\u003e \u003cp\u003eAppendix A. Useful Tools in Applied Probability 431\u003c\/p\u003e \u003cp\u003eAppendix B. Useful Probability Distributions 440\u003c\/p\u003e \u003cp\u003eAppendix C. Generating Functions 449\u003c\/p\u003e \u003cp\u003eAppendix D. The Discrete Fast Fourier Transform 455\u003c\/p\u003e \u003cp\u003eAppendix E. Laplace Transform Theory 458\u003c\/p\u003e \u003cp\u003eAppendix F. Numerical Laplace Inversion 462\u003c\/p\u003e \u003cp\u003eAppendix G. The Root-Finding Problem 470\u003c\/p\u003e \u003cp\u003eReferences 474\u003c\/p\u003e \u003cp\u003eIndex 475\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e  \"…successfully combined theory and real world examples into a systematic introduction...an excellent reference for the applied statistician who deals in various queuing models.\" (\u003ci\u003eTechnometrics\u003c\/i\u003e, August 2005)  \u003cp\u003e“…clear and straightforward…plenty of worked (or orientated) examples as well as a substantial set of exercises…” (\u003ci\u003eShort Book Reviews\u003c\/i\u003e, August 2004)\u003c\/p\u003e \u003cp\u003e\u003cb\u003eHenk C. Tijms\u003c\/b\u003e is a Dutch mathematician and Emeritus Professor of Operations Research at the VU University Amsterdam. He studied mathematics in Amsterdam where he graduated from the University of Amsterdam in 1972 under supervision of Gijsbert de Leve.\u003c\/p\u003e  The field of applied probability has changed profoundly in the past twenty years. The development of computational methods has greatly contributed to a better understanding of the theory. \u003ci\u003eA First Course in Stochastic Models\u003c\/i\u003e provides a self-contained introduction to the theory and applications of stochastic models. Emphasis is placed on establishing the theoretical foundations of the subject, thereby providing a framework in which the applications can be understood. Without this solid basis in theory no applications can be solved.  \u003cul\u003e \u003cli\u003eProvides an introduction to the use of stochastic models through an integrated presentation of theory, algorithms and applications.\u003c\/li\u003e \u003cli\u003eIncorporates recent developments in computational probability.\u003c\/li\u003e \u003cli\u003eIncludes a wide range of examples that illustrate the models and make the methods of solution clear.\u003c\/li\u003e \u003cli\u003eFeatures an abundance of motivating exercises that help the student learn how to apply the theory.\u003c\/li\u003e \u003cli\u003eAccessible to anyone with a basic knowledge of probability.\u003c\/li\u003e \u003c\/ul\u003e \u003ci\u003eA First Course in Stochastic Models\u003c\/i\u003e is suitable for senior undergraduate and graduate students from computer science, engineering, statistics, operations research, and any other discipline where stochastic modelling takes place. It stands out amongst other textbooks on the subject because of its integrated presentation of theory, algorithms and applications.","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988628062437,"sku":"NP9780471498803","price":97.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780471498803.jpg?v=1761781034","url":"https:\/\/k12savings.com\/es\/products\/a-first-course-in-stochastic-models-isbn-9780471498803","provider":"K12savings","version":"1.0","type":"link"}