A first course in stochastic models:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
2003
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| Subjects: | |
| Online Access: | Publisher description Table of contents Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | VIII, 478 S. |
| ISBN: | 0471498807 0471498815 |
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| 245 | 1 | 0 | |a A first course in stochastic models |c Henk C. Tijms |
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2003 | |
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| adam_text | Contents Preface ix 1 The Poisson Process and Related Processes 1 .0 Introduction The Poisson Process 1.1.1 The Memoryless Property 1.1.2 Merging and Splitting of Poisson Processes 1.1.3 The M/G/co Queue 1.1.4 The Poisson Process and the Uniform Distribution 1.2 Compound Poisson Processes 1.3 Non-Stationary Poisson Processes 1.4 Markov Modulated Batch Poisson Processes Exercises Bibliographic Notes References 1 1 2 6 9 15 18 22 24 28 32 32 1 1.1 2 Renewal-Reward Processes 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 3 33 .0 Introduction Renewal Theory 2.1.1 The Renewal Function 2.1.2 The Excess Variable Renewal-Reward Processes The Formula of Little Poisson Arrivals See Time Averages The Pollaczek-Khintchine Formula A Controlled Queue with RemovableServer An Up- And Downcrossing Technique Exercises Bibliographic Notes References 33 34 35 37 39 50 53 58 66 69 71 78 78 Discrete-Time Markov Chains 3.0 Introduction 3.1 The Model 81 ,, 81 82
vi CONTENTS 3.2 Transient Analysis 3.2.1 Absorbing States 3.2.2 Mean First-Passage Times 3.2.3 Transient and Recurrent States 3.3 The Equilibrium Probabilities 3.3.1 Preliminaries 3.3.2 The Equilibrium Equations 3.3.3 The Long-run Average Reward per Time Unit 3.4 Computation of the Equilibrium Probabilities 3.4.1 Methods for a Finite-State Markov Chain 3.4.2 Geometric Tail Approach for an Infinite State Space 3.4.3 Metropolis—Hastings Algorithm 3.5 Theoretical Considerations 3.5.1 State Classification 3.5.2 Ergodic Theorems Exercises Bibliographic Notes References 4 Continuous-Time Markov Chains .0 Introduction The Model The Flow Rate Equation Method Ergodic Theorems Markov Processes on a Semi-Infinite Strip Transient State Probabilities 4.5.1 The Method of Linear Differential Equations 4.5.2 The Uniformization Method 4.5.3 First Passage Time Probabilities 4.6 Transient Distribution of Cumulative Rewards 4.6.1 Transient Distribution of Cumulative Sojourn Times 4.6.2 Transient Reward Distribution for the General Case Exercises Bibliographic Notes References 4 4.1 4.2 4.3 4.4 4.5 5 Markov Chains and Queues 5.0 Introduction 5.1 The Erlang Delay Model 5.1.1 The M/M/ճ Queue 5.1.2 The Μ/М/с Queue 5.1.3 The Output Process and Time Reversibility 5.2 Loss Models 5.2.1 The Erlang Loss Model 5.2.2 The Engset Model 5.3 Service-System Design 5.4 Insensitivity 5.4.1 A Closed Two-node Network with Blocking 5.4.2 The M/G/X Queue with Processor Sharing 5.5 A Phase Method 87 89 92 93 96 96 98 103 106 107 111 116 119 119 126 134 139 139 141 141 142 147 154 157 162 163 166 170 172 173 176 179
185 185 187 187 187 188 190 192 194 194 196 198 202 203 208 209
CONTENTS 5.6 Queueing Networks 5.6.1 Open Network Model 5.6.2 Closed Network Model Exercises Bibliographic Notes References 6 Discrete-Time Markov Decision Processes vii 214 215 219 224 230 231 233 .0 Introduction The Model The Policy-Improvement Idea The Relative Value Function Policy-Iteration Algorithm Linear Programming Approach Value-Iteration Algorithm Convergence Proofs Exercises Bibliographic Notes References 233 234 237 243 247 252 259 267 272 275 276 7 Semi-Markov Decision Processes 279 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 7 7.1 7.2 7.3 7.4 7.5 .0 Introduction The Semi-Markov Decision Model Algorithms for an Optimal Policy Value Iteration and Fictitious Decisions Optimization of Queues One-Step Policy Improvement Exercises Bibliographic Notes References 8 Advanced Renewal Theory 8 .0 Introduction 8.1 The Renewal Function 8.1.1 The Renewal Equation 8.1.2 Computation of the Renewal Function 8.2 Asymptotic Expansions 8.3 Alternating Renewal Processes 8.4 Ruin Probabilities Exercises Bibliographic Notes References 9 Algorithmic Analysis of Queueing Models 9.0 Introduction 9.1 Basic Concepts 279 280 284 287 290 295 300 304 305 307 307 307 308 310 313 321 326 334 337 338 339 339 341
viii CONTENTS 9.2 The M/G! Queue 9.2.1 The State Probabilities 9.2.2 The Waiting-Time Probabilities 9.2.3 Busy Period Analysis 9.2.4 Work in System 9.3 The Mx IG¡ Queue 9.3.1 The State Probabilities 9.3.2 The Waiting-Time Probabilities 9.4 Μ/G/l Queues with Bounded Waiting Times 9.4.1 The Finite-Buffer Μ/G/ Queue 9.4.2 An MjG/X Queue with Impatient Customers 9.5 The G7/G/l Queue 9.5.1 Generalized Erlangian Services 9.5.2 Coxian-2 Services 9.5.3 The GI / Ph/І Queue 9.5.4 The PhlG[ Queue 9.5.5 Two-moment Approximations 9.6 Multi-Server Queues with Poisson Input 9.6.1 The M¡D¡c Queue 9.6.2 The Ml GIc Queue 9.6.3 The Mx IG/c Queue 9.7 The Gl / G/c Queue 9.7.1 The GI/М/с Queue 9.7.2 The Gl/D/c Queue 9.8 Finite-Capacity Queues 9.8.1 The Μ/G/c/c + N Queue 9.8.2 A Basic Relation for the Rejection Probability 9.8.3 The Mx/G/c/c + A Queue with Batch Arrivals 9.8.4 Discrete-Time Queueing Systems Exercises Bibliographic Notes References Appendices Appendix A. Useful Tools in Applied Probability Index 345 346 349 353 358 360 361 363 366 366 369 371 371 372 373 374 375 377 378 384 392 398 400 406 408 408 410 413 417 420 428 428 431 431 Appendix B. Useful Probability Distributions 440 Appendix C. Generating Functions 449 Appendix D. The Discrete Fast Fourier Transform 455 Appendix E. Laplace Transform Theory 458 Appendix F. Numerical Laplace Inversion 462 Appendix G. The Root-Finding Problem 470 References 474 475
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| adam_txt |
Contents Preface ix 1 The Poisson Process and Related Processes 1 .0 Introduction The Poisson Process 1.1.1 The Memoryless Property 1.1.2 Merging and Splitting of Poisson Processes 1.1.3 The M/G/co Queue 1.1.4 The Poisson Process and the Uniform Distribution 1.2 Compound Poisson Processes 1.3 Non-Stationary Poisson Processes 1.4 Markov Modulated Batch Poisson Processes Exercises Bibliographic Notes References 1 1 2 6 9 15 18 22 24 28 32 32 1 1.1 2 Renewal-Reward Processes 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 3 33 .0 Introduction Renewal Theory 2.1.1 The Renewal Function 2.1.2 The Excess Variable Renewal-Reward Processes The Formula of Little Poisson Arrivals See Time Averages The Pollaczek-Khintchine Formula A Controlled Queue with RemovableServer An Up- And Downcrossing Technique Exercises Bibliographic Notes References 33 34 35 37 39 50 53 58 66 69 71 78 78 Discrete-Time Markov Chains 3.0 Introduction 3.1 The Model 81 ,, 81 82
vi CONTENTS 3.2 Transient Analysis 3.2.1 Absorbing States 3.2.2 Mean First-Passage Times 3.2.3 Transient and Recurrent States 3.3 The Equilibrium Probabilities 3.3.1 Preliminaries 3.3.2 The Equilibrium Equations 3.3.3 The Long-run Average Reward per Time Unit 3.4 Computation of the Equilibrium Probabilities 3.4.1 Methods for a Finite-State Markov Chain 3.4.2 Geometric Tail Approach for an Infinite State Space 3.4.3 Metropolis—Hastings Algorithm 3.5 Theoretical Considerations 3.5.1 State Classification 3.5.2 Ergodic Theorems Exercises Bibliographic Notes References 4 Continuous-Time Markov Chains .0 Introduction The Model The Flow Rate Equation Method Ergodic Theorems Markov Processes on a Semi-Infinite Strip Transient State Probabilities 4.5.1 The Method of Linear Differential Equations 4.5.2 The Uniformization Method 4.5.3 First Passage Time Probabilities 4.6 Transient Distribution of Cumulative Rewards 4.6.1 Transient Distribution of Cumulative Sojourn Times 4.6.2 Transient Reward Distribution for the General Case Exercises Bibliographic Notes References 4 4.1 4.2 4.3 4.4 4.5 5 Markov Chains and Queues 5.0 Introduction 5.1 The Erlang Delay Model 5.1.1 The M/M/ճ Queue 5.1.2 The Μ/М/с Queue 5.1.3 The Output Process and Time Reversibility 5.2 Loss Models 5.2.1 The Erlang Loss Model 5.2.2 The Engset Model 5.3 Service-System Design 5.4 Insensitivity 5.4.1 A Closed Two-node Network with Blocking 5.4.2 The M/G/X Queue with Processor Sharing 5.5 A Phase Method 87 89 92 93 96 96 98 103 106 107 111 116 119 119 126 134 139 139 141 141 142 147 154 157 162 163 166 170 172 173 176 179
185 185 187 187 187 188 190 192 194 194 196 198 202 203 208 209
CONTENTS 5.6 Queueing Networks 5.6.1 Open Network Model 5.6.2 Closed Network Model Exercises Bibliographic Notes References 6 Discrete-Time Markov Decision Processes vii 214 215 219 224 230 231 233 .0 Introduction The Model The Policy-Improvement Idea The Relative Value Function Policy-Iteration Algorithm Linear Programming Approach Value-Iteration Algorithm Convergence Proofs Exercises Bibliographic Notes References 233 234 237 243 247 252 259 267 272 275 276 7 Semi-Markov Decision Processes 279 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 7 7.1 7.2 7.3 7.4 7.5 .0 Introduction The Semi-Markov Decision Model Algorithms for an Optimal Policy Value Iteration and Fictitious Decisions Optimization of Queues One-Step Policy Improvement Exercises Bibliographic Notes References 8 Advanced Renewal Theory 8 .0 Introduction 8.1 The Renewal Function 8.1.1 The Renewal Equation 8.1.2 Computation of the Renewal Function 8.2 Asymptotic Expansions 8.3 Alternating Renewal Processes 8.4 Ruin Probabilities Exercises Bibliographic Notes References 9 Algorithmic Analysis of Queueing Models 9.0 Introduction 9.1 Basic Concepts 279 280 284 287 290 295 300 304 305 307 307 307 308 310 313 321 326 334 337 338 339 339 341
viii CONTENTS 9.2 The M/G!\ Queue 9.2.1 The State Probabilities 9.2.2 The Waiting-Time Probabilities 9.2.3 Busy Period Analysis 9.2.4 Work in System 9.3 The Mx IG¡\ Queue 9.3.1 The State Probabilities 9.3.2 The Waiting-Time Probabilities 9.4 Μ/G/l Queues with Bounded Waiting Times 9.4.1 The Finite-Buffer Μ/G/ \ Queue 9.4.2 An MjG/X Queue with Impatient Customers 9.5 The G7/G/l Queue 9.5.1 Generalized Erlangian Services 9.5.2 Coxian-2 Services 9.5.3 The GI / Ph/І Queue 9.5.4 The PhlG[\ Queue 9.5.5 Two-moment Approximations 9.6 Multi-Server Queues with Poisson Input 9.6.1 The M¡D¡c Queue 9.6.2 The Ml GIc Queue 9.6.3 The Mx IG/c Queue 9.7 The Gl / G/c Queue 9.7.1 The GI/М/с Queue 9.7.2 The Gl/D/c Queue 9.8 Finite-Capacity Queues 9.8.1 The Μ/G/c/c + N Queue 9.8.2 A Basic Relation for the Rejection Probability 9.8.3 The Mx/G/c/c + A Queue with Batch Arrivals 9.8.4 Discrete-Time Queueing Systems Exercises Bibliographic Notes References Appendices Appendix A. Useful Tools in Applied Probability Index 345 346 349 353 358 360 361 363 366 366 369 371 371 372 373 374 375 377 378 384 392 398 400 406 408 408 410 413 417 420 428 428 431 431 Appendix B. Useful Probability Distributions 440 Appendix C. Generating Functions 449 Appendix D. The Discrete Fast Fourier Transform 455 Appendix E. Laplace Transform Theory 458 Appendix F. Numerical Laplace Inversion 462 Appendix G. The Root-Finding Problem 470 References 474 475 |
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| spelling | Tijms, Henk C. 1944- Verfasser (DE-588)114608474 aut A first course in stochastic models Henk C. Tijms Chichester [u.a.] Wiley 2003 VIII, 478 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Processos estocásticos larpcal Processus stochastiques Stochastische modellen gtt Stochastic Processes Stochastic processes Stochastik (DE-588)4121729-9 gnd rswk-swf Stochastik (DE-588)4121729-9 s DE-604 http://www.loc.gov/catdir/description/wiley035/2002193371.html Publisher description http://www.loc.gov/catdir/toc/wiley031/2002193371.html Table of contents Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014276357&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tijms, Henk C. 1944- A first course in stochastic models Processos estocásticos larpcal Processus stochastiques Stochastische modellen gtt Stochastic Processes Stochastic processes Stochastik (DE-588)4121729-9 gnd |
| subject_GND | (DE-588)4121729-9 |
| title | A first course in stochastic models |
| title_auth | A first course in stochastic models |
| title_exact_search | A first course in stochastic models |
| title_exact_search_txtP | A first course in stochastic models |
| title_full | A first course in stochastic models Henk C. Tijms |
| title_fullStr | A first course in stochastic models Henk C. Tijms |
| title_full_unstemmed | A first course in stochastic models Henk C. Tijms |
| title_short | A first course in stochastic models |
| title_sort | a first course in stochastic models |
| topic | Processos estocásticos larpcal Processus stochastiques Stochastische modellen gtt Stochastic Processes Stochastic processes Stochastik (DE-588)4121729-9 gnd |
| topic_facet | Processos estocásticos Processus stochastiques Stochastische modellen Stochastic Processes Stochastic processes Stochastik |
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