Introduction to queueing theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
North Holland
1981
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| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 346 S. |
| ISBN: | 0444003797 |
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Datensatz im Suchindex
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| adam_text | Titel: Introduction to queueing theory
Autor: Cooper, Robert B
Jahr: 1981
Contents List of Exercises xi Preface to the Second Edition xiii 1 Scope and Nature of Queueing Theory 1 2 Review of Topics from the Theory of Probability and Stochastic Processes 9 2.1 Random Variables 9 2.2 Birth-and-Death Processes 14 2.3 Statistical Equilibrium 19 2.4 Probability-Generating Functions 26 2.5 Some Important Probability Distributions 34 Bernoulli Distribution 34 Binomial Distribution 34 Multinomial Distribution 35 Geometric Distribution 36 Negative-Binomial (Pascal) Distribution 37 Uniform Distribution 38 Negative-Exponential Distribution 42 Erlangian (Gamma) Distribution 50 Poisson Distribution 64 2.6 Remarks 71 3 Birth-and-Death Queueing Models 73 3.1 Introduction 73 3.2 Relationship Between the Outside Observer’s Distribution and the Arriving Customer’s Distribution 77 3.3 Poisson Input, j Servers, Blocked Customers Cleared: The Erlang Loss System 79
Contents Vili 3.4 Poisson Input, s Servers with Exponential Service Times, Blocked 90 Customers Delayed: The Erlang Delay System 3.5 Quasirandom Input 102 3.6 Equality of the Arriving Customer’s »-Source Distribution and the Outside Observer’s (n- l)-Source Distribution for Birth-and-Death Systems with Quasirandom Input 105 3.7 Quasirandom Input, s Servers, Blocked Customers Cleared: The 108 Engset Formula 3.8 Quasirandom Input, j Servers with Exponential Service Times, Blocked Customers Delayed 111 3.9 Summary 116 Multidimensional Birth-and-Death Queueing Models 123 4.1 Introduction 123 4.2 Product Solutions (Mixed Traffic, Queues in Tandem) 126 Infinite-Server Group with Two Types of Customers Finite-Server Group with Two Types of Customers and Blocked 126 Customers Cleared 128 Queues in Tandem 132 4.3 Generating Functions (Overflow Traffic) 139 4.4 Macrostates (Priority Reservation) 150 4.5 Indirect Solution of Equations (Load Carried by Each Server of an Ordered Group) 153 4.6
Numerical Solution of State Equations by Iteration (Gauss-Seidel and Overrelaxation Methods) 158 4.7 The Equivalent Random Method 165 4.8 The Method of Phases 171 5 Imbedded-Markov-Chain Queueing Models 176 5.1 Introduction 176 5.2 The Equation L = W ( Little’s Theorem) 178 5.3 Equality of State Distributions at Arrival and Departure Epochs 185 5.4 Mean Queue Length and Mean Waiting Time in the M/G/l Queue 189 5.5 Riemann-Stieltjes Integrals 192 5.6 Laplace-Stieltjes Transforms 197 5.7 Some Results from Renewal Theory 200 5.8 The Ai/G/1 Queue 208 The Mean Waiting Time 209 The Imbedded Markov Chain 210 The Pollaczek-Khintchine Formula 216 The Busy Period 228 5.9 The A//G/1 Queue with Finite Waiting Room 235 5.10 The Af/G/1 Queue with Batch Arrivals 241 5.11 Optimal Design and Control of Queues: The A-Policy and the T-Policy 243 5.12 The Ai/G/1 Queue with Service in Random Order 253 5.13 Queues Served in Cyclic Order 261 5.14 The GI/M/s Queue 267 5.15 The GI/M/s Queue with Service in
Random Order 275
Contents IX 6 Simulation of Queueing Models 281 6.1 Introduction 281 6.2 Generation of Stochastic Variables 284 6.3 Simulation Programming Languages 287 6.4 Statistical Questions 288 6.5 Examples 298 Waiting Times in a Queue with Quasirandom Input and Constant Service Times 298 Response Times in a Processor-Sharing Operating System 301 7 Annotated Bibliography 308 Appendix 315 References 325 Index 341
|
| adam_txt |
Titel: Introduction to queueing theory
Autor: Cooper, Robert B
Jahr: 1981
Contents List of Exercises xi Preface to the Second Edition xiii 1 Scope and Nature of Queueing Theory 1 2 Review of Topics from the Theory of Probability and Stochastic Processes 9 2.1 Random Variables 9 2.2 Birth-and-Death Processes 14 2.3 Statistical Equilibrium 19 2.4 Probability-Generating Functions 26 2.5 Some Important Probability Distributions 34 Bernoulli Distribution 34 Binomial Distribution 34 Multinomial Distribution 35 Geometric Distribution 36 Negative-Binomial (Pascal) Distribution 37 Uniform Distribution 38 Negative-Exponential Distribution 42 Erlangian (Gamma) Distribution 50 Poisson Distribution 64 2.6 Remarks 71 3 Birth-and-Death Queueing Models 73 3.1 Introduction 73 3.2 Relationship Between the Outside Observer’s Distribution and the Arriving Customer’s Distribution 77 3.3 Poisson Input, j Servers, Blocked Customers Cleared: The Erlang Loss System 79
Contents Vili 3.4 Poisson Input, s Servers with Exponential Service Times, Blocked 90 Customers Delayed: The Erlang Delay System 3.5 Quasirandom Input 102 3.6 Equality of the Arriving Customer’s »-Source Distribution and the Outside Observer’s (n- l)-Source Distribution for Birth-and-Death Systems with Quasirandom Input 105 3.7 Quasirandom Input, s Servers, Blocked Customers Cleared: The 108 Engset Formula 3.8 Quasirandom Input, j Servers with Exponential Service Times, Blocked Customers Delayed 111 3.9 Summary 116 Multidimensional Birth-and-Death Queueing Models 123 4.1 Introduction 123 4.2 Product Solutions (Mixed Traffic, Queues in Tandem) 126 Infinite-Server Group with Two Types of Customers Finite-Server Group with Two Types of Customers and Blocked 126 Customers Cleared 128 Queues in Tandem 132 4.3 Generating Functions (Overflow Traffic) 139 4.4 Macrostates (Priority Reservation) 150 4.5 Indirect Solution of Equations (Load Carried by Each Server of an Ordered Group) 153 4.6
Numerical Solution of State Equations by Iteration (Gauss-Seidel and Overrelaxation Methods) 158 4.7 The Equivalent Random Method 165 4.8 The Method of Phases 171 5 Imbedded-Markov-Chain Queueing Models 176 5.1 Introduction 176 5.2 The Equation L = \ W ( Little’s Theorem) 178 5.3 Equality of State Distributions at Arrival and Departure Epochs 185 5.4 Mean Queue Length and Mean Waiting Time in the M/G/l Queue 189 5.5 Riemann-Stieltjes Integrals 192 5.6 Laplace-Stieltjes Transforms 197 5.7 Some Results from Renewal Theory 200 5.8 The Ai/G/1 Queue 208 The Mean Waiting Time 209 The Imbedded Markov Chain 210 The Pollaczek-Khintchine Formula 216 The Busy Period 228 5.9 The A//G/1 Queue with Finite Waiting Room 235 5.10 The Af/G/1 Queue with Batch Arrivals 241 5.11 Optimal Design and Control of Queues: The A-Policy and the T-Policy 243 5.12 The Ai/G/1 Queue with Service in Random Order 253 5.13 Queues Served in Cyclic Order 261 5.14 The GI/M/s Queue 267 5.15 The GI/M/s Queue with Service in
Random Order 275
Contents IX 6 Simulation of Queueing Models 281 6.1 Introduction 281 6.2 Generation of Stochastic Variables 284 6.3 Simulation Programming Languages 287 6.4 Statistical Questions 288 6.5 Examples 298 Waiting Times in a Queue with Quasirandom Input and Constant Service Times 298 Response Times in a Processor-Sharing Operating System 301 7 Annotated Bibliography 308 Appendix 315 References 325 Index 341 |
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| spelling | Cooper, Robert B. Verfasser aut Introduction to queueing theory Robert B. Cooper 2. ed. New York [u.a.] North Holland 1981 346 S. txt rdacontent n rdamedia nc rdacarrier Files d'attente, Théorie des Wachttijdproblemen gtt file attente inriac modèle file attente inriac processus stochastique inriac simulation file attente inriac théorie file attente inriac théorie probabilité inriac Queuing theory Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Warteschlangentheorie (DE-588)4255044-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015190457&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cooper, Robert B. Introduction to queueing theory Files d'attente, Théorie des Wachttijdproblemen gtt file attente inriac modèle file attente inriac processus stochastique inriac simulation file attente inriac théorie file attente inriac théorie probabilité inriac Queuing theory Warteschlangentheorie (DE-588)4255044-0 gnd |
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| title | Introduction to queueing theory |
| title_auth | Introduction to queueing theory |
| title_exact_search | Introduction to queueing theory |
| title_exact_search_txtP | Introduction to queueing theory |
| title_full | Introduction to queueing theory Robert B. Cooper |
| title_fullStr | Introduction to queueing theory Robert B. Cooper |
| title_full_unstemmed | Introduction to queueing theory Robert B. Cooper |
| title_short | Introduction to queueing theory |
| title_sort | introduction to queueing theory |
| topic | Files d'attente, Théorie des Wachttijdproblemen gtt file attente inriac modèle file attente inriac processus stochastique inriac simulation file attente inriac théorie file attente inriac théorie probabilité inriac Queuing theory Warteschlangentheorie (DE-588)4255044-0 gnd |
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