Stochastic dynamic programming and the control of queueing systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Wiley-Interscience
1999
|
| Schriftenreihe: | Wiley series in probability and statistics
A Wiley-Interscience publication |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 328 S. graph. Darst. |
| ISBN: | 0471161209 |
Internformat
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| 650 | 7 | |a optimisation |2 inriac | |
| 650 | 7 | |a programmation dynamique stochastique |2 inriac | |
| 650 | 7 | |a système temps continu |2 inriac | |
| 650 | 7 | |a théorie queue |2 inriac | |
| 650 | 4 | |a Dynamic programming | |
| 650 | 4 | |a Queuing theory | |
| 650 | 4 | |a Stochastic programming | |
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Datensatz im Suchindex
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| adam_text | IMAGE 1
STOCHASTIC DYNAMIC
PROGRAMMING AND THE CONTROL OF QUEUEING SYSTEMS
LINN I. SENNOTT ILLINOIS STATE UNIVERSITY
A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC. NEW YORK *
CHICHESTER * WEINHEIM * BRISBANE * SINGAPORE * TORONTO
IMAGE 2
CONTENTS
PREFACE 1 INTRODUCTION
1.1 EXAMPLES, 2 1.2 ASPECTS OF CONTROL, 8 1.3 GOALS AND SUMMARY OF
CHAPTERS, 12 BIBLIOGRAPHIE NOTES, 13 PROBLEMS, 14
2 OPTIMIZATION CRITERIA
2.1 BASIC NOTATION, 15 2.2 POLICIES, 20 2.3 CONDITIONAL COST
DISTRIBUTIONS, 22 2.4 OPTIMIZATION CRITERIA, 24
2.5 APPROXIMATING SEQUENCE METHOD, 27 BIBLIOGRAPHIE NOTES, 33 PROBLEMS,
33
3 FINITE HORIZON OPTIMIZATION
3.1 FINITE HORIZON OPTIMALITY EQUATION, 35 3.2 ASM FOR THE FINITE
HORIZON, 41 3.3 WHEN DOES FH(A,N) HOLD?, 45 3.4 A QUEUEING EXAMPLE, 51
BIBLIOGRAPHIE NOTES, 58 PROBLEMS, 58
IMAGE 3
VIII
CONTENTS
4 INFINITE HORIZON DISCOUNTED COST OPTIMIZATION 60
4.1 INFINITE HORIZON DISCOUNTED COST OPTIMALITY EQUATION, 60 4.2
SOLUTIONS TO THE OPTIMALITY EQUATION, 65 4.3 CONVERGENCE OF FINITE
HORIZON VALUE FUNCTIONS, 66
4.4 CHARACTERIZATION OF OPTIMAL POLICIES, 67 4.5 ANALYTIC PROPERTIES OF
THE VALUE FUNCTION, 70 4.6 ASM FOR THE INFINITE HORIZON DISCOUNTED CASE,
73 4.7 WHEN DOES DC(A) HOLD?, 77
BIBLIOGRAPHIE NOTES, 81 PROBLEMS, 81
5 AN INVENTORY MODEL 83
5.1 FORMULATION OF THE MDC, 83 5.2 OPTIMALITY EQUATIONS, 87 5.3 AN
APPROXIMATING SEQUENCE, 88 5.4 NUMERICAL RESULTS, 90
BIBLIOGRAPHIE NOTES, 95 PROBLEMS, 95
6 AVERAGE COST OPTIMIZATION FOR FINITE STATE SPACES 97
6.1 A FUNDAMENTAL RELATIONSHIP FOR 5 COUNTABLE, 97 6.2 AN OPTIMAL
STATIONARY POLICY EXISTS, 98 6.3 AN AVERAGE COST OPTIMALITY EQUATION,
101 6.4 ACOE FOR CONSTANT MINIMUM AVERAGE COST, 107 6.5 SOLUTIONS TO THE
ACOE, 111 6.6 METHOD OF CALCULATION, 115 6.7 AN EXAMPLE, 122
BIBLIOGRAPHIE NOTES, 123 PROBLEMS, 125
7 AVERAGE COST OPTIMIZATION THEORY FOR COUNTABLE STATE SPACES 127
7.1 COUNTEREXAMPLES, 128 7.2 THE (SEN) ASSUMPTIONS, 132 7.3 AN EXAMPLE,
138 7.4 AVERAGE COST OPTIMALITY INEQUALITY, 139 7.5 SUFFICIENT
CONDITIONS FOR THE (SEN) ASSUMPTIONS, 143
IMAGE 4
CONTENTS
IX
7.6 EXAMPLES, 149 7.7 WEAKENING THE (SEN) ASSUMPTIONS, 157 BIBLIOGRAPHIE
NOTES, 162 PROBLEMS, 165
8 COMPUTATION OF AVERAGE COST OPTIMAL POLICIES FOR INFINITE STATE SPACES
168
8.1 THE (AC) ASSUMPTIONS, 169 8.2 VERIFICATION OF THE ASSUMPTIONS, 171
8.3 EXAMPLES, 176 *8.4 ANOTHER EXAMPLE, 179
8.5 SERVICE RATE CONTROL QUEUE, 181 8.6 ROUTING TO PARALLEL QUEUES, 186
8.7 WEAKENING THE (AC) ASSUMPTIONS, 193 BIBLIOGRAPHIE NOTES, 194
PROBLEMS, 196
9 OPTIMIZATION UNDER ACTIONS AT SELECTED EPOCHS 199
9.1 SINGLE- AND MULTIPLE-SAMPLE MODELS, 199 9.2 PROPERTIES OF AN MS
DISTRIBUTION, 202 9.3 SERVICE CONTROL OF THE SINGLE-SERVER QUEUE, 207
9.4 ARRIVAL CONTROL OF THE SINGLE-SERVER QUEUE, 211 9.5 AVERAGE COST
OPTIMIZATION OF EXAMPLE 9.3.1, 214 9.6 AVERAGE COST OPTIMIZATION OF
EXAMPLE 9.3.2, 221 9.7 COMPUTATION UNDER DETERMINISTIC SERVICE TIMES,
227
9.8 COMPUTATION UNDER GEOMETRIE SERVICE TIMES, 229 BIBLIOGRAPHIE NOTES,
232 PROBLEMS, 233
10 AVERAGE COST OPTIMIZATION OF CONTINUOUS TIME PROCESSES 237
10.1 EXPONENTIAL DISTRIBUTIONS AND THE POISSON PROCESS, 238 10.2
CONTINUOUS TIME MARKOV DECISION CHAINS, 241 10.3 AVERAGE COST
OPTIMIZATION OF A CTMDC, 243 10.4 SERVICE RATE CONTROL OF THE M/M/L
QUEUE, 248
10.5 M/M/AET QUEUE WITH DYNAMIC SERVICE POOL, 251 10.6 CONTROL OF A
POLLING SYSTEM, 258 BIBLIOGRAPHIE NOTES, 265 PROBLEMS, 266
IMAGE 5
X
CONTENTS
APPENDIX A RESULTS FROM ANALYSIS 270
A.L USEFUL THEOREMS, 270 A.2 FATOU S LEMMA AND THE DOMINATED CONVERGENCE
THEOREM, 275 A.3 POWER SERIES, 279 A.4 A TAUBERIAN THEOREM, 280 A.5 AN
EXAMPLE, 286
BIBLIOGRAPHIE NOTES, 287
APPENDIX B SEQUENCES OF STATIONARY POLICIES 288
BIBLIOGRAPHIE NOTES, 291
APPENDIX C MARKOV CHAINS 292
C.L BASIC THEORY, 292 C.2 MARKOV CHAINS WITH COSTS, 298 C.3 MARKOV
CHAINS WITH FINITE STATE SPACE, 302 C.4 APPROXIMATING SEQUENCES FOR
MARKOV CHAINS, 302
C.5 SUFFICIENT CONDITIONS FOR CONFORMITY, 308 BIBLIOGRAPHIE NOTES, 314
BIBLIOGRAPHY 316
INDEX 325
|
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| spelling | Sennott, Linn I. Verfasser aut Stochastic dynamic programming and the control of queueing systems Linn I. Sennott New York, NY [u.a.] Wiley-Interscience 1999 XIV, 328 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics A Wiley-Interscience publication Controleleer gtt Dynamische programmering gtt Files d'attente, Théorie des ram Programmation dynamique ram Programmation stochastique ram Stochastische programmering gtt Wachttijdproblemen gtt contrôle optimal inriac optimisation stochastique inriac optimisation inriac programmation dynamique stochastique inriac système temps continu inriac théorie queue inriac Dynamic programming Queuing theory Stochastic programming Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf Dynamische Optimierung (DE-588)4125677-3 gnd rswk-swf Stochastische Optimierung (DE-588)4057625-5 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 s Stochastische Optimierung (DE-588)4057625-5 s Dynamische Optimierung (DE-588)4125677-3 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008346441&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sennott, Linn I. Stochastic dynamic programming and the control of queueing systems Controleleer gtt Dynamische programmering gtt Files d'attente, Théorie des ram Programmation dynamique ram Programmation stochastique ram Stochastische programmering gtt Wachttijdproblemen gtt contrôle optimal inriac optimisation stochastique inriac optimisation inriac programmation dynamique stochastique inriac système temps continu inriac théorie queue inriac Dynamic programming Queuing theory Stochastic programming Warteschlangentheorie (DE-588)4255044-0 gnd Dynamische Optimierung (DE-588)4125677-3 gnd Stochastische Optimierung (DE-588)4057625-5 gnd |
| subject_GND | (DE-588)4255044-0 (DE-588)4125677-3 (DE-588)4057625-5 |
| title | Stochastic dynamic programming and the control of queueing systems |
| title_auth | Stochastic dynamic programming and the control of queueing systems |
| title_exact_search | Stochastic dynamic programming and the control of queueing systems |
| title_full | Stochastic dynamic programming and the control of queueing systems Linn I. Sennott |
| title_fullStr | Stochastic dynamic programming and the control of queueing systems Linn I. Sennott |
| title_full_unstemmed | Stochastic dynamic programming and the control of queueing systems Linn I. Sennott |
| title_short | Stochastic dynamic programming and the control of queueing systems |
| title_sort | stochastic dynamic programming and the control of queueing systems |
| topic | Controleleer gtt Dynamische programmering gtt Files d'attente, Théorie des ram Programmation dynamique ram Programmation stochastique ram Stochastische programmering gtt Wachttijdproblemen gtt contrôle optimal inriac optimisation stochastique inriac optimisation inriac programmation dynamique stochastique inriac système temps continu inriac théorie queue inriac Dynamic programming Queuing theory Stochastic programming Warteschlangentheorie (DE-588)4255044-0 gnd Dynamische Optimierung (DE-588)4125677-3 gnd Stochastische Optimierung (DE-588)4057625-5 gnd |
| topic_facet | Controleleer Dynamische programmering Files d'attente, Théorie des Programmation dynamique Programmation stochastique Stochastische programmering Wachttijdproblemen contrôle optimal optimisation stochastique optimisation programmation dynamique stochastique système temps continu théorie queue Dynamic programming Queuing theory Stochastic programming Warteschlangentheorie Dynamische Optimierung Stochastische Optimierung |
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