Stochastic modeling and the theory of queues:
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Englewood Cliffs, NJ
Prentice Hall
1989
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Schriftenreihe: | Prentice Hall international series in industrial and systems engineering
|
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XIX, 556 S. graph. Darst. |
ISBN: | 0138466920 0138498458 |
Internformat
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245 | 1 | 0 | |a Stochastic modeling and the theory of queues |c Ronald W. Wolff, University of California, Berkeley |
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650 | 7 | |a théorie queue |2 inriac | |
650 | 7 | |a théorie renouvellement |2 inriac | |
650 | 4 | |a Mathematisches Modell | |
650 | 4 | |a Queuing theory | |
650 | 4 | |a Stochastic processes |x Mathematical models | |
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adam_text | IMAGE 1
STOCHASTIC MODELING
AND
THE THEORY OF QUEUES
RONALD W. WOLFF UNIVERSITY OF CALIFORNIA, BERKELEY
PRENTICE HALL, ENGLEWOOD CLIFFS, NEW JERSEY 07632
IMAGE 2
CONTENTS
PREFACE XIII
INTRODUCTION XVII
1 PROBABILITY THEORY 1
1-1 INTERPRETATIONS OF PROBABILITY 1
1-2 THE PROBABILITY SPACE AND THE ALGEBRA OF
EVENTS 6
1-3 PROBABILITY MEASURE 7
1-4 CONDITIONAL PROBABILITY; BAYES THEOREM 9
1-5 RANDOM VARIABLES 12
1-6 DISCRETE DISTRIBUTIONS 13
1-7 CONTINUOUS DISTRIBUTIONS 14
1-8 JOINT DISTRIBUTIONS 16
1-9 MATHEMATICAL EXPECTATION; MAGNITUDE AND DISPERSION OF RANDOM
VARIABLES 18 1-10 SUMS OF RANDOM VARIABLES; CORRELATION, INDEPENDENCE,
AND CONVOLUTION 23
IMAGE 3
1-11 FUNCTIONS OF RANDOM VARIABLES;
TRANSFORMATIONS 26 1-12 GENERATING FUNCTIONS AND OTHER INTEGRAL
TRANSFORMS 28
1-13 CONDITIONAL DISTRIBUTIONS AND CONDITIONAL
EXPECTATION 31
1-14 APPLICATIONS OF INDICATOR FUNCTIONS 35
1-15 LAWS OF LARGE NUMBERS 38
1-16 MODES OF CONVERGENCE; THE CENTRAL LIMIT THEOREM 42
PROBLEMS 44
RENEWAL THEORY AND REGENERATIVE PROCESSES
2-1 DEFINITION OF A STOCHASTIC PROCESS;
REALIZATIONS 53
2-2 RENEWAL PROCESSES 55
2-3 REWARD AND COST MODELS; CUMULATIVE PROCESSES 59 2-4 OBSERVING A
PROCESS AT RANDOM; THE EQUILIBRIUM DISTRIBUTION AND THE INSPECTION
PARADOX 65
2-5 THE DISCRETE CASE-BATCH EFFECTS 68
2-6 THE POISSON PROCESS 69
2-7 STOPPING TIMES FOR A POISSON PROCESS 77
2-8 THE CONNECTION BETWEEN TIME AVERAGES AND POINTWISE LIMITS 79 2-9
POINT PROCESSES; GENERALIZATIONS OF POISSON
PROCESSES 81
2-10 DEFECTIVE RENEWAL PROCESSES 87
2-11 REGENERATIVE PROCESSES 89
2-12 THE RELATION BETWEEN A TIME AVERAGE AND THE MEAN OF A LIMITING
DISTRIBUTION 92 2-13 WALD S EQUATION 97
IMAGE 4
CONTENTS
VII
2-14 PROOF OF THE EXPECTED-VALUE VERSION OF THE
ELEMENTARY RENEWAL THEOREM 100
2-15 THE RENEWAL EQUATION FOR ORDINARY RENEWAL PROCESSES; TRANSIENT
BEHAVIOR 102
2-16 THE RENEWAL EQUATION FOR GENERAL RENEWAL PROCESSES; STATIONARY
REGENERATIVE PROCESSES 108
2-17 A DIRECT METHOD FOR FINDING TRANSIENT EXPRESSIONS 113
2-18 LATTICE DISTRIBUTIONS; EXAMPLES WHERE POINTWISE LIMITS DO NOT EXIST
115
2-19 BLACKWELL S THEOREM, THE KEY RENEWAL THEOREM, AND POINTWISE LIMITS
116
2-20* ASYMPTOTIC NORMALITY AND THE REGENERATIVE METHOD 121
2-21 SUMMARY AND LITERATURE GUIDE 125
PROBLEMS 130
3 DISCRETE MARKOV CHAINS 148
3-1 DISCRETE MARKOV CHAINS; TRANSITION
PROBABILITIES 149
3-2 CONNECTION WITH RENEWAL THEORY 151
3-3 COMMUNICATION CLASSES AND CLASS
PROPERTIES 153
3-4 IRREDUCIBLE CHAINS-POSITIVE STATES 157
3-5 FREQUENCIES AND RELATIVE FREQUENCIES FOR POSITIVE IRREDUCIBLE CHAINS
160 3-6 COSTS AND REWARDS FOR POSITIVE IRREDUCIBLE
CHAINS 163
3-7 TRANSIENT BEHAVIOR 165
3-8 PERIODIC AND APERIODIC STATES; POINTWISE LIMITS 172
3-9 BRANCHING PROCESSES 174
IMAGE 5
VIUE CONTENTS
3-10 REVERSED AND REVERSIBLE POSITIVE IRREDUCIBLE CHAINS 180
3-11* STATIONARY MEASURES FOR RECURRENT IRREDUCIBLE CHAINS 185
PROBLEMS 191
4 CONTINUOUS-TIME MARKOV CHAINS 201
4-1 PURE-JUMP CONTINUOUS-TIME CHAINS 201
4-2 SOME EXAMPLES 206
4-3 REGULAER CHAINS 207
4-4 THE BIRTH AND DEATH PROCESS 213
4-5 TIME AND TRANSITION AVERAGES FOR RECURRENT
IRREDUCIBLE CHAINS 215
4-6 THE BACKWARD AND FORWARD EQUATIONS 218
4-7 UNIFORMIZABLE CHAINS 219
4-8 SEMI-MARKOV PROCESSES 220
4-9* MINIMAL SOLUTIONS TO THE BACKWARD AND FORWARD EQUATIONS 225
PROBLEMS 229
5 INTRODUCTION TO QUEUEING THEORY 232
5-1 CONCEPTS, DEFINITIONS, AND NOTATION 233
5-2 THE BASIC RELATION: L = XVV 235
5-3 SERVICE FACILITIES; THE RULES OF THE GAME 238
5-4 DETERMINISTIC QUEUES-CONTINUOUS
APPROXIMATION 240
5-5 THE MIMLL QUEUE 245
5-6 ARRIVAL AND TIME AVERAGES; FIFO WAITING
TIMES 250
5-7 THE M/M/] QUEUE WITH QUEUE LIMIT 252
5-8 BIRTH AND DEATH MODELS 253
5-9 THE MIM/C QUEUE; COMPARISON WITH SINGLECHANNEL QUEUES 256
IMAGE 6
CONTENTS IX
5-10 THE SCOPE OF MARKOVIAN QUEUES 260
5-11 THE MIGIC LOSS SYSTEM-INSENSITIVITY 271
5-12 SOLVING BALANCE EQUATIONS-GENERATING
FUNCTIONS 273
5-13 WORK AND THE M/G/L QUEUE 278
5-14 THE EFFECT OF ORDER OF SERVICE ON SYSTEM PERFORMANCE; PRIORITIES
282 5-15* ON L = W AND GENERALIZATIONS OF THIS RESULT 286
5-16 ON POISSON ARRIVALS SEE TIME AVERAGES
(PASTA) 293
5-17 CONCLUSIONS AND RELATED LITERATURE 297
PROBLEMS 300
6 REVERSIBILITY AND QUEUEING NETWORKS 308
6-1 REVERSIBLE CHAINS 308
6-2 TANDEM QUEUES 313
6-3 JACKSON NETWORKS 317
6-4 COMPUTING THE THROUGHPUT OF CLOSED JACKSON NETWORKS 327 6-5
APPROXIMATING CLOSED NETWORKS; THE FIXEDPOPULATION-MEAN (FPM) METHOD 328
6-6 OPEN NETWORKS WITH GENERAL CUSTOMER
ROUTES 333
6-7 NETWORKS OF QUASI-REVERSIBLE STATIONS 336
6-8 SYMMETRIE QUEUES 338
6-9 LITERATURE NOTES 340
PROBLEMS 341
7 OVERFLOWS AND RETRIALS 345
7-1 THE TWO-STAGE MODEL 346
7-2 THE GIIMI* QUEUE 347
IMAGE 7
X CONTENTS
7-3 THE GI/M/F LOSS SYSTEM 349
7-4 THE TWO-STAGE MODEL WITH POISSON ARRIVALS 350
7-5 THE EQUIVALENT RANDOM METHOD AND
HAYWARD S APPROXIMATION 353
7-6 THE BM/G/OC QUEUE 358
7-7 THE BM/G/F LOSS SYSTEM 360
7-8 LARGE TWO-STAGE MODELS; HEAVY TRAFFIC 362
7-9 RETRIALS AND THE ORBIT MODEL; THE RTA
APPROXIMATION 367
7-10 MONOTONICITY AND AN UPPER BOUND 370
7-11 THE FREDERICKS AND REISNER APPROXIMATION FOR THE ORBIT MODEL 372
7-12 THE QUALITY OF THE ORBIT MODEL APPROXIMATIONS 373 7-13 THE M/G/1
LOSS SYSTEM WITH INFINITE
ORBITS 376
7-14 OTHER MODELS AND THE LITERATURE 377
PROBLEMS 379
8 THE M/GA AND GI/M/C QUEUES 381
8-1 ANALYSIS OF AN EMBEDDED MARKOV CHAIN FOR
THE M/G/1 QUEUE 381
8-2 FIFO WAITING TIMES FOR THE M/G/1 QUEUE 385
8-3 TIME AND TRANSITION AVERAGES 387
8-4 THE M/G/1 BUSY PERIOD 388
8-5 THE M/G/1 QUEUE WITH EXCEPTIONAL FIRST
SERVICE; LIFO WAITING TIMES 392
8-6 THE G//M/1 QUEUE 395
8-7 THE GI/M/C QUEUE 398
PROBLEMS 399
IMAGE 8
CONTENTS XI
9 RANDOM WALKS AND THE GI/G/L QUEUE 405
9-1 THE GI/G/L QUEUE 405
9-2 RANDOM WALKS AND LADDER VARIABLES; BASIC
TERMINOLOGY AND NOTATION 406
9-3 DUALITY 409
9-4 A REPRESENTATION OF THE LADDER HEIGHT DISTRIBUTION 413 9-5
CONDITIONS FOR FINITE LADDER HEIGHT
MOMENTS 415
9-6 A COMBINATORIAL RESULT 416
9-7 THE DISTRIBUTION OF LADDER EPOCHS 417
9-8 STABILITY CONDITIONS FOR THE GI/G/L QUEUE;
ASSOCIATED QUEUES 419
9-9 BUSY PERIODS 420
9-10 CONDITIONS FOR FINITE DELAY MOMENTS 422
9-11 PREEMPTIVE LIFO AND WORK 424
9-12 WIENER-HOPF FACTORIZATION; THE DELAY
DISTRIBUTION TRANSFORM 426
9-13 LITERATURE NOTES 430
PROBLEMS 431
10 WORK CONSERVATION AND PRIORITY QUEUES 436
10-1 WORK CONSERVATION AND OTHER CONSERVATION
PRINCIPLES 437
10-2 FIXED PRIORITY CLASSES 439
10-3 OVERALL DELAY AND COST CONSIDERATIONS 444
10-4 PRIORITY RULES BASED ON ATTAINED SERVICE; TAGGING JOBS 448 10-5 THE
M/G/L QUEUE WITH GENERALIZED
VACATIONS 457
10-6 RELATED LITERATURE 464
PROBLEMS 465
IMAGE 9
XII
CONTENTS
11 BOUNDS AND APPROXIMATIONS 473
11-1 GI/G/L DELAY IN QUEUE 474
11-2 BOUNDS ON EXPECTED DELAY FOR GENERAL GI/G/L
QUEUES 476
11-3 TAIL PROPERTIES OF DISTRIBUTIONS 480
11-4 GI/G/L BOUNDS BASED ON TAIL PROPERTIES OF THE INTER-ARRIVAL
DISTRIBUTION 481 11-5 COMPARISON METHODS WITH APPLICATIONS TO THE
GI/G/L QUEUE 485
11-6 THE GI/G/C QUEUE-BASIC PROPERTIES 493
11-7 BOUNDS FOR THE GI/G/C QUEUE; DELAY
MOMENTS 496
11-8 APPROXIMATIONS FOR THE MLGIC QUEUE; QUEUE LIMITS AND RETRIALS 504
11-9 TANDEM QUEUES-SOME GENERAL AND LIGHTTRAFFIC RESULTS 506
11-10 GI/G/L AND GI/G/C QUEUES IN HEAVY TRAFFIC 517
11-11 BOUNDS ON DELAY DISTRIBUTIONS FOR GI/G/L
QUEUES 519
11-12 FURTHER DISCUSSION AND LITERATURE NOTES 520
PROBLEMS 522
APPENDIX 526
A-L SEQUENCES AND SERIES; LIMITS AND
CONVERGENCE 526
A-2 INTEGRATION; DF NOTATION 530
A-3 INTERCHANGING LIMIT AND INTEGRAL 535
A-4 DIFFERENTIATING INTEGRALS AND SUMS 536
REFERENCES 539
INDEX 549
|
any_adam_object | 1 |
author | Wolff, Ronald W. |
author_GND | (DE-588)170640930 |
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callnumber-first | Q - Science |
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dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 519 - Probabilities and applied mathematics |
dewey-raw | 519.2 |
dewey-search | 519.2 |
dewey-sort | 3519.2 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
format | Book |
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id | DE-604.BV006144133 |
illustrated | Illustrated |
indexdate | 2024-07-09T16:41:00Z |
institution | BVB |
isbn | 0138466920 0138498458 |
language | English |
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series2 | Prentice Hall international series in industrial and systems engineering |
spelling | Wolff, Ronald W. (DE-588)170640930 aut Stochastic modeling and the theory of queues Ronald W. Wolff, University of California, Berkeley Englewood Cliffs, NJ Prentice Hall 1989 XIX, 556 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Prentice Hall international series in industrial and systems engineering Files d'attente, Théorie des Files d'attente, Théorie des ram Processos estocasticos especiais larpcal Processus stochastiques - Modèles mathématiques Processus stochastiques ram approximation inriac chaîne Markov inriac marche aléatoire inriac réversibilité inriac théorie probabilité inriac théorie queue inriac théorie renouvellement inriac Mathematisches Modell Queuing theory Stochastic processes Mathematical models Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Stochastisches Modell (DE-588)4057633-4 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003884164&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Wolff, Ronald W. Stochastic modeling and the theory of queues Files d'attente, Théorie des Files d'attente, Théorie des ram Processos estocasticos especiais larpcal Processus stochastiques - Modèles mathématiques Processus stochastiques ram approximation inriac chaîne Markov inriac marche aléatoire inriac réversibilité inriac théorie probabilité inriac théorie queue inriac théorie renouvellement inriac Mathematisches Modell Queuing theory Stochastic processes Mathematical models Stochastisches Modell (DE-588)4057633-4 gnd Warteschlangentheorie (DE-588)4255044-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
subject_GND | (DE-588)4057633-4 (DE-588)4255044-0 (DE-588)4057630-9 |
title | Stochastic modeling and the theory of queues |
title_auth | Stochastic modeling and the theory of queues |
title_exact_search | Stochastic modeling and the theory of queues |
title_full | Stochastic modeling and the theory of queues Ronald W. Wolff, University of California, Berkeley |
title_fullStr | Stochastic modeling and the theory of queues Ronald W. Wolff, University of California, Berkeley |
title_full_unstemmed | Stochastic modeling and the theory of queues Ronald W. Wolff, University of California, Berkeley |
title_short | Stochastic modeling and the theory of queues |
title_sort | stochastic modeling and the theory of queues |
topic | Files d'attente, Théorie des Files d'attente, Théorie des ram Processos estocasticos especiais larpcal Processus stochastiques - Modèles mathématiques Processus stochastiques ram approximation inriac chaîne Markov inriac marche aléatoire inriac réversibilité inriac théorie probabilité inriac théorie queue inriac théorie renouvellement inriac Mathematisches Modell Queuing theory Stochastic processes Mathematical models Stochastisches Modell (DE-588)4057633-4 gnd Warteschlangentheorie (DE-588)4255044-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
topic_facet | Files d'attente, Théorie des Processos estocasticos especiais Processus stochastiques - Modèles mathématiques Processus stochastiques approximation chaîne Markov marche aléatoire réversibilité théorie probabilité théorie queue théorie renouvellement Mathematisches Modell Queuing theory Stochastic processes Mathematical models Stochastisches Modell Warteschlangentheorie Stochastischer Prozess |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003884164&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT wolffronaldw stochasticmodelingandthetheoryofqueues |