Stochastic process limits: an introduction to stochastic process limits and their application to queues
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, [u.a.]
Springer
[2002]
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| Series: | Springer series in operations research
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis Seite 541 - 568 |
| Physical Description: | xxiii, 602 Seiten Illustrationen |
| ISBN: | 0387953582 |
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| 245 | 1 | 0 | |a Stochastic process limits |b an introduction to stochastic process limits and their application to queues |c Ward Whitt |
| 246 | 1 | 3 | |a Stochastic-process limits |
| 264 | 1 | |a New York, [u.a.] |b Springer |c [2002] | |
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| 300 | |a xxiii, 602 Seiten |b Illustrationen | ||
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| 500 | |a Literaturverzeichnis Seite 541 - 568 | ||
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| 650 | 4 | |a Teoría de las colas (Matemáticas) | |
| 650 | 4 | |a Queuing theory | |
| 650 | 4 | |a Stochastic processes | |
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Record in the Search Index
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| adam_text |
WARD WHITT STOCHASTIC-PROCESS LIMITS AN INTRODUCTION TO
STOCHASTIC-PROCESS LIMITS AND THEIR APPLICATION TO QUEUES WITH 68
ILLUSTRATIONS SPRINGER CONTENTS PREFACE VII 1 EXPERIENCING STATISTICAL
REGULARITY 1 1.1 A SIMPLE GAME OF CHANCE 1 1.1.1 PLOTTING RANDOM WALKS 2
1.1.2 WHEN THE GAME IS FAIR 3 1.1.3 THE FINAL POSITION 7 1.1.4 MAKING AN
INTERESTING GAME 12 1.2 STOCHASTIC-PROCESS LIMITS 16 1.2.1 A PROBABILITY
MODEL 16 1.2.2 CLASSICAL PROBABILITY LIMITS 20 1.2.3 IDENTIFYING THE
LIMIT PROCESS 22 1.2.4 LIMITS FOR THE PLOTS 25 1.3 INVARIANCE PRINCIPLES
27 1.3.1 THE RANGE OF BROWNIAN MOTION 28 1.3.2 RELAXING THE IID
CONDITIONS 30 1.3.3 DIFFERENT STEP DISTRIBUTIONS 31 1.4 THE EXCEPTION
MAKES THE RULE 34 1.4.1 EXPLAINING THE IRREGULARITY 35 1.4.2 THE
CENTERED RANDOM WALK WITH P = 3/2 37 1.4.3 BACK TO THE UNCENTERED RANDOM
WALK WITH P = 1/2 . 43 1.5 SUMMARY 45 XVIII CONTENTS 2 RANDOM WALKS IN
APPLICATIONS 49 2.1 STOCK PRICES 49 2.2 THE KOLMOGOROV-SMIRNOV STATISTIC
51 2.3 A QUEUEING MODEL FOR A BUFFER IN A SWITCH 55 2.3.1 DERIVING THE
PROPER SCALING 56 2.3.2 SIMULATION EXAMPLES 59 2.4 ENGINEERING
SIGNIFICANCE 63 2.4.1 BUFFER SIZING 64 2.4.2 SCHEDULING SERVICE FOR
MULTIPLE SOURCES 68 3 THE FRAMEWORK FOR STOCHASTIC-PROCESS LIMITS 75 3.1
INTRODUCTION 75 3.2 THE SPACE V 76 3.3 THE SPACE D 78 3.4 THE
CONTINUOUS-MAPPING APPROACH 84 3.5 USEFUL FUNCTIONS 86 3.6 ORGANIZATION
OF THE BOOK 89 4 A PANORAMA OF STOCHASTIC-PROCESS LIMITS 95 4.1
INTRODUCTION 95 4.2 SELF-SIMILAR PROCESSES 96 4.2.1 GENERAL CLT'S AND
FCLT'S 96 4.2.2 SELF-SIMILARITY 97 4.2.3 THE NOAH AND JOSEPH EFFECTS 99
4.3 DONSKER'S THEOREM 101 4.3.1 THE BASIC THEOREMS 101 4.3.2
MULTIDIMENSIONAL VERSIONS 104 4.4 BROWNIAN LIMITS WITH WEAK DEPENDENCE
106 4.5 THE NOAH EFFECT: HEAVY TAILS 109 4.5.1 STABLE LAWS ILL 4.5.2
CONVERGENCE TO STABLE LAWS 114 4.5.3 CONVERGENCE TO STABLE LEVY MOTION
116 4.5.4 EXTREME-VALUE LIMITS 118 4.6 THE JOSEPH EFFECT: STRONG
DEPENDENCE 120 4.6.1 STRONG POSITIVE DEPENDENCE 121 4.6.2 ADDITIONAL
STRUCTURE 122 4.6.3 CONVERGENCE TO FRACTIONAL BROWNIAN MOTION 124 4.7
HEAVY TAILS PLUS DEPENDENCE 130 4.7.1 ADDITIONAL STRUCTURE 130 4.7.2
CONVERGENCE TO STABLE LEVY MOTION 131 4.7.3 LINEAR FRACTIONAL STABLE
MOTION 132 4.8 SUMMARY 136 CONTENTS XIX HEAVY-TRAFFIC LIMITS FOR FLUID
QUEUES 137 5.1 INTRODUCTION 137 5.2 A GENERAL FLUID-QUEUE MODEL 139
5.2.1 INPUT AND AVAILABLE-PROCESSING PROCESSES 139 5.2.2 INFINITE
CAPACITY 140 5.2.3 FINITE CAPACITY 143 5.3 UNSTABLE QUEUES 145 5.3.1
FLUID LIMITS FOR FLUID QUEUES 146 5.3.2 STOCHASTIC REFINEMENTS 149 5.4
HEAVY-TRAFFIC LIMITS FOR STABLE QUEUES 153 5.5 HEAVY-TRAFFIC SCALING 157
5.5.1 THE IMPACT OF SCALING UPON PERFORMANCE 158 5.5.2 IDENTIFYING
APPROPRIATE SCALING FUNCTIONS 160 5.6 LIMITS AS THE SYSTEM SIZE
INCREASES 162 5.7 BROWNIAN APPROXIMATIONS 165 5.7.1 THE BROWNIAN LIMIT
166 5.7.2 THE STEADY-STATE DISTRIBUTION 167 5.7.3 THE OVERFLOW PROCESS
170 5.7.4 ONE-SIDED REFLECTION 173 5.7.5 FIRST-PASSAGE TIMES 176 5.8
PLANNING QUEUEING SIMULATIONS 178 5.8.1 THE STANDARD STATISTICAL
PROCEDURE 180 5.8.2 INVOKING THE BROWNIAN APPROXIMATION 181 5.9
HEAVY-TRAFFIC LIMITS FOR OTHER PROCESSES 183 5.9.1 THE DEPARTURE PROCESS
183 5.9.2 THE PROCESSING TIME 184 5.10 PRIORITIES 187 5.10.1 A
HEIRARCHICAL APPROACH 189 5.10.2 PROCESSING TIMES 190 UNMATCHED JUMPS IN
THE LIMIT PROCESS 193 6.1 INTRODUCTION 193 6.2 LINEARLY INTERPOLATED
RANDOM WALKS 195 6.2.1 ASYMPTOTIC EQUIVALENCE WITH M\ 195 6.2.2
SIMULATION EXAMPLES 196 6.3 HEAVY-TAILED RENEWAL PROCESSES 200 6.3.1
INVERSE PROCESSES 201 6.3.2 THE SPECIAL CASE WITH M = 1 202 6.4 A QUEUE
WITH HEAVY-TAILED DISTRIBUTIONS 205 6.4.1 THE STANDARD SINGLE-SERVER
QUEUE 206 6.4.2 HEAVY-TRAFFIC LIMITS 208 6.4.3 SIMULATION EXAMPLES 210
6.5 RARE LONG SERVICE INTERRUPTIONS 216 6.6 TIME-DEPENDENT ARRIVAL RATES
220 XX CONTENTS 7 MORE STOCHASTIC-PROCESS LIMITS 225 7.1 INTRODUCTION
225 7.2 CENTRAL LIMIT THEOREM FOR PROCESSES 226 7.2.1 HAHN'S THEOREM 226
7.2.2 A SECOND LIMIT 230 7.3 COUNTING PROCESSES 233 7.3.1 CLT
EQUIVALENCE 234 7.3.2 FCLT EQUIVALENCE 235 7.4 RENEWAL-REWARD PROCESSES
238 8 FLUID QUEUES WITH ON-OFF SOURCES 243 8.1 INTRODUCTION 243 8.2 A
FLUID QUEUE FED BY ON-OFF SOURCES 245 8.2.1 THE ON-OFF SOURCE MODEL 245
8.2.2 SIMULATION EXAMPLES 248 8.3 HEAVY-TRAFFIC LIMITS FOR THE ON-OFF
SOURCES 250 8.3.1 A SINGLE SOURCE 251 8.3.2 MULTIPLE SOURCES 255 8.3.3
M/G/OO SOURCES 259 8.4 BROWNIAN APPROXIMATIONS 260 8.4.1 THE BROWNIAN
LIMIT 260 8.4.2 MODEL SIMPLIFICATION 263 8.5 STABLE-LEVY APPROXIMATIONS
264 8.5.1 THE RSLM HEAVY-TRAFFIC LIMIT 265 8.5.2 THE STEADY-STATE
DISTRIBUTION 268 8.5.3 NUMERICAL COMPARISONS 270 8.6 SECOND
STOCHASTIC-PROCESS LIMITS 272 8.6.1 M/G/L/K APPROXIMATIONS 273 8.6.2
LIMITS FOR LIMIT PROCESSES 277 8.7 REFLECTED FRACTIONAL BROWNIAN MOTION
279 8.7.1 AN INCREASING NUMBER OF SOURCES 279 8.7.2 GAUSSIAN INPUT 280
8.8 REFLECTED GAUSSIAN PROCESSES 283 9 SINGLE-SERVER QUEUES 287 9.1
INTRODUCTION 287 9.2 THE STANDARD SINGLE-SERVER QUEUE 288 9.3
HEAVY-TRAFFIC LIMITS 292 9.3.1 THE SCALED PROCESSES 292 9.3.2
DISCRETE-TIME PROCESSES 294 9.3.3 CONTINUOUS-TIME PROCESSES 297 9.4
SUPERPOSITION ARRIVAL PROCESSES 301 9.5 SPLIT PROCESSES 305 9.6 BROWNIAN
APPROXIMATIONS 306 9.6.1 VARIABILITY PARAMETERS 307 CONTENTS XXI 9.6.2
MODELS WITH MORE STRUCTURE 310 9.7 VERY HEAVY TAILS 313 9.7.1
HEAVY-TRAFFIC LIMITS 314 9.7.2 FIRST PASSAGE TO HIGH LEVELS 316 9.8 AN
INCREASING NUMBER OF ARRIVAL PROCESSES 318 9.8.1 ITERATED AND DOUBLE
LIMITS 318 9.8.2 SEPARATION OF TIME SCALES 322 9.9 APPROXIMATIONS FOR
QUEUEING NETWORKS 326 9.9.1 PARAMETRIC-DECOMPOSITION APPROXIMATIONS 326
9.9.2 APPROXIMATELY CHARACTERIZING ARRIVAL PROCESSES 330 9.9.3 A NETWORK
CALCULUS 331 9.9.4 EXOGENOUS ARRIVAL PROCESSES 337 9.9.5 CONCLUDING
REMARKS 338 10 MULTISERVER QUEUES 341 10.1 INTRODUCTION 341 10.2 QUEUES
WITH MULTIPLE SERVERS 342 10.2.1 A QUEUE WITH AUTONOMOUS SERVICE 342
10.2.2 THE STANDARD M-SERVER MODEL 345 10.3 INFINITELY MANY SERVERS 348
10.3.1 HEAVY-TRAFFIC LIMITS 349 10.3.2 GAUSSIAN APPROXIMATIONS 352 10.4
AN INCREASING NUMBER OF SERVERS 355 10.4.1 INFINITE-SERVER
APPROXIMATIONS 356 10.4.2 HEAVY-TRAFFIC LIMITS FOR DELAY MODELS 357
10.4.3 HEAVY-TRAFFIC LIMITS FOR LOSS MODELS 360 10.4.4 PLANNING
SIMULATIONS OF LOSS MODELS 361 11 MORE ON THE MATHEMATICAL FRAMEWORK 367
11.1 INTRODUCTION 367 11.2 TOPOLOGIES 368 11.2.1 DEFINITIONS 368 11.2.2
SEPARABILITY AND COMPLETENESS 371 11.3 THE SPACE V 372 11.3.1
PROBABILITY SPACES 372 11.3.2 CHARACTERIZING WEAK CONVERGENCE 373 11.3.3
RANDOM ELEMENTS 375 11.4 PRODUCT SPACES 377 11.5 THE SPACE D 380 11.5.1
J 2 AND M 2 METRICS 381 11.5.2 THE FOUR SKOROHOD TOPOLOGIES 382 11.5.3
MEASURABILITY ISSUES 385 11.6 THE COMPACTNESS APPROACH 386 XXII CONTENTS
12 THE SPACE D 391 12.1 INTRODUCTION 391 12.2 REGULARITY PROPERTIES OF D
392 12.3 STRONG AND WEAK M 1 TOPOLOGIES 394 12.3.1 DEFINITIONS 394
12.3.2 METRIC PROPERTIES 396 12.3.3 PROPERTIES OF PARAMETRIC
REPRESENTATIONS 398 12.4 LOCAL UNIFORM CONVERGENCE AT CONTINUITY POINTS
401 12.5 ALTERNATIVE CHARACTERIZATIONS OF M\ CONVERGENCE 403 12.5.1 SMI
CONVERGENCE 403 12.5.2 WM X CONVERGENCE 408 12.6 STRENGTHENING THE MODE
OF CONVERGENCE 409 12.7 CHARACTERIZING CONVERGENCE WITH MAPPINGS 410
12.8 TOPOLOGICAL COMPLETENESS 413 12.9 NONCOMPACT DOMAINS 414 12.10
STRONG AND WEAK M 2 TOPOLOGIES 416 12.11 ALTERNATIVE CHARACTERIZATIONS
OF M 2 CONVERGENCE 418 12.11.1 M2 PARAMETRIC REPRESENTATIONS 418 12.11.2
SM 2 CONVERGENCE 419 12.11.3 WM 2 CONVERGENCE 421 12.11.4 ADDITIONAL
PROPERTIES OF M 2 CONVERGENCE 422 12.12 COMPACTNESS 424 13 USEFUL
FUNCTIONS 427 13.1 INTRODUCTION 427 13.2 COMPOSITION 428 13.3
COMPOSITION WITH CENTERING 431 13.4 SUPREMUM 435 13.5 ONE-DIMENSIONAL
REFLECTION 439 13.6 INVERSE 441 13.6.1 THE STANDARD TOPOLOGIES 442
13.6.2 THE M[ TOPOLOGY 444 13.6.3 FIRST PASSAGE TIMES 446 13.7 INVERSE
WITH CENTERING 447 13.8 COUNTING FUNCTIONS 453 14 QUEUEING NETWORKS 457
14.1 INTRODUCTION 457 14.2 THE MULTIDIMENSIONAL REFLECTION MAP 460
14.2.1 A SPECIAL CASE 460 14.2.2 DEFINITION AND CHARACTERIZATION 462
14.2.3 CONTINUITY AND LIPSCHITZ PROPERTIES 465 14.3 THE INSTANTANEOUS
REFLECTION MAP 473 14.3.1 DEFINITION AND CHARACTERIZATION 474 14.3.2
IMPLICATIONS FOR THE REFLECTION MAP 480 CONTENTS XXIII 14.4 REFLECTIONS
OF PARAMETRIC REPRESENTATIONS 482 14.5 MI CONTINUITY RESULTS AND
COUNTEREXAMPLES 485 14.5.1 M X CONTINUITY RESULTS 485 14.5.2
COUNTEREXAMPLES 487 14.6 LIMITS FOR STOCHASTIC FLUID NETWORKS 490 14.6.1
MODEL CONTINUITY 492 14.6.2 HEAVY-TRAFFIC LIMITS 493 14.7 QUEUEING
NETWORKS WITH SERVICE INTERRUPTIONS 495 14.7.1 MODEL DEFINITION 495
14.7.2 HEAVY-TRAFFIC LIMITS 499 14.8 THE TWO-SIDED REGULATOR 505 14.8.1
DEFINITION AND BASIC PROPERTIES 505 14.8.2 WITH THE M X TOPOLOGIES 509
14.9 RELATED LITERATURE 511 15 THE SPACES E AND F 515 15.1 INTRODUCTION
515 15.2 THREE TIME SCALES 516 15.3 MORE COMPLICATED OSCILLATIONS 519
15.4 THE SPACE E 523 15.5 CHARACTERIZATIONS OF M 2 CONVERGENCE IN E 527
15.6 CONVERGENCE TO EXTREMAL PROCESSES 530 15.7 THE SPACE F 533 15.8
QUEUEING APPLICATIONS 535 REFERENCES 541 APPENDIX A REGULAR VARIATION
569 APPENDIX B CONTENTS OF THE INTERNET SUPPLEMENT 573 NOTATION INDEX
577 AUTHOR INDEX 579 SUBJECT INDEX 585 |
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| ctrlnum | (OCoLC)318282860 (DE-599)BVBBV014173147 |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| isbn | 0387953582 |
| language | English |
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| publisher | Springer |
| record_format | marc |
| series2 | Springer series in operations research |
| spelling | Whitt, Ward 1942- (DE-588)170183033 aut Stochastic process limits an introduction to stochastic process limits and their application to queues Ward Whitt Stochastic-process limits New York, [u.a.] Springer [2002] © 2002 xxiii, 602 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Springer series in operations research Literaturverzeichnis Seite 541 - 568 Procesos estocásticos Teoría de las colas (Matemáticas) Queuing theory Stochastic processes 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 Erscheint auch als Online-Ausgabe 978-0-387-21748-2 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009715895&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Whitt, Ward 1942- Stochastic process limits an introduction to stochastic process limits and their application to queues Procesos estocásticos Teoría de las colas (Matemáticas) Queuing theory Stochastic processes Warteschlangentheorie (DE-588)4255044-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4255044-0 (DE-588)4057630-9 |
| title | Stochastic process limits an introduction to stochastic process limits and their application to queues |
| title_alt | Stochastic-process limits |
| title_auth | Stochastic process limits an introduction to stochastic process limits and their application to queues |
| title_exact_search | Stochastic process limits an introduction to stochastic process limits and their application to queues |
| title_full | Stochastic process limits an introduction to stochastic process limits and their application to queues Ward Whitt |
| title_fullStr | Stochastic process limits an introduction to stochastic process limits and their application to queues Ward Whitt |
| title_full_unstemmed | Stochastic process limits an introduction to stochastic process limits and their application to queues Ward Whitt |
| title_short | Stochastic process limits |
| title_sort | stochastic process limits an introduction to stochastic process limits and their application to queues |
| title_sub | an introduction to stochastic process limits and their application to queues |
| topic | Procesos estocásticos Teoría de las colas (Matemáticas) Queuing theory Stochastic processes Warteschlangentheorie (DE-588)4255044-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Procesos estocásticos Teoría de las colas (Matemáticas) Queuing theory Stochastic processes Warteschlangentheorie Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009715895&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT whittward stochasticprocesslimitsanintroductiontostochasticprocesslimitsandtheirapplicationtoqueues AT whittward stochasticprocesslimits |