Heavy traffic analysis of controlled queueing and communication networks:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2001
|
| Schriftenreihe: | Applications of mathematics
47 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 485 - 503 |
| Beschreibung: | XIX, 513 S. graph. Darst. |
| ISBN: | 0387952640 |
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| 245 | 1 | 0 | |a Heavy traffic analysis of controlled queueing and communication networks |c Harold J. Kushner |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2001 | |
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Datensatz im Suchindex
| _version_ | 1804133367326703616 |
|---|---|
| adam_text | HAROLD J. KUSHNER HEAVY TRAFFIC ANALYSIS OF CONTROLLED QUEUEING AND
COMMUNICATION NETWORKS WITH 50 ILLUSTRATIONS SPRINGER CONTENTS PREFACE
VII INTRODUCTION: MODELS AND APPLICATIONS 1 1.1 A SINGLE QUEUE: HEAVY
TRAFFIC MODELING 4 1.1.1 SIMPLE ONE DIMENSIONAL MODELS 4 1.1.2 THE
WORKLOAD FORM 13 1.2 NETWORKS 14 1.2.1 SIMPLE NETWORKS 15 1.2.2 CLOSED
AND OPEN/CLOSED NETWORKS 22 1.3 - SERVER SCHEDULING AND ASSIGNMENT
PROBLEMS 23 1.3.1 MULTIPLE INPUT CLASSES AND CONTROLLED POLLING . . . .
24 1.4 COMMUNICATION AND COMPUTER NETWORKS: THE MULTIPLEXER 34 1.5
CONTROLLED ADMISSION IN A MULTISERVICE SYSTEM: FORMULATION 39
MARTINGALES AND WEAK CONVERGENCE 45 2.1 MARTINGALES AND THE WIENER
PROCESS 46 2.1.1 MARTINGALES 46 2.1.2 THE WIENER PROCESS 49 2.2
STOCHASTIC INTEGRALS 51 2.2.1 DEFINITION AND PROPERTIES 51 2.2.2 ITO S
LEMMA 54 2.3 POISSON MEASURES 56 I CONTENTS 2.3.1 THE POISSON PROCESS
AND POISSON RANDOM MEASURES 56 2.3.2 MARTINGALE DECOMPOSITION OF A JUMP
PROCESS . . . . 58 2.4 - THE DOOB-MEYER PROCESS 60 2.4.1 INTRODUCTION
AND ITO S FORMULA 60 2.4.2 THE DOOB-MEYER PROCESS FOR A JUMP PROCESS . .
. . 62 2.5 WEAK CONVERGENCE 63 2.5.1 MOTIVATION AND EXAMPLES 63 2.5.2
BASIC THEOREMS OF WEAK CONVERGENCE 65 2.5.3 THE FUNCTION SPACE D(M K
;0,OO) 68 2.5.4 THE FUNCTION SPACES D(S; 0, T) AND D(S; 0, OO) . . . 69
2.5.5 TRUNCATED PROCESSES 70 2.6 THE TIME TRANSFORMATION METHOD 72 2.7
MEASURE-VALUED PROCESSES 77 2.8 TIGHTNESS AND CONVERGENCE TO WIENER
PROCESSES 79 2.8.1 CRITERIA FOR WEAK CONVERGENCE TO MARTINGALES . . . .
79 2.8.2 TIGHTNESS AND WIENER PROCESS LIMITS 82 STOCHASTIC DIFFERENTIAL
EQUATIONS: CONTROLLED AND UNCONTROLLED 89 3.1 STOCHASTIC DIFFERENTIAL
EQUATIONS AND DIFFUSION PROCESSES 91 3.1.1 DEFINITIONS: UNCONTROLLED
SDES 91 3.1.2 CONTROLLED DIFFUSIONS 92 3.1.3 CONSTRUCTION OF A STRONG
SOLUTION 94 3.1.4 THE GIRSANOV TRANSFORMATION 96 3.2 RELAXED CONTROLS 97
3.2.1 EXISTENCE OF A DETERMINISTIC OPTIMAL CONTROL . . . . 98 3.2.2 THE
TOPOLOGY ON THE SPACE OF RELAXED CONTROLS . . 101 3.2.3 STOCHASTIC
RELAXED CONTROLS 102 3.3 IMPULSIVE AND SINGULAR CONTROL PROBLEMS 105 3.4
REFLECTED DIFFUSIONS 108 3.4.1 INTRODUCTION AND EXAMPLES 108 3.4.2
REFLECTED BROWNIAN MOTION AND RELATED MODELS . . ILL 3.5 THE SKOROHOD
PROBLEM 118 3.5.1 DEFINITIONS AND LIPSCHITZ CONDITIONS 118 3.5.2
REFLECTED STOCHASTIC DIFFERENTIAL EQUATIONS 124 3.5.3 IMPULSIVE AND
SINGULAR CONTROL PROBLEMS 129 3.6 TIGHTNESS FOR THE SKOROHOD PROBLEM 130
3.7 REFLECTED JUMP-DIFFUSION PROCESSES 134 3.8 APPROXIMATIONS OF OPTIMAL
CONTROLS 136 INVARIANT MEASURES AND THE ERGODIC PROBLEM 141 4.1
CONVERGENCE TO INVARIANT MEASURES 142 4.2 PROPERTIES OF SOLUTIONS 145
CONTENTS XVII 4.3 THE PROCESS MODEL 148 4.4 OPTIMAL FEEDBACK CONTROLS
155 4.5 A MAXIMUM PRINCIPLE 161 4.6 OPTIMALITY OVER ALL ADMISSIBLE
CONTROLS 166 4.7 FUNCTIONAL OCCUPATION MEASURES . 168 4.8 APPROXIMATING
CONTROLS 176 THE SINGLE-PROCESSOR PROBLEM 179 5.1 A CANONICAL
SINGLE-SERVER PROBLEM 182 5.1.1 THE BASIC MODEL 182 5.1.2 MULTIPLE
ARRIVAL STREAMS OF DIFFERENT RATES 190 5.1.3 THE FICTITIOUS SERVICES
MODEL 193 5.2 TIGHTNESS OF THE REFLECTION TERMS 195 5.3 THE WORKLOAD
PROCESSES 200 5.3.1 THE WORKLOAD EQUATION FOR THE BASIC MODEL .... 200
5.3.2 SEVERAL INPUT STREAMS: DIFFERENT WORK REQUIREMENTS 202 5.3.3
ASYMPTOTIC RELATIONS BETWEEN THE QUEUE SIZE AND WORKLOAD 203 5.4
EXTENSIONS 207 5.4.1 BATCH ARRIVALS AND SERVICES 207 5.4.2 MANY SERVERS
210 5.5 CORRELATED PROCESSES: BURSTY ARRIVALS 212 5.6 PROCESSOR
INTERRUPTIONS, PRIORITIES, AND VACATIONS 217 5.6.1 SHORT AND FREQUENT
VACATIONS 217 5.6.2 PRIORITIES 220 5.6.3 SHORT AND INFREQUENT VACATIONS
222 5.6.4 LONG BUT INFREQUENT VACATIONS 223 5.7 AN ALTERNATIVE SCALING:
FAST ARRIVALS AND SERVICES 227 UNCONTROLLED NETWORKS 229 6.1 THE HEAVY
TRAFFIC LIMIT THEOREM 231 6.1.1 INDEPENDENT ROUTING 231 6.1.2 MARTINGALE
DIFFERENCE INTERVALS 237 6.1.3 CORRELATED ROUTING 242 6.1.4 A GENERAL
SKOROHOD PROBLEM MODEL 244 6.2 EXTENSIONS 245 6.2.1 CLOSED NETWORKS 245
6.2.2 NONBOTTLENECK PROCESSORS 248 6.2.3 BATCH ARRIVALS, MULTIPLE
SERVERS, MULTICAST AND FORK-JOIN QUEUES 249 6.3 BLOCKING 253 6.4 THE
WORKLOAD FORMULATION AND PRIORITIES 257 6.4.1 QUEUED WORKLOAD 257 6.4.2
A MULTICLASS FEEDFORWARD SYSTEM 258 XVIII CONTENTS 6.5 FLUID SCALING AND
LIMITS 264 6.5.1 A SINGLE-CLASS NETWORK 264 6.6 AN ALTERNATIVE SCALING:
FAST ARRIVALS AND SERVICES 267 7 UNCONTROLLED NETWORKS, CONTINUED 269
7.1 A MANUFACTURING SYSTEM 270 7.1.1 THE BASIC MODEL 270 7.1.2 MULTIPLE
TYPES OF FINAL PRODUCTS I 272 7.1.3 MULTIPLE TYPES OF FINAL PRODUCTS: II
. ILL 7.2 SHARED BUFFERS 279 7.3 PROCESS INTERRUPTIONS AND VACATIONS
282 7.3.1 SHORT VACATIONS 283 7.3.2 LONG BUT INFREQUENT INTERRUPTIONS
285 7.4 CORRELATED SERVICE TIMES 290 7.4.1 A SIMPLE FEEDFORWARD SYSTEM
291 7.4.2 RANDOM ROUTING IN A FEEDFORWARD SYSTEM 292 7.4.3 A FEEDBACK
SYSTEM WITH CORRELATED SERVICE TIMES 294 7.5 PROCESSOR SHARING 298 8
STATE DEPENDENCE 305 8.1 MARGINAL STATE DEPENDENCE ........... . X 307
8.2 POISSON-TYPE INPUT AND SERVICE PROCESS 316 8.2.1 THE BASIC MODEL 316
8.2.2 A GENERALIZATION: RELATIONSHIPS WITH SECTION 1 ... 321 8.2.3
VACATIONS 322 8.3 SELF-SERVICE WITH FAST ARRIVALS 323 8.4 DISCONTINUOUS
DYNAMICS 326 8.5 AN APPLICATION TO THE MULTIPLEXER-BUFFER SYSTEM 329
8.5.1 INTRODUCTION AND PROBLEM DESCRIPTION 329 8.5.2 CONVERGENCE 332 8.6
BALKING, WITHDRAWING, AND RETRIALS 337 9 BOUNDED CONTROLS 341 9.1
DISCOUNTED COST 343 9.1.1 A CANONICAL MODEL AND ASSUMPTIONS 343 9.1.2
CONTROLS APPEARING LINEARLY 350 9.1.3 CONTROLS APPEARING NONLINEARLY 352
9.1.4 EXTENSIONS 356 9.2 THE ERGODIC COST PROBLEM 359 9.3 EXAMPLES 363
9.3.1 SERVICE RATE AND ASSIGNMENT CONTROLS 363 9.3.2 THE MULTIPLEXER
PROBLEM: CONVERGENCE 364 9.4 DATA FOR THE MULTIPLEXER PROBLEM 368
CONTENTS XIX 10 SINGULAR CONTROLS 375 10.1 A CANONICAL MODEL 377 10.2
VACATIONS .384 10.3 CONTROLLED ADMISSION 391 10.3.1 INTRODUCTION: THE
BASIC SYSTEM 391 10.3.2 UPPER LIMIT TO THE BANDWIDTH FOR THE BE-SHARING
CUSTOMERS 396 10.4 REROUTING AND SINGULAR CONTROL 398 10.4.1 REROUTING
WITH PENALTY 398 10.4.2 REROUTING ONLY WHEN A QUEUE IS FULL 401 11
POLLING AND CONTROL OF POLLING 405 11.1 AN AVERAGING PRINCIPLE FOR THE
INDIVIDUAL QUEUES 408 11.1.1 CONTINUOUS SWITCHING POLICIES 408 11.1.2
LOWER THRESHOLDS 417 11.2 RATE OF SWITCHING AND NONZERO SWITCHING TIME
420 11.2.1 SWITCHING RATE 420 11.2.2 NONZERO SWITCHING TIME 422 11.3
GATED POLLING 423 11.4 THE CONTROL PROBLEM: SWITCHING COST AND TIME 424
11.4.1 SWITCHING COST 424 11.4.2 NONZERO SWITCHING TIME 427 11.5
CONTROLLED POLLING WITH INTERRUPTIONS 428 11.6 WEAK CONVERGENCE 431 11.7
THE LIMIT CONTROL PROBLEM 434 11.8 EXTENSIONS AND COMMENTS 439 11.8.1
MINIMIZING THE TOTAL EXPECTED WORKLOAD 439 11.8.2 NO VACATIONS: THE
ASYMPTOTIC OPTIMALITY OF THE C/I-RULE 441 11.9 RELAXED POISSON MEASURES
442 .11.9.1 A DIFFICULTY WITH CONTROLLED JUMPS 442 11.9.2 THE RELAXED
POISSON MEASURE 446 12 ASSIGNMENT AND SCHEDULING: MANY CLASSES AND
PROCESSORS 453 12.1 MANY INPUT CLASSES AND A SINGLE PROCESSOR 455 12.2 A
ONE-STAGE, TWO-CLASS AND TWO-PROCESSOR PROBLEM . . . 459 12.3 MANY INPUT
CLASSES AND SERVERS: ONE STAGE 466 12.4 FEEDFORWARD NETWORKS 476
REFERENCES 485 SYMBOL INDEX 504 INDEX 508
|
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| id | DE-604.BV019851759 |
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| indexdate | 2024-07-09T20:07:35Z |
| institution | BVB |
| isbn | 0387952640 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013176446 |
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| physical | XIX, 513 S. graph. Darst. |
| publishDate | 2001 |
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| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series | Applications of mathematics |
| series2 | Applications of mathematics |
| spelling | Kushner, Harold J. 1933- Verfasser (DE-588)11559163X aut Heavy traffic analysis of controlled queueing and communication networks Harold J. Kushner New York [u.a.] Springer 2001 XIX, 513 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 47 Literaturverz. S. 485 - 503 Warteschlangentheorie - Stochastische Differentialgleichung Queuing theory Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 s Stochastische Differentialgleichung (DE-588)4057621-8 s DE-604 Applications of mathematics 47 (DE-604)BV000895226 47 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013176446&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kushner, Harold J. 1933- Heavy traffic analysis of controlled queueing and communication networks Applications of mathematics Warteschlangentheorie - Stochastische Differentialgleichung Queuing theory Stochastische Differentialgleichung (DE-588)4057621-8 gnd Warteschlangentheorie (DE-588)4255044-0 gnd |
| subject_GND | (DE-588)4057621-8 (DE-588)4255044-0 |
| title | Heavy traffic analysis of controlled queueing and communication networks |
| title_auth | Heavy traffic analysis of controlled queueing and communication networks |
| title_exact_search | Heavy traffic analysis of controlled queueing and communication networks |
| title_full | Heavy traffic analysis of controlled queueing and communication networks Harold J. Kushner |
| title_fullStr | Heavy traffic analysis of controlled queueing and communication networks Harold J. Kushner |
| title_full_unstemmed | Heavy traffic analysis of controlled queueing and communication networks Harold J. Kushner |
| title_short | Heavy traffic analysis of controlled queueing and communication networks |
| title_sort | heavy traffic analysis of controlled queueing and communication networks |
| topic | Warteschlangentheorie - Stochastische Differentialgleichung Queuing theory Stochastische Differentialgleichung (DE-588)4057621-8 gnd Warteschlangentheorie (DE-588)4255044-0 gnd |
| topic_facet | Warteschlangentheorie - Stochastische Differentialgleichung Queuing theory Stochastische Differentialgleichung Warteschlangentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013176446&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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