Elements of queueing theory: Palm Martingale calculus and stochastic recurrences
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York
Springer-Verlag
[2003]
|
| Edition: | second edition |
| Series: | Applications of mathematics
26 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIV, 334 Seiten Diagramme |
| ISBN: | 3540660887 9783642085376 9783662116579 |
Staff View
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| 100 | 1 | |a Baccelli, François |d 1954- |0 (DE-588)171962206 |4 aut | |
| 245 | 1 | 0 | |a Elements of queueing theory |b Palm Martingale calculus and stochastic recurrences |c François Baccelli ; Pierre Brémaud |
| 250 | |a second edition | ||
| 264 | 1 | |a Berlin ; Heidelberg ; New York |b Springer-Verlag |c [2003] | |
| 264 | 4 | |c © 2003 | |
| 300 | |a XIV, 334 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applications of mathematics |v 26 | |
| 500 | |a Includes bibliographical references and index | ||
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| 650 | 4 | |a Processus ponctuels | |
| 650 | 7 | |a Stationaire processen |2 gtt | |
| 650 | 7 | |a Wachttijdproblemen |2 gtt | |
| 650 | 4 | |a Queuing theory | |
| 650 | 4 | |a Point processes | |
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Record in the Search Index
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| adam_text |
FRANCOIS BACCELLI PIERRE BREMAUD ELEMENTS OF QUEUEING THEORY PALM
MARTINGALE CALCULUS AND STOCHASTIC RECURRENCES SECOND EDITION SPRINGER
CONTENTS PREFACE V 1. THE PALM CALCULUS OF POINT PROCESSES 1 1.1
STATIONARY MARKED POINT PROCESS 2 1.1.1 THE CANONICAL SPACE OF A POINT
PROCESS 2 1.1.2 STATIONARY POINT PROCESS 3 1.1.3 MARKS OF A POINT
PROCESS 6 1.1.4 TWO PROPERTIES OF STATIONARY POINT PROCESSES 11 1.1.5
INTENSITY OF A STATIONARY POINT PROCESS 12 1.1.6 THE CAMPBELL MEASURE 13
1.2 PALM PROBABILITY 14 1.2.1 THE MATTHES DEFINITION IN TERMS OF
COUNTING 14 1.2.2 INVARIANCE OF PALM PROBABILITY 16 1.2.3 MECKE'S
FORMULA 17 1.2.4 THE INVERSION FORMULA 20 1.3 BASIC FORMULAS OF PALM
CALCULUS 21 1.3.1 THE MEAN-VALUE FORMULAS 21 1.3.2 THE NEVEU EXCHANGE
FORMULA 21 1.3.3 THE MIYAZAWA CONSERVATION PRINCIPLE 23 1.3.4 FORWARD
AND BACKWARD RECURRENCE TIME 24 1.3.5 THE SLIVNYAK INVERSE CONSTRUCTION
25 1.3.6 OTHER INVERSION FORMULAS 27 1.3.7 THE SWISS ARMY FORMULA 28 1.4
EXAMPLES 32 1.4.1 RENEWAL PROCESS 32 1.4.2 SUPERPOSITION OF INDEPENDENT
POINT PROCESSES 33 1.4.3 SELECTED MARKS AND CONDITIONING 35 1.4.4
SELECTED TRANSITIONS OF A STATIONARY MARKOV CHAIN . 38 1.4.5
STATIONARY SEMI-MARKOV PROCESS 39 1.4.6 DELAYED MARKED POINT PROCESS 42
1.5 LOCAL ASPECT OF PALM PROBABILITY 44 1.5.1 THE KOROLYUK AND DOBRUSHIN
INFINITESIMAL ESTIMATES . 44 1.5.2 CONDITIONING AT A POINT 45 1.6
ERGODICITY OF A POINT PROCESS 46 XII CONTENTS 1.6.1 ERGODICITY OF A FLOW
46 1.6.2 INVARIANT EVENT 50 1.6.3 ERGODICITY UNDER THE STATIONARY
PROBABILITY AND UNDER THE PALM PROBABILITY 52 1.6.4 THE CROSS-ERGODIC
THEOREMS 52 1.7 PALM THEORY IN DISCRETE TIME 53 1.8 STOCHASTIC INTENSITY
55 1.8.1 PREDICTABLE PROCESS 55 1.8.2 STOCHASTIC INTENSITY KERNEL 58
1.8.3 STOCHASTIC INTENSITY INTEGRATION FORMULA 60 1.8.4 WATANABE'S
CHARACTERIZATION OF POISSON PROCESSES . 61 1.9 PALM PROBABILITY AND
STOCHASTIC INTENSITY 64 1.9.1 INVARIANCE OF STOCHASTIC INTENSITY 64
1.9.2 THE PAPANGELOU FORMULA 65 1.10 SOLUTIONS TO EXERCISES 69 1.11
BIBLIOGRAPHICAL COMMENTS 73 2. STATIONARITY AND COUPLING 75 2.1
STABILITY OF THE SINGLE SERVER QUEUE 76 2.1.1 THE SINGLE SERVER QUEUE 76
2.1.2 THE LOYNES STABILITY THEOREM 78 2.1.3 CONSTRUCTION POINTS AND
CYCLES 80 2.2 PROOF OF LOYNES' THEOREM 83 2.2.1 REDUCTION TO THE PALM
SETTING 83 2.2.2 CONSTRUCTION OF THE WORKLOAD SEQUENCE 84 2.2.3
UNIQUENESS OF THE STATIONARY WORKLOAD 87 2.2.4 CONSTRUCTION POINTS 89
2.2.5 QUEUEING PROOF OF THE ERGODIC THEOREM 89 2.3 THE MULTISERVER QUEUE
91 2.3.1 ORDERED WORKLOAD VECTOR 91 2.3.2 EXISTENCE OF A FINITE
STATIONARY WORKLOAD 92 2.3.3 THE MAXIMAL SOLUTION 94 2.4 COUPLING 98
2.4.1 COUPLING AND CONVERGENCE IN VARIATION 98 2.4.2 COUPLING IN THE
SINGLE SERVER QUEUE 100 2.5 STOCHASTIC RECURRENCES AND THEIR STATIONARY
REGIMES 104 2.5.1 STOCHASTIC RECURRENCES 104 2.5.2 THE LOYNES THEOREM
FOR STOCHASTIC RECURRENCES 107 2.5.3 EXACT SAMPLING OF MARKOV CHAINS 109
2.5.4 THE BOROVKOV THEORY OF RENOVATING EVENTS 114 2.6 STABILITY OF THE
G/G/1/0 QUEUE 121 2.6.1 COUNTER-EXAMPLES 121 2.6.2 COUPLING IN THE
G/G/1/0 QUEUE 123 2.6.3 ENRICHED PROBABILITY SPACE 124 2.7 THE FLUID
QUEUE 128 CONTENTS XIII 2.7.1 DEPARTURE AND WORKLOAD PROCESSES IN FLUID
QUEUES. . . 128 2.7.2 THE LOYNES THEOREM FOR FLUID QUEUES 131 2.8 OTHER
QUEUEING SYSTEMS 133 2.8.1 THE PURE DELAY QUEUE 133 2.8.2 SERVICE
DISCIPLINES AND RESIDUAL SERVICES 135 2.8.3 SINGLE SERVER QUEUES WITH
VACATIONS 138 2.8.4 SINGLE SERVER QUEUES WITH MUTUAL SERVICE 140 2.9
STABILITY OF QUEUEING NETWORKS VIA COUPLING 141 2.9.1 SINGLE SERVER
QUEUES IN TANDEM 141 2.9.2 KELLY-TYPE NETWORKS 141 2.10 QUEUEING NETWORK
STABILITY VIA RECURRENCE EQUATIONS 145 2.10.1 FINITE CAPACITY QUEUES IN
TANDEM WITH BLOCKING . 145 2.10.2 EXISTENCE OF A STATIONARY SOLUTION
147 2.10.3 UNIQUENESS OF THE STATIONARY SOLUTIONS 151 2.10.4 TANDEM
QUEUES 153 2.11 NON-EXPANSIVE STOCHASTIC RECURRENCES 154 2.11.1 THE
CRANDALL-TARTAR THEOREM 154 2.11.2 MONOTONE-HOMOGENEOUS STOCHASTIC
RECURRENCES 158 2.11.3 THE MONOTONE-HOMOGENEOUS-SEPARABLE FRAMEWORK . .
161 2.11.4 THE SATURATION RULE 165 2.12 SOLUTIONS TO EXERCISES 171 2.13
BIBLIOGRAPHICAL COMMENTS 179 3. FORMULAS 181 3.1 THE LITTLE FORMULA 182
3.1.1 THE ^(-FRAMEWORK FOR STATIONARY QUEUEING SYSTEMS . 182 3.1.2 L =
\W 185 3.1.3 THE LITTLE FORMULA FOR FLUID QUEUES 193 3.2 OTHER
APPLICATIONS OF CAMPBELL'S FORMULA 195 3.2.1 THE FUNCTION SPACE
CAMPBELL-LITTLE-MECKE FORMULA . 195 3.2.2 THE POLLACZEK-KHINCHIN
MEAN-VALUE FORMULAS 195 3.2.3 EXTENSION OF THE H = \G FORMULA 197 3.2.4
THE KLEINROCK CONSERVATION LAW 201 3.2.5 THE KEILSON ASYMPTOTIC
EQUIVALENCE FOR RARE EVENTS . 205 3.3 EVENT AND TIME AVERAGES 211 3.3.1
POISSON ARRIVALS SEE TIME AVERAGES 211 3.3.2 APPLICATIONS OF
PAPANGELOU'S FORMULA 213 3.3.3 MEAN-VALUE ANALYSIS 218 3.4 FORMULAS
DERIVED FROM CONSERVATION EQUATIONS 221 3.4.1 FIRST ORDER EQUIVALENCE
221 3.4.2 THE BRILL AND POSNER FORMULA 228 3.4.3 THE TAKACS FORMULA AND
QUEUES WITH VACATIONS 231 3.4.4 BACKWARD AND FORWARD RECURRENCE TIMES
236 3.5 APPLICATIONS OF THE STOCHASTIC INTENSITY INTEGRATION FORMULA .
237 3.5.1 REMINDER 237 XIV CONTENTS 3.5.2 PRIORITIES IN M/GI/L/OO 238
3.5.3 MEAN-VALUE FORMULA FOR FLUID QUEUES 244 3.6 SOLUTIONS TO EXERCISES
248 3.7 BIBLIOGRAPHICAL COMMENTS 257 4. STOCHASTIC ORDERING OF QUEUES
259 4.1 COMPARISON OF SERVICE DISCIPLINES 261 4.1.1 PARTIAL ORDERINGS
ONR" 261 4.1.2 OPTIMALITY OF SRPT FOR SINGLE SERVER QUEUES 264 4.1.3
OPTIMALITY OF FIFO 266 4.2 COMPARISON OF QUEUES 272 4.2.1 INTEGRAL
STOCHASTIC ORDERINGS 272 4.2.2 ANALYTICAL CHARACTERIZATIONS 274 4.2.3
THE STRASSEN POINTWISE REPRESENTATION THEOREMS 277 4.2.4 COMPARISON OF
STOCHASTIC RECURRENCES 278 4.2.5 BOUNDS BASED ON INTEGRAL ORDERINGS 279
4.2.6 STABILITY OF STOCHASTIC ORDERS BY LIMITS 281 4.2.7 COMPARISON OF
BASIC QUEUES 282 4.2.8 OTHER QUEUEING SYSTEMS 285 4.3 ASSOCIATION
PROPERTIES OF QUEUES 288 4.3.1 ASSOCIATION OF RANDOM VARIABLES 288 4.3.2
BOUNDS BY ASSOCIATION 292 4.4 STOCHASTIC COMPARISON OF TIME-STATIONARY
QUEUES 294 4.4.1 COMPARISON OF POINT PROCESSES 294 4.4.2 COMPARISON
UNDER TIME-STATIONARY PROBABILITIES 300 4.4.3 COMPARISON OF CONTINUOUS
TIME CHARACTERISTICS 304 4.5 SOLUTIONS TO EXERCISES 308 4.6
BIBLIOGRAPHICAL COMMENTS 314 REFERENCES 317 INDEX 329 |
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| id | DE-604.BV013182589 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-23T01:10:11Z |
| institution | BVB |
| isbn | 3540660887 9783642085376 9783662116579 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008981968 |
| oclc_num | 722945034 |
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| physical | XIV, 334 Seiten Diagramme |
| publishDate | 2003 |
| publishDateSearch | 2003 |
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| publisher | Springer-Verlag |
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| series | Applications of mathematics |
| series2 | Applications of mathematics |
| spelling | Baccelli, François 1954- (DE-588)171962206 aut Elements of queueing theory Palm Martingale calculus and stochastic recurrences François Baccelli ; Pierre Brémaud second edition Berlin ; Heidelberg ; New York Springer-Verlag [2003] © 2003 XIV, 334 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 26 Includes bibliographical references and index Files d'attente, Théorie des Processus ponctuels Stationaire processen gtt Wachttijdproblemen gtt Queuing theory Point processes Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 s DE-604 Brémaud, Pierre (DE-588)1060028131 aut Erscheint auch als Online-Ausgabe 978-3-662-11657-9 Applications of mathematics 26 (DE-604)BV000895226 26 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008981968&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baccelli, François 1954- Brémaud, Pierre Elements of queueing theory Palm Martingale calculus and stochastic recurrences Applications of mathematics Files d'attente, Théorie des Processus ponctuels Stationaire processen gtt Wachttijdproblemen gtt Queuing theory Point processes Warteschlangentheorie (DE-588)4255044-0 gnd |
| subject_GND | (DE-588)4255044-0 |
| title | Elements of queueing theory Palm Martingale calculus and stochastic recurrences |
| title_auth | Elements of queueing theory Palm Martingale calculus and stochastic recurrences |
| title_exact_search | Elements of queueing theory Palm Martingale calculus and stochastic recurrences |
| title_full | Elements of queueing theory Palm Martingale calculus and stochastic recurrences François Baccelli ; Pierre Brémaud |
| title_fullStr | Elements of queueing theory Palm Martingale calculus and stochastic recurrences François Baccelli ; Pierre Brémaud |
| title_full_unstemmed | Elements of queueing theory Palm Martingale calculus and stochastic recurrences François Baccelli ; Pierre Brémaud |
| title_short | Elements of queueing theory |
| title_sort | elements of queueing theory palm martingale calculus and stochastic recurrences |
| title_sub | Palm Martingale calculus and stochastic recurrences |
| topic | Files d'attente, Théorie des Processus ponctuels Stationaire processen gtt Wachttijdproblemen gtt Queuing theory Point processes Warteschlangentheorie (DE-588)4255044-0 gnd |
| topic_facet | Files d'attente, Théorie des Processus ponctuels Stationaire processen Wachttijdproblemen Queuing theory Point processes Warteschlangentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008981968&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000895226 |
| work_keys_str_mv | AT baccellifrancois elementsofqueueingtheorypalmmartingalecalculusandstochasticrecurrences AT bremaudpierre elementsofqueueingtheorypalmmartingalecalculusandstochasticrecurrences |