Palm probabilities and stationary queues:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; Nw York ; London ; Paris ; Tokyo
Springer-Verlag
[1987]
|
| Series: | Lecture notes in statistics
41 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 106 Seiten Illustrationen |
| ISBN: | 9780387965147 3540965149 0387965149 |
Staff View
MARC
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| 100 | 1 | |a Baccelli, François |d 1954- |0 (DE-588)171962206 |4 aut | |
| 245 | 1 | 0 | |a Palm probabilities and stationary queues |c François Baccelli ; Pierre Brémaud |
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| 490 | 1 | |a Lecture notes in statistics |v 41 | |
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| 650 | 4 | |a Queuing theory | |
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Record in the Search Index
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|---|---|
| adam_text | TABLES OF COMTEMTS
PART 1. Stationary point processes and Palm probabilities 1
1. Stationary marked point processes 2
1.1. The canonical space of point processes onIR
1.2. Stationary point processes
1.3. Stationary marked point processes
1.4. Two properties of stationary point processes
2. Intensity 7
2.1. Intensity of a stationary point process
2.2. Intensity measure of a stationary marked point process
3. Palm probability 8
3.1. Mecke s definition
3.2. Invariance of the Palm probability
3.3. Campbell s formula
3.1. The exchange formula (or cycle formula) and Wald s equality
4. From Palm probability to stationary probability 13
1.1. The inversion formula
4.2. Feller s paradox
4.3. The mean value formulae
4.4. The inverse construction
5. Examples 18
5.1. Palm probability of a superposition of independent point processes
5.2. Palm probability associated with selected marks
5.3. Palm probability of selected transitions of a Markov chain
6. Local aspects of Palm probability 21
6.1. Korolyuk and Dobrushin s infinitesimal estimates
6.2. Conditioning at a point
7. Characterization of Poisson processes 23
7.1. Predictable o fields
7.2. Stochastic intensity and Radon Nikodym derivatives
7.3. Palm view at Watanabe s characterization theorem
8. Ergodiclty of point processes 27
8.1. Invariant events
8.2. Ergodicity under the stationary probability and its Palm probability
8.3. The cross ergodic theorem
References for Part 1 : Palm probabilities 31
VI
PABT 2. Stationary queueulng sy3ta»3 33
1. The G/G/1/» queue : construction of the customer stationary state 34
1.1. Loynes1 problem
1.2. Existence of a finite stationary load
1.3. Uniqueness of the stationary load
1.4. Construction points
1.5. Initial workload and long term behaviour
2. Formulae for the G/G/1/« queue 40
2.1. Construction of the time stationary workload
2.2. Little1 s formulae : the FIFO case
2.3. Probability of emptiness
2.4. Takacs formulae
3. The G/G/s/ ° queue 43
3.1. The ordered workload vector
3.2. Existence of a finite stationary workload vector
3.3. Construction points
3.4. The busy cycle formulae
4. The G/G/1/0 queue 48
4.1. Definition and examples
4.2. Construction of an enriched probability space
4.3. Construction of a stationary solution
5. Other queueing systems 54
5.1. The G/G/» pure delay system
5.2. The G/G/1/» queue in random environment
5.3. Priorities in G/G/1/° : the vector of residual service times
5.4. Optimality properties of the SPRT rule
6. The Bedienungssysteme 62
6.1. The mechanism and the input
6.2. A heuristic description of the dynamics
6.3. The initial generalized state
6.4. The evolution
6.5. Examples
7. The insensitivlty balance equations 69
7.1. Stability and regularity assumptions
7.2. Insensitivity balance equations
7.3. Examples
7.4. Assumption on the input
7.5. Two immediate consequences of the insensitivity balance equations
VII
8. The Insensitivity theorem 73
8.1. The Palm version
8.2.From Palm to stationary
8.3.The stationary version and Hatthes product form
9. Insensitivity balance equations are necessary for Insensitivity 77
9.1. The converse theorem
9.2. The method of stages
9.3. Proof of the converse theorem
9.1. Example
10. Polsson streams 84
10.1. Privileged transitions
10.2. Sufficient conditions for Poissonian streams
Appendix 86
1. Change of scale
2. Proof of insensitivity
3. The transition marks
H. Proof of (8.3.5)
5. Proof of (9.1.3)
6. Proof of the converse theorem in the general case
References for part 2: Stationary queueing systems 95
Bibliography 100
|
| any_adam_object | 1 |
| author | Baccelli, François 1954- Brémaud, Pierre |
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| author_facet | Baccelli, François 1954- Brémaud, Pierre |
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| author_sort | Baccelli, François 1954- |
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| dewey-full | 519.2/32 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/32 |
| dewey-search | 519.2/32 |
| dewey-sort | 3519.2 232 |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV000656468 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:17:18Z |
| institution | BVB |
| isbn | 9780387965147 3540965149 0387965149 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000409375 |
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| physical | VII, 106 Seiten Illustrationen |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Springer-Verlag |
| record_format | marc |
| series | Lecture notes in statistics |
| series2 | Lecture notes in statistics |
| spelling | Baccelli, François 1954- (DE-588)171962206 aut Palm probabilities and stationary queues François Baccelli ; Pierre Brémaud Berlin ; Heidelberg ; Nw York ; London ; Paris ; Tokyo Springer-Verlag [1987] © 1987 VII, 106 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics 41 Point processes Queuing theory Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf Punktprozess (DE-588)4138173-7 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Punktprozess (DE-588)4138173-7 s Warteschlangentheorie (DE-588)4255044-0 s Zeitreihenanalyse (DE-588)4067486-1 s DE-604 Brémaud, Pierre (DE-588)1060028131 aut Erscheint auch als Online-Ausgabe 978-1-4615-7561-0 Lecture notes in statistics 41 (DE-604)BV002447846 41 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000409375&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baccelli, François 1954- Brémaud, Pierre Palm probabilities and stationary queues Lecture notes in statistics Point processes Queuing theory Warteschlangentheorie (DE-588)4255044-0 gnd Punktprozess (DE-588)4138173-7 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4255044-0 (DE-588)4138173-7 (DE-588)4067486-1 |
| title | Palm probabilities and stationary queues |
| title_auth | Palm probabilities and stationary queues |
| title_exact_search | Palm probabilities and stationary queues |
| title_full | Palm probabilities and stationary queues François Baccelli ; Pierre Brémaud |
| title_fullStr | Palm probabilities and stationary queues François Baccelli ; Pierre Brémaud |
| title_full_unstemmed | Palm probabilities and stationary queues François Baccelli ; Pierre Brémaud |
| title_short | Palm probabilities and stationary queues |
| title_sort | palm probabilities and stationary queues |
| topic | Point processes Queuing theory Warteschlangentheorie (DE-588)4255044-0 gnd Punktprozess (DE-588)4138173-7 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Point processes Queuing theory Warteschlangentheorie Punktprozess Zeitreihenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000409375&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002447846 |
| work_keys_str_mv | AT baccellifrancois palmprobabilitiesandstationaryqueues AT bremaudpierre palmprobabilitiesandstationaryqueues |