Stability of queueing networks: École d'Été de Probabilités de Saint-Flour XXXVI - 2006
Queueing networks constitute a large family of stochastic models, involving jobs that enter a network, compete for service, and eventually leave the network upon completion of service. Since the early 1990s, substantial attention has been devoted to the question of when such networks are stable. Thi...
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
2008
|
| Schriftenreihe: | Lecture notes in mathematics
1950 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Queueing networks constitute a large family of stochastic models, involving jobs that enter a network, compete for service, and eventually leave the network upon completion of service. Since the early 1990s, substantial attention has been devoted to the question of when such networks are stable. This volume presents a summary of such work. Emphasis is placed on the use of fluid models in showing stability, and on examples of queueing networks that are unstable even when the arrival rate is less than the service rate. The material of this volume is based on a series of nine lectures given at the Saint-Flour Probability Summer School 2006. Lectures were also given by Alice Guionnet and Steffen Lauritzen. |
| Beschreibung: | Literaturverz. S. 175 - 179 |
| Beschreibung: | VIII, 190 Seiten Diagramme 235 mm x 155 mm |
| ISBN: | 9783540688952 |
Internformat
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| 100 | 1 | |a Bramson, Maury |d 1951- |0 (DE-588)136007945 |4 aut | |
| 245 | 1 | 0 | |a Stability of queueing networks |b École d'Été de Probabilités de Saint-Flour XXXVI - 2006 |c Maury Bramson |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c 2008 | |
| 300 | |a VIII, 190 Seiten |b Diagramme |c 235 mm x 155 mm | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1950 | |
| 500 | |a Literaturverz. S. 175 - 179 | ||
| 520 | 3 | |a Queueing networks constitute a large family of stochastic models, involving jobs that enter a network, compete for service, and eventually leave the network upon completion of service. Since the early 1990s, substantial attention has been devoted to the question of when such networks are stable. This volume presents a summary of such work. Emphasis is placed on the use of fluid models in showing stability, and on examples of queueing networks that are unstable even when the arrival rate is less than the service rate. The material of this volume is based on a series of nine lectures given at the Saint-Flour Probability Summer School 2006. Lectures were also given by Alice Guionnet and Steffen Lauritzen. | |
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Datensatz im Suchindex
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| adam_text | Contents
1
Introduction
............................................... 1
1.1 The
M/M/l Queue
...................................... 2
1.2
Basic Concepts
of Queueing
Networks
...................... 3
1.3
Queueing Network Equations
and Fluid Models.............
11
1.4
Outline of Lectures
...................................... 14
2
The Classical Networks
.................................... 17
2.1
Main Results
........................................... 18
2.2
Stationarity and Reversibility
............................. 23
2.3
Homogeneous Nodes of Kelly Type
........................ 27
2.4
Symmetric Nodes
........................................ 32
2.5
Quasi-Reversibility
...................................... 39
3
Instability of
Subcriticai
Queueing Networks
.............. 53
3.1
Basic Examples of Unstable Networks
...................... 54
3.2
Examples of Unstable FIFO Networks
...................... 60
3.3
Other Examples of Unstable Networks
..................... 71
4
Stability of Queueing Networks
............................ 77
4.1
Some Markov Process Background
......................... 80
4.2
Results for Bounded Sets
................................. 92
4.3
Fluid Models and Fluid Limits
............................100
4.4
Demonstration of Stability
................................116
4.5
Appendix
..............................................127
5
Applications and Some Further Theory
....................139
5.1
Single Class Networks
....................................140
5.2
FBFS and LBFS Reentrant Lines
..........................144
5.3
FIFO Networks of Kelly Type
.............................147
5.4
Global Stability
.........................................155
5.5
Relationship Between QN and
FM
Stability
.................163
VIII Contents
References
.....................................................175
Index
..........................................................181
List of Participants
............................................185
List of Short Lectures
.........................................189
|
| adam_txt |
Contents
1
Introduction
. 1
1.1 The
M/M/l Queue
. 2
1.2
Basic Concepts
of Queueing
Networks
. 3
1.3
Queueing Network Equations
and Fluid Models.
11
1.4
Outline of Lectures
. 14
2
The Classical Networks
. 17
2.1
Main Results
. 18
2.2
Stationarity and Reversibility
. 23
2.3
Homogeneous Nodes of Kelly Type
. 27
2.4
Symmetric Nodes
. 32
2.5
Quasi-Reversibility
. 39
3
Instability of
Subcriticai
Queueing Networks
. 53
3.1
Basic Examples of Unstable Networks
. 54
3.2
Examples of Unstable FIFO Networks
. 60
3.3
Other Examples of Unstable Networks
. 71
4
Stability of Queueing Networks
. 77
4.1
Some Markov Process Background
. 80
4.2
Results for Bounded Sets
. 92
4.3
Fluid Models and Fluid Limits
.100
4.4
Demonstration of Stability
.116
4.5
Appendix
.127
5
Applications and Some Further Theory
.139
5.1
Single Class Networks
.140
5.2
FBFS and LBFS Reentrant Lines
.144
5.3
FIFO Networks of Kelly Type
.147
5.4
Global Stability
.155
5.5
Relationship Between QN and
FM
Stability
.163
VIII Contents
References
.175
Index
.181
List of Participants
.185
List of Short Lectures
.189 |
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| id | DE-604.BV035001853 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:40:45Z |
| indexdate | 2024-07-09T21:19:55Z |
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| isbn | 9783540688952 |
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| spelling | Bramson, Maury 1951- (DE-588)136007945 aut Stability of queueing networks École d'Été de Probabilités de Saint-Flour XXXVI - 2006 Maury Bramson Berlin ; Heidelberg Springer 2008 VIII, 190 Seiten Diagramme 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1950 Literaturverz. S. 175 - 179 Queueing networks constitute a large family of stochastic models, involving jobs that enter a network, compete for service, and eventually leave the network upon completion of service. Since the early 1990s, substantial attention has been devoted to the question of when such networks are stable. This volume presents a summary of such work. Emphasis is placed on the use of fluid models in showing stability, and on examples of queueing networks that are unstable even when the arrival rate is less than the service rate. The material of this volume is based on a series of nine lectures given at the Saint-Flour Probability Summer School 2006. Lectures were also given by Alice Guionnet and Steffen Lauritzen. Queuing networks (Data transmission) Congresses Stabilität (DE-588)4056693-6 gnd rswk-swf Warteschlangennetz (DE-588)4225823-6 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2006 Saint-Flour gnd-content Warteschlangennetz (DE-588)4225823-6 s Stabilität (DE-588)4056693-6 s DE-604 Lecture notes in mathematics 1950 (DE-604)BV000676446 1950 Digitalisierung TU Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016671245&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bramson, Maury 1951- Stability of queueing networks École d'Été de Probabilités de Saint-Flour XXXVI - 2006 Lecture notes in mathematics Queuing networks (Data transmission) Congresses Stabilität (DE-588)4056693-6 gnd Warteschlangennetz (DE-588)4225823-6 gnd |
| subject_GND | (DE-588)4056693-6 (DE-588)4225823-6 (DE-588)1071861417 |
| title | Stability of queueing networks École d'Été de Probabilités de Saint-Flour XXXVI - 2006 |
| title_auth | Stability of queueing networks École d'Été de Probabilités de Saint-Flour XXXVI - 2006 |
| title_exact_search | Stability of queueing networks École d'Été de Probabilités de Saint-Flour XXXVI - 2006 |
| title_exact_search_txtP | Stability of queueing networks École d'Été de Probabilités de Saint-Flour XXXVI - 2006 |
| title_full | Stability of queueing networks École d'Été de Probabilités de Saint-Flour XXXVI - 2006 Maury Bramson |
| title_fullStr | Stability of queueing networks École d'Été de Probabilités de Saint-Flour XXXVI - 2006 Maury Bramson |
| title_full_unstemmed | Stability of queueing networks École d'Été de Probabilités de Saint-Flour XXXVI - 2006 Maury Bramson |
| title_short | Stability of queueing networks |
| title_sort | stability of queueing networks ecole d ete de probabilites de saint flour xxxvi 2006 |
| title_sub | École d'Été de Probabilités de Saint-Flour XXXVI - 2006 |
| topic | Queuing networks (Data transmission) Congresses Stabilität (DE-588)4056693-6 gnd Warteschlangennetz (DE-588)4225823-6 gnd |
| topic_facet | Queuing networks (Data transmission) Congresses Stabilität Warteschlangennetz Konferenzschrift 2006 Saint-Flour |
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