Fundamentals of queueing networks: performance, asymptotics, and optimization
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York ; Berlin ; Heidelberg
Springer
2001
|
| Schriftenreihe: | Applications of mathematics
46 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | xvi, 405 Seiten Diagramme 24 cm |
| ISBN: | 0387951660 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV013902984 | ||
| 003 | DE-604 | ||
| 005 | 20231013 | ||
| 007 | t | ||
| 008 | 010828s2001 gw |||| |||| 00||| eng d | ||
| 016 | 7 | |a 962216038 |2 DE-101 | |
| 020 | |a 0387951660 |9 0-387-95166-0 | ||
| 035 | |a (OCoLC)248546792 | ||
| 035 | |a (DE-599)BVBBV013902984 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-739 |a DE-703 |a DE-29T |a DE-824 |a DE-91 |a DE-521 |a DE-20 |a DE-634 |a DE-83 |a DE-11 | ||
| 050 | 0 | |a QA274.8.C44 2001 | |
| 082 | 0 | |a 519.8/2 21 | |
| 082 | 0 | |a 519.82 | |
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 084 | |a 27 |2 sdnb | ||
| 084 | |a 60K20 |2 msc | ||
| 084 | |a MAT 608f |2 stub | ||
| 084 | |a 90B15 |2 msc | ||
| 100 | 1 | |a Chen, Hong |d 1922-2002 |0 (DE-588)1020678151 |4 aut | |
| 245 | 1 | 0 | |a Fundamentals of queueing networks |b performance, asymptotics, and optimization |c Hong Chen ; David D. Yao |
| 264 | 1 | |a New York ; Berlin ; Heidelberg |b Springer |c 2001 | |
| 300 | |a xvi, 405 Seiten |b Diagramme |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applications of mathematics |v 46 | |
| 500 | |a Literaturangaben | ||
| 650 | 4 | |a Warteschlangentheorie | |
| 650 | 4 | |a Queuing theory | |
| 650 | 4 | |a Stochastic analysis | |
| 650 | 0 | 7 | |a Warteschlangentheorie |0 (DE-588)4255044-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastik |0 (DE-588)4121729-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Netzwerk |0 (DE-588)4171529-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Netzwerk |0 (DE-588)4171529-9 |D s |
| 689 | 0 | 1 | |a Stochastik |0 (DE-588)4121729-9 |D s |
| 689 | 0 | 2 | |a Warteschlangentheorie |0 (DE-588)4255044-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Yao, David D. |d 1950- |0 (DE-588)12312140X |4 aut | |
| 830 | 0 | |a Applications of mathematics |v 46 |w (DE-604)BV000895226 |9 46 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009514415&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009514415 | ||
Datensatz im Suchindex
| _version_ | 1804128747705597952 |
|---|---|
| adam_text | Contents
Preface vii
List of Figures xv
List of Tables xvii
1 Birth—Death Queues 1
1.1 Basics 1
1.2 Time Reversibility 4
1.3 Stochastic Orders 8
1.4 Notes 11
1.5 Exercises 11
References 13
2 Jackson Networks 15
2.1 Open Network 16
2.2 Closed Network 19
2.3 Semiopen Network 21
2.4 Throughput Function 23
2.5 Throughput Computation 25
2.5.1 Convolution Algorithm 26
2.5.2 Mean Value Analysis 27
2.6 Time Reversal 28
x Contents
2.7 Notes 32
2.8 Exercises 33
References 35
3 Stochastic Comparisons 37
3.1 Monotonicity 38
3.1.1 PF2 Property 38
3.1.2 Likelihood Ratio Ordering 39
3.1.3 Shifted Likelihood Ratio Ordering 42
3.2 Concavity and Convexity 46
3.3 Multiple Servers 49
3.4 Resource Sharing 52
3.4.1 Aggregation of Servers 52
3.4.2 Aggregation of Nodes 53
3.5 Arrangement and Majorization 56
3.6 Notes 61
3.7 Exercises 63
References 65
4 Kelly Networks 69
4.1 Quasi Reversible Queues 70
4.2 Symmetric Queues 76
4.2.1 Phase Type Distributions and Processes 76
4.2.2 Multiclass M/PH/1 Queue 77
4.3 A Multiclass Network 81
4.4 Poisson Flows 87
4.5 Arrival Theorems 89
4.6 Notes 91
4.7 Exercises 93
References 95
5 Technical Desiderata 97
5.1 Convergence and Limits 98
5.2 Some Useful Theorems 100
5.3 Brownian Motion 102
5.4 Two Fundamental Processes 106
5.5 Limit Theorems for the Two Fundamental Processes .... 108
5.5.1 Functional Strong Law of Large Numbers 109
5.5.2 Functional Central Limit Theorem 110
5.5.3 Functional Law of the Iterated Logarithm Ill
5.5.4 Functional Strong Approximation 112
5.6 Exponential Rate of Convergence 114
Contents xi
5.7 Notes 116
5.8 Exercises 117
References 123
6 Single Station Queues 125
6.1 Queue Length and Workload Processes 126
6.2 One Dimensional Reflection Mapping 127
6.3 Fluid Limit (FSLLN) 135
6.4 Diffusion Limit (FCLT) 138
6.5 Approximating the G/G/l Queue 142
6.6 Functional Law of the Iterated Logarithm 144
6.7 Strong Approximation 146
6.8 Exponential Rate of Convergence 151
6.9 Notes 153
6.10 Exercises 154
References 157
7 Generalized Jackson Networks 159
7.1 The Queueing Network Model 160
7.2 Oblique Reflection Mapping 164
7.3 A Homogeneous Fluid Network 167
7.4 A Reflected Brownian Motion 172
7.5 Approximating the Network 175
7.6 Functional Law of the Iterated Logarithm 179
7.7 Strong Approximation 183
7.8 Fluid Limit (FSLLN) 186
7.9 Diffusion Limit (FCLT) 188
7.10 Closed Networks 196
7.10.1 Reflection Mapping, Fluid Model, and RBM .... 196
7.10.2 Approximating a Generalized Closed Network .... 200
7.10.3 Fluid Limit (FSLLN) 201
7.10.4 Diffusion Limit (FCLT) 202
7.11 Notes 204
7.12 Exercises 206
References 213
8 A Two Station Multiclass Network 215
8.1 Model Description and Motivation 215
8.2 A Fluid Model with Priorities 220
8.3 Stability 227
8.4 Fluid Limit 233
8.5 Diffusion Limit 236
xii Contents
8.6 More Examples 243
8.7 Notes 247
8.8 Exercises 250
References 255
9 Feedforward Networks 259
9.1 The Single Station Model 260
9.2 FLIL: The Single Station Case 263
9.3 Strong Approximation: The Single Station Case 267
9.4 The Feedforward Network Model 274
9.4.1 Primitive Data and Assumptions 274
9.4.2 Performance Measures and Dynamics 277
9.5 FLIL: The Network Case 278
9.6 Strong Approximation: The Network Case 279
9.7 Performance Analysis and Approximations 285
9.8 Numerical Examples 287
9.8.1 A Single Station with Two Job Classes 287
9.8.2 Two Stations in Tandem 289
9.9 Notes 291
9.10 Exercises 294
References 297
10 Brownian Approximations 299
10.1 The Queueing Network Model 300
10.1.1 Notation and Conventions 300
10.1.2 The Primitive Processes 302
10.1.3 The Derived Processes 303
10.2 Two Moment Characterization of Primitive Processes . . . 305
10.3 The SRBM Approximation 308
10.4 Discussions and Variations 313
10.4.1 Issues Surrounding the SRBM 313
10.4.2 Kumar Seidman Network 315
10.4.3 State Space Collapse 316
10.5 Stationary Distribution of the SRBM 318
10.6 Special Cases and Numerical Results 320
10.6.1 A Single Class Queue with Breakdown 320
10.6.2 A Variation of the Bramson Network 321
10.6.3 A More Complex Multiclass Network 325
10.7 Notes 327
10.8 Exercises 331
References 333
Contents xiii
11 Conservation Laws 337
11.1 Polymatroid 338
11.1.1 Definitions and Properties 338
11.1.2 Optimization 340
11.2 Conservation Laws 342
11.2.1 Polymatroid Structure 342
11.2.2 Examples 344
11.2.3 Optimal Scheduling 347
11.3 Generalized Conservation Laws 349
11.3.1 Definition 349
11.3.2 Examples 351
11.4 Extended Polymatroid 353
11.4.1 Equivalent Definitions 353
11.4.2 Connections to Sub/Supermodularity 355
11.5 Optimization over EP 360
11.6 Notes 364
11.7 Exercises 366
References 369
12 Scheduling of Fluid Networks 375
12.1 Problem Formulation and Global Optimality 375
12.2 The Myopic Procedure via LP 378
12.3 Properties of the Myopic Procedure 380
12.3.1 Termination Rules 380
12.3.2 Stability and Clearing Time 382
12.4 The Single Station Model 385
12.4.1 Description of the Solution Procedure 385
12.4.2 Summary of the Algorithm 388
12.4.3 Remarks 390
12.5 Proof of Global Optimality: Single Station Model 391
12.6 Notes 395
12.7 Exercises 396
References 399
Index 401
|
| any_adam_object | 1 |
| author | Chen, Hong 1922-2002 Yao, David D. 1950- |
| author_GND | (DE-588)1020678151 (DE-588)12312140X |
| author_facet | Chen, Hong 1922-2002 Yao, David D. 1950- |
| author_role | aut aut |
| author_sort | Chen, Hong 1922-2002 |
| author_variant | h c hc d d y dd ddy |
| building | Verbundindex |
| bvnumber | BV013902984 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.8.C44 2001 |
| callnumber-search | QA274.8.C44 2001 |
| callnumber-sort | QA 3274.8 C44 42001 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 |
| classification_tum | MAT 608f |
| ctrlnum | (OCoLC)248546792 (DE-599)BVBBV013902984 |
| dewey-full | 519.8/221 519.82 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.8/2 21 519.82 |
| dewey-search | 519.8/2 21 519.82 |
| dewey-sort | 3519.8 12 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02097nam a2200553 cb4500</leader><controlfield tag="001">BV013902984</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20231013 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">010828s2001 gw |||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">962216038</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387951660</subfield><subfield code="9">0-387-95166-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)248546792</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV013902984</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-739</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-521</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA274.8.C44 2001</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.8/2 21</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.82</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 820</subfield><subfield code="0">(DE-625)143258:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">27</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60K20</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 608f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">90B15</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Chen, Hong</subfield><subfield code="d">1922-2002</subfield><subfield code="0">(DE-588)1020678151</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Fundamentals of queueing networks</subfield><subfield code="b">performance, asymptotics, and optimization</subfield><subfield code="c">Hong Chen ; David D. Yao</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York ; Berlin ; Heidelberg</subfield><subfield code="b">Springer</subfield><subfield code="c">2001</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xvi, 405 Seiten</subfield><subfield code="b">Diagramme</subfield><subfield code="c">24 cm</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Applications of mathematics</subfield><subfield code="v">46</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturangaben</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Warteschlangentheorie</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Queuing theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stochastic analysis</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Warteschlangentheorie</subfield><subfield code="0">(DE-588)4255044-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastik</subfield><subfield code="0">(DE-588)4121729-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Netzwerk</subfield><subfield code="0">(DE-588)4171529-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Netzwerk</subfield><subfield code="0">(DE-588)4171529-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Stochastik</subfield><subfield code="0">(DE-588)4121729-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Warteschlangentheorie</subfield><subfield code="0">(DE-588)4255044-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Yao, David D.</subfield><subfield code="d">1950-</subfield><subfield code="0">(DE-588)12312140X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Applications of mathematics</subfield><subfield code="v">46</subfield><subfield code="w">(DE-604)BV000895226</subfield><subfield code="9">46</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009514415&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009514415</subfield></datafield></record></collection> |
| id | DE-604.BV013902984 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:54:10Z |
| institution | BVB |
| isbn | 0387951660 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009514415 |
| oclc_num | 248546792 |
| open_access_boolean | |
| owner | DE-739 DE-703 DE-29T DE-824 DE-91 DE-BY-TUM DE-521 DE-20 DE-634 DE-83 DE-11 |
| owner_facet | DE-739 DE-703 DE-29T DE-824 DE-91 DE-BY-TUM DE-521 DE-20 DE-634 DE-83 DE-11 |
| physical | xvi, 405 Seiten Diagramme 24 cm |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series | Applications of mathematics |
| series2 | Applications of mathematics |
| spelling | Chen, Hong 1922-2002 (DE-588)1020678151 aut Fundamentals of queueing networks performance, asymptotics, and optimization Hong Chen ; David D. Yao New York ; Berlin ; Heidelberg Springer 2001 xvi, 405 Seiten Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 46 Literaturangaben Warteschlangentheorie Queuing theory Stochastic analysis Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf Netzwerk (DE-588)4171529-9 gnd rswk-swf Netzwerk (DE-588)4171529-9 s Stochastik (DE-588)4121729-9 s Warteschlangentheorie (DE-588)4255044-0 s DE-604 Yao, David D. 1950- (DE-588)12312140X aut Applications of mathematics 46 (DE-604)BV000895226 46 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009514415&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chen, Hong 1922-2002 Yao, David D. 1950- Fundamentals of queueing networks performance, asymptotics, and optimization Applications of mathematics Warteschlangentheorie Queuing theory Stochastic analysis Warteschlangentheorie (DE-588)4255044-0 gnd Stochastik (DE-588)4121729-9 gnd Netzwerk (DE-588)4171529-9 gnd |
| subject_GND | (DE-588)4255044-0 (DE-588)4121729-9 (DE-588)4171529-9 |
| title | Fundamentals of queueing networks performance, asymptotics, and optimization |
| title_auth | Fundamentals of queueing networks performance, asymptotics, and optimization |
| title_exact_search | Fundamentals of queueing networks performance, asymptotics, and optimization |
| title_full | Fundamentals of queueing networks performance, asymptotics, and optimization Hong Chen ; David D. Yao |
| title_fullStr | Fundamentals of queueing networks performance, asymptotics, and optimization Hong Chen ; David D. Yao |
| title_full_unstemmed | Fundamentals of queueing networks performance, asymptotics, and optimization Hong Chen ; David D. Yao |
| title_short | Fundamentals of queueing networks |
| title_sort | fundamentals of queueing networks performance asymptotics and optimization |
| title_sub | performance, asymptotics, and optimization |
| topic | Warteschlangentheorie Queuing theory Stochastic analysis Warteschlangentheorie (DE-588)4255044-0 gnd Stochastik (DE-588)4121729-9 gnd Netzwerk (DE-588)4171529-9 gnd |
| topic_facet | Warteschlangentheorie Queuing theory Stochastic analysis Stochastik Netzwerk |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009514415&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000895226 |
| work_keys_str_mv | AT chenhong fundamentalsofqueueingnetworksperformanceasymptoticsandoptimization AT yaodavidd fundamentalsofqueueingnetworksperformanceasymptoticsandoptimization |