Introduction to stochastic networks:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York, [u.a.]
Springer
[1999]
|
| Series: | Applications of mathematics
44 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiv, 300 Seiten |
| ISBN: | 0387987738 |
Staff View
MARC
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| 100 | 1 | |a Serfozo, Richard |4 aut | |
| 245 | 1 | 0 | |a Introduction to stochastic networks |c Richard Serfozo |
| 264 | 1 | |a New York, [u.a.] |b Springer |c [1999] | |
| 264 | 4 | |c © 1999 | |
| 300 | |a xiv, 300 Seiten | ||
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| 490 | 1 | |a Applications of mathematics |v 44 | |
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Record in the Search Index
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Contents
Preface vii
1 Jackson and Whittle Networks 1
1.1 Preliminaries on Networks and Markov Processes 1
1.2 Tandem Network 7
1.3 Definitions of Jackson and Whittle Processes 9
1.4 Properties of Service and Routing Rates 12
1.5 Equilibrium Behavior 14
1.6 Production Maintenance Network 18
1.7 Networks with Special Structures 19
1.8 Properties of Jackson Equilibrium Distributions 20
1.9 Convolutions for Single Server Nodes 24
1.10 Throughputs and Expected Sojourn Times 26
1.11 Algorithms for Performance Parameters 30
1.12 Monte Carlo Estimation of Network Parameters 32
1.13 Properties of Whittle Networks 35
1.14 Exercises 39
1.15 Bibliographical Notes 42
2 Reversible Processes 44
2.1 Reversibility 44
2.2 Time Reversal 47
2.3 Invariant Measures 50
2.4 Construction of Reversible Processes 53
2.5 More Birth Death Processes 55
xii Contents
2.6 Reversible Network Processes 58
2.7 Examples of Reversible Networks 61
2.8 Partition Reversible Processes 64
2.9 Examples of Partition Reversible Processes 68
2.10 Exercises 71
2.11 Bibliographical Notes 73
3 Miscellaneous Networks 74
3.1 Networks with Multiple Types of Units 74
3.2 Kelly Networks: Route dependent Services 79
3.3 BCMP Networks: Class Node Service Dependencies 81
3.4 Networks with Cox and General Service Times 82
3.5 Networks with Constraints 85
3.6 Networks with Blocking and Rerouting 87
3.7 Bottlenecks in Closed Jackson Networks 90
3.8 Modeling Whittle Networks by Locations of the Units 91
3.9 Partially Balanced Networks 93
3.10 Exercises 96
3.11 Bibliographical Notes 97
4 Network Flows and Travel Times 99
4.1 Point Process Notation 99
4.2 Extended Levy Formula for Markov Processes 102
4.3 Poisson Functionals of Markov Processes 104
4.4 Multivariate Compound Poisson Processes 109
4.5 Poisson Flows in Jackson and Whittle Networks 112
4.6 Palm Probabilities for Markov Processes 115
4.7 Sojourn and Travel Times of Markov Processes 120
4.8 Palm Probabilities of Jackson and Whittle Networks 122
4.9 Travel Times on Overtake Free Routes 127
4.10 Exercises 131
4.11 Bibliographical Notes 133
5 Little Laws 135
5.1 Little Laws for Markovian Systems 136
5.2 Little Laws for General Queueing Systems 139
5.3 Preliminary Laws of Large Numbers 141
5.4 Utility Processes 143
5.5 Omnibus Little Laws 145
5.6 Little Laws for Regenerative Systems 149
5.7 Exercises 153
5.8 Bibliographical Notes 153
6 Stationary Systems 155
6.1 Preliminaries on Stationary Processes 155
Contents xiii
6.2 Palm Probabilities 157
6.3 Campbell Mecke Formulas for Palm Probabilities 161
6.4 Little Laws for Stationary Systems 166
6.5 Sojourn Times and Related Functionals 171
6.6 Travel Times for Stochastic Processes 172
6.7 Sojourn and Travel Times in Networks 174
6.8 Exercises 179
6.9 Bibliographical Notes 180
7 Networks with String Transitions 181
7.1 Definition of a String Net 181
7.2 Invariant Measures of String Nets 184
7.3 Traffic Equations, Partial Balance, and Throughputs 187
7.4 String Nets with Unit Vector Transitions 191
7.5 Networks with One Stage Batch Transitions 193
7.6 Networks with Compound Rate String Transitions 195
7.7 Networks with Multiple, Compound Rate String Transitions . . 199
7.8 String Nets with Two Node Batch Transitions 201
7.9 Single Service Station With String Transitions 204
7.10 Bibliographical Notes 205
8 Quasi Reversible Networks and Product Form Distributions 206
8.1 Quasi Reversibility 207
8.2 Network to be Studied 210
8.3 Characterization of Product Form Distributions 212
8.4 Quasi Reversibility and Biased Local Balance 215
8.5 Networks with Reversible Routing 219
8.6 Queueing Networks 221
8.7 Time Reversals and Departure Arrival Reversals 224
8.8 Networks with Multiclass Transitions 225
8.9 Exercises 227
8.10 Bibliographical Notes 228
9 Space Time Poisson Models 230
9.1 Introductory Examples 230
9.2 Laplace Functionals of Point Processes 232
9.3 Transformations of Poisson Processes 233
9.4 Translations, Partitions, and Clusters 238
9.5 Service Systems with No Queueing 242
9.6 Network of M/G/oo Service Stations 246
9.7 Particle Systems 249
9.8 Poisson Convergence of Space Time Processes 255
9.9 Transformations into Large Spaces 257
9.10 Particle Flows in Large Spaces 259
9.11 Exercises 261
xiv Contents
9.12 Bibliographical Notes 263
10 Spatial Queueing Systems 264
10.1 Preliminaries 265
10.2 Stationary Distributions and Ergodicity 269
10.3 Properties of Stationary Distributions and Examples 273
10.4 Throughputs and Expected Sojourn Times 278
10.5 Poisson Flows in Open Systems 281
10.6 Systems with Multiclass Units 284
10.7 Bibliographical Notes 287
References 289
Index 297 |
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| indexdate | 2024-12-05T11:02:20Z |
| institution | BVB |
| isbn | 0387987738 |
| language | German |
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| physical | xiv, 300 Seiten |
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| series2 | Applications of mathematics |
| spelling | Serfozo, Richard aut Introduction to stochastic networks Richard Serfozo New York, [u.a.] Springer [1999] © 1999 xiv, 300 Seiten txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 44 Queuing theory Stochastic analysis Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Warteschlangennetz (DE-588)4225823-6 gnd rswk-swf Warteschlangennetz (DE-588)4225823-6 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4612-1482-3 Applications of mathematics 44 (DE-604)BV000895226 44 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008677676&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Serfozo, Richard Introduction to stochastic networks Applications of mathematics Queuing theory Stochastic analysis Stochastisches Modell (DE-588)4057633-4 gnd Warteschlangennetz (DE-588)4225823-6 gnd |
| subject_GND | (DE-588)4057633-4 (DE-588)4225823-6 |
| title | Introduction to stochastic networks |
| title_auth | Introduction to stochastic networks |
| title_exact_search | Introduction to stochastic networks |
| title_full | Introduction to stochastic networks Richard Serfozo |
| title_fullStr | Introduction to stochastic networks Richard Serfozo |
| title_full_unstemmed | Introduction to stochastic networks Richard Serfozo |
| title_short | Introduction to stochastic networks |
| title_sort | introduction to stochastic networks |
| topic | Queuing theory Stochastic analysis Stochastisches Modell (DE-588)4057633-4 gnd Warteschlangennetz (DE-588)4225823-6 gnd |
| topic_facet | Queuing theory Stochastic analysis Stochastisches Modell Warteschlangennetz |
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