Probabilistic modelling:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1998
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| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Publisher description Table of contents Inhaltsverzeichnis |
| Physical Description: | X, 223 S. Ill. |
| ISBN: | 0521585112 0521585309 |
Staff View
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| 100 | 1 | |a Mitrani, Isi |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Probabilistic modelling |c Isi Mitrani |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1998 | |
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| 650 | 7 | |a Stochastische modellen |2 gtt | |
| 650 | 7 | |a Waarschijnlijkheidstheorie |2 gtt | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Probabilities | |
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| adam_text | Contents
Preface page ix
1 Introduction to probability theory 1
1.1 Sample points, events and probabilities 1
1.1.1 An algebra of events 3
1.1.2 Probabilities 4
1.1.3 Conditional probability 7
1.2 Random variables 10
1.2.1 Distribution functions 11
1.2.2 Probability density functions 13
1.2.3 Joint distributions 15
1.2.4 Largest and smallest 18
1.3 Expectation and other moments 20
1.3.1 Properties of expectation 23
1.3.2 Variance and covariance 24
1.4 Bernoulli trials and related random variables 28
1.4.1 The geometric distribution 28
1.4.2 The binomial distribution 31
1.5 Sums, transforms and limits 36
1.5.1 Generating functions 37
1.5.2 Laplace transforms and characteristic functions 39
1.5.3 The normal distribution and central limit theorem 41
1.6 Literature 46
2 Arrivals and services 47
2.1 Renewal processes 47
2.1.1 Forward and backward renewal times 50
2.1.2 The paradox of residual life 53
2.2 The exponential distribution and its properties 55
v
vi Contents
2.2.1 First and last 56
2.3 The Poisson process 59
2.3.1 Properties of the Poisson process 61
2.3.2 Arrivals during a random interval 67
2.4 Application: ALOHA and CSMA 69
2.5 Literature 73
3 Queueing systems: average performance 74
3.1 Little s theorem and applications 75
3.1.1 Utilization and response time laws 77
3.2 The single class M/G/l queue 81
3.2.1 Busy periods 86
3.2.2 The M/M/l queue 88
3.3 Different scheduling policies 92
3.3.1 The Processor Sharing policy 94
3.3.2 Symmetric policies and multiclass queues 96
3.3.3 Which policy is better? 98
3.4 Priority scheduling 99
3.4.1 Preemptive resume priorities 104
3.4.2 Averaging and lumping job types 105
3.5 Optimal scheduling policies 107
3.5.1 A conservation law for waiting times 108
3.5.2 The c/p rule 110
3.5.3 Optimization with preemptions 112
3.5.4 Characterization of achievable performance 116
3.6 Literature 119
4 Queueing networks 122
4.1 Open networks 124
4.1.1 Traffic equations 125
4.1.2 Performance measures 128
4.2 Closed networks 136
4.2.1 Mean value analysis 138
4.3 Multiclass networks 146
4.3.1 Closed multiclass networks 150
4.4 Literature 154
5 Markov chains and processes 156
5.1 Markov chains 157
5.1.1 Steady state 161
5.2 A Markov chain embedded in the M/G/l model 168
5.3 Markov processes 172
Contents vii
5.3.1 Transient behaviour 178
5.3.2 Steady state 180
5.4 First passages and absorptions 184
5.5 Birth and Death queueing models 186
5.5.1 The M/M/n model 188
5.5.2 The M/M/n/n and M/M/oo systems 192
5.5.3 The M/M/l/N queue 194
5.5.4 The M/M/n/ /K model 195
5.6 Literature 199
6 Queues in Markovian environments 201
6.1 Quasi Birth and Death models 202
6.1.1 The MMPP/M/1 queue 204
6.1.2 A multiserver queue with breakdowns and repairs 205
6.1.3 Manufacturing blocking 207
6.1.4 Phase type distributions 208
6.2 Solution methods 210
6.2.1 Spectral expansion method 211
6.2.2 Matrix geometric solution 215
6.3 Generalizations 216
6.4 Literature 219
Index 221
|
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| discipline | Informatik Mathematik Wirtschaftswissenschaften |
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| language | English |
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| spelling | Mitrani, Isi Verfasser aut Probabilistic modelling Isi Mitrani 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1998 X, 223 S. Ill. txt rdacontent n rdamedia nc rdacarrier Stochastische modellen gtt Waarschijnlijkheidstheorie gtt Mathematisches Modell Probabilities Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 s DE-604 Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Mathematisches Modell (DE-588)4114528-8 s DE-188 http://www.loc.gov/catdir/description/cam028/97026099.html Publisher description http://www.loc.gov/catdir/toc/cam027/97026099.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008210665&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mitrani, Isi Probabilistic modelling Stochastische modellen gtt Waarschijnlijkheidstheorie gtt Mathematisches Modell Probabilities Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4079013-7 (DE-588)4057633-4 |
| title | Probabilistic modelling |
| title_auth | Probabilistic modelling |
| title_exact_search | Probabilistic modelling |
| title_full | Probabilistic modelling Isi Mitrani |
| title_fullStr | Probabilistic modelling Isi Mitrani |
| title_full_unstemmed | Probabilistic modelling Isi Mitrani |
| title_short | Probabilistic modelling |
| title_sort | probabilistic modelling |
| topic | Stochastische modellen gtt Waarschijnlijkheidstheorie gtt Mathematisches Modell Probabilities Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| topic_facet | Stochastische modellen Waarschijnlijkheidstheorie Mathematisches Modell Probabilities Mathematical models Wahrscheinlichkeitstheorie Stochastisches Modell |
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