Fundamentals of stochastic networks:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2011
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz.: S. 276 - 279 |
| Physical Description: | XII, 295 S. graph. Darst. |
| ISBN: | 9781118065679 9781118092972 |
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| 245 | 1 | 0 | |a Fundamentals of stochastic networks |c Oliver C. Ibe |
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2011 | |
| 300 | |a XII, 295 S. |b graph. Darst. | ||
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| adam_text | CONTENTS
Preface
xi
Acknowledgments,
xii
1
Basic Concepts in Probability
1
1.1
Introduction,
1
1.2
Random Variables,
1
1.2.1
Distribution Functions,
2
1.2.2
Discrete Random Variables,
3
1.2.3
Continuous Random Variables,
3
1.2.4
Expectations,
4
1.2.5
Moments of Random Variables and the Variance,
4
1.3
Transform Methods,
5
1.3.1
The s-Transform,
5
1.3.2
Moment-Generating Property of the s-Transform,
5
1.3.3
The z-Transform,
6
1.3.4
Moment-Generating Property of the z-Transform,
7
1.4
Covariance and Correlation Coefficient,
8
1.5
Sums of Independent Random Variables,
8
1.6
Random Sum of Random Variables,
9
1.7
Some Probability Distributions,
11
1.7.1
The Bernoulli Distribution,
11
1.7.2
The Binomial Distribution,
12
1.7.3
The Geometric Distribution,
13
1.7.4
The Pascal Distribution,
13
1.7.5
The
Poisson
Distribution,
14
1.7.6
The Exponential Distribution,
14
1.7.7
The
Erlang
Distribution,
15
1.7.8
The Uniform Distribution,
15
1.7.9
The Hyperexponential Distribution,
16
1.7.10
The Coxian Distribution,
17
vi
CONTENTS
1.7.11
The General Phase-Type Distribution,
19
1.7.12
Normal Distribution,
19
1.8
Limit Theorems,
21
1.8.1
Markov Inequality,
21
1.8.2
Chebyshev Inequality,
22
1.8.3
Law of Large Numbers,
22
1.8.4
The Central Limit Theorem,
23
2
Overview of Stochastic Processes
26
2.1
Introduction,
26
2.2
Classification of Stochastic Processes,
27
2.3
Stationary Random Processes,
27
2.3.1
Strict-Sense Stationary Processes,
27
2.3.2
WSS Processes,
28
2.4
Counting Processes,
28
2.5
Independent Increment Processes,
29
2.6
Stationary Increment Process,
29
2.7
Poisson
Processes,
30
2.8
Renewal Processes,
32
2.8.1
The Renewal Equation,
33
2.8.2
The Elementary Renewal Theorem,
34
2.8.3
Random Incidence and Residual Time,
35
2.9
Markov Processes,
37
2.9.1
Discrete-Time Markov Chains,
38
2.9.1.1
State Transition Probability Matrix,
39
2.9.1.2
The
η
-Step
State Transition Probability,
39
2.9.1.3
State Transition Diagrams,
41
2.9.1.4
Classification of States,
42
2.9.1.5
Limiting State Probabilities,
44
2.9.1.6
Doubly Stochastic Matrix,
47
2.9.2
Continuous-Time Markov Chains,
48
2.9.2.1
Birth and Death Processes,
51
2.9.2.2
Local Balance Equations,
54
2.10
Gaussian Processes,
56
3
Elementary Queueing Theory
61
3.1
Introduction,
61
3.2
Description of a Queueing System,
61
3.3
The Kendall Notation,
64
3.4
The Little s Formula,
65
3.5
The M/M/l Queueing System,
66
3.5.1
Stochastic Balance,
69
3.5.2
Total Time and Waiting Time Distributions of the
M/M/l Queueing System,
70
CONTENTS
vii
3.6
Examples of Other M/M Queueing Systems,
71
3.6.1
The M/M/c Queue: The
с
-Server
System,
72
3.6.2
The M/M/l/K Queue: The Single-Server
Finite-Capacity System,
74
3.6.3
The M/M/c/c Queue: The
с
-Server
Loss System,
76
3.6.4
The M/M/1//K Queue: The Single Server Finite
Customer Population System,
77
3.7
M/G/1 Queue,
79
3.7.1
Waiting Time Distribution of the M/G/1 Queue,
81
3.7.2
The M/E^/l Queue,
84
3.7.3
The M/D/l Queue,
85
3.7.4
The M/M/l Queue,
86
3.7.5
The M/Ht/l Queue,
86
4
Advanced Queueing Theory
93
4.1
Introduction,
93
4.2
M/G/1 Queue with Priority,
93
4.2.1,
Nonpreemptive Priority,
94
4.2.2
Preemptive-Resume Priority,
96
4.2.3
Preemptive-Repeat Priority,
97
4.3
G/M/l Queue,
99
4.3.1
The E^/M/l Queue,
103
4.3.2
The D/M/l Queue,
104
4.3.3
The
Њ/М
/l
Queue,
104
4.4
The G/G/l Queue,
105
4.4.1
Lindley s Integral Equation,
106
4.4.2
Laplace Transform of Fw(w),
107
4.4.3
Bounds of Mean Waiting Time,
109
4.5
Special Queueing Systems,
109
4.5.1
M/M/l Vacation Queueing Systems with
Exceptional First Vacation,
109
4.5.2
M/M/l Threshold Queueing Systems,
115
5
Queueing Networks
124
5.1
Introduction,
124
5.2
Burke s Output Theorem and Tandem Queues,
126
5.3
Jackson or Open Queueing Networks,
128
5.4
Closed Queueing Networks,
130
5.5
BCMP Networks,
132
5.5.1
Routing Behavior,
132
5.5.2
Service Time Distributions,
133
5.5.3
Service Disciplines,
134
5.5.4
The BCMP Theorem,
134
liii
CONTENTS
5.6
Algorithms for Product-Form Queueing Networks,
138
5.6.1
The Convolution Algorithm,
138
5.6.2
The
MVA, 142
5.7
Networks with Positive and Negative Customers,
144
5.7.1
G-Networks with Signals,
145
5.7.2
Extensions of the G-Network,
146
6
Approximations of Queueing Systems and Networks
150
6.1
Introduction,
150
6.2
Fluid Approximation,
151
6.2.1
Fluid Approximation of a G/G/l Queue,
151
6.2.2
Fluid Approximation of a Queueing Network,
155
6.3
Diffusion Approximations,
155
6.3.1
Diffusion Approximation of a G/G/l Queue,
156
6.3.2
Brownian Approximation for a G/G/l Queue,
159
6.3.2.1
Brownian Motion with Drift,
161
6.3.2.2
Reflected Brownian Motion,
161
6.3.2.3
Scaled Brownian Motion,
162
6.3.2.4
Functional Central Limit Theorem,
163
6.3.2.5
Brownian Motion Approximation of the
G/G/l Queue,
163
6.3.3
Diffusion Approximation of Open Queueing
Networks,
165
6.3.4
Diffusion Approximation of Closed Queueing
Networks,
168
7
Elements of Graph Theory
172
7.1
Introduction,
172
7.2
Basic Concepts,
172
7.2.1
Subgraphs and Cliques,
174
7.2.2
Adjacency Matrix,
175
7.2.3
Directed Graphs,
175
7.2.4
Weighted Graphs,
176
7.3
Connected Graphs,
177
7.4
Cut Sets, Bridges, and Cut Vertices,
177
7.5
Euler
Graphs,
178
7.6
Hamiltonian Graphs,
178
7.7
Trees and Forests,
179
7.8
Minimum Weight Spanning Trees,
181
7.9
Bipartite Graphs and Matchings,
182
7.9.1
The Hungarian Algorithm,
184
7.10
Independent Set, Domination, and Covering,
186
7.11
Complement of a Graph,
188
7.12
Isomorphic Graphs,
188
CONTENTS
¡x
7.13
Planar
Graphs,
189
7.13.1
Euler s Formula for Planar Graphs,
190
7.14
Graph Coloring,
191
7.14.1
Edge Coloring,
191
7.14.2
The Four-Color Problem,
192
7.15
Random Graphs,
192
7.15.1
Bernoulli Random Graphs,
192
7.15.1.1
Phase Transition,
193
7.15.2
Geometric Random Graphs,
193
7.15.3
Markov Random Graph,
194
7.16
Matrix Algebra of Graphs,
195
7.16.1
Adjacency Matrix,
196
7.16.2
Connection Matrix,
197
7.16.3
Path Matrix,
197
7.16.4
Laplacian Matrix,
198
7.17
Spectral Properties of Graphs,
198
7.17.1
Spectral Radius,
200
7.17.2
Spectral Gap,
200
7.18
Graph Entropy,
201
7.19
Directed Acyclic Graphs,
201
7.20
Moral Graphs,
202
7.21
Triangulated Graphs,
202
7.22
Chain Graphs,
203
7.23
Factor Graphs,
204
8
Bayesian Networks
209
8.1
Introduction,
209
8.2
Bayesian Networks,
210
8.3
Classification of BNs,
214
8.4
General Conditional Independence and d-Separation,
215
8.5
Probabilistic Inference in BNs,
215
8.5.1
The Sum-Product Algorithm,
217
8.5.2
The Junction Tree Algorithm,
221
8.5.2.1
Belief Propagation in a Junction Tree,
225
8.6
Learning BNs,
227
8.6.1
Parameter Learning,
227
8.6.1.1
Maximum Likelihood Estimation
228
8.6.1.2
Maximum A Posteriori Estimation,
230
8.6.2
Structure Learning,
231
8.7
Dynamic Bayesian Networks,
231
9
Boolean Networks
235
9.1
Introduction,
235
9.2
Introduction to GRNs,
236
% CONTENTS
9.3
Boolean
Network Basics, 236
9.4 Random
Boolean
Networks, 238
9.5 State Transition Diagram, 239
9.6
Behavior of Boolean
Networks, 240
9.7
Petri
Net Analysis of Boolean Networks,
242
9.7.1
Introduction to PNs,
242
9.7.2
Behavioral Properties of PNs,
245
9.7.3
PN Model of Boolean Networks,
246
9.8
Probabilistic Boolean Networks,
250
9.9
Dynamics of a PBN,
251
9.10
Advantages and Disadvantages of Boolean Networks,
252
10
Random Networks
255
10.1
Introduction,
255
10.2
Characterization of Complex Networks,
256
10.2.1
Degree Distribution,
256
10.2.2
Geodesic Distances,
257
10.2.3
Centrality Measures,
257
10.2.4
Clustering,
258
10.2.5
Network Entropy,
259
10.2.6
Percolation and the Emergence of Giant
Component,
259
10.3
Models of Complex Networks,
261
10.3.1
The Small-World Network,
261
10.3.2
Scale-Free Networks,
263
10.4
Random Networks,
265
10.4.1
Degree Distribution,
265
10.4.2
Emergence of Giant Component,
266
10.4.3
Connectedness and Diameter,
266
10.4.4
Clustering Coefficient,
267
10.4.5
Scale-Free Properties,
267
10.5
Random Regular Networks,
267
10.6
Consensus over Random Networks,
268
10.6.1
Consensus over Fixed Networks,
270
10.6.1.1
Time to Convergence in a Fixed Network,
272
10.6.2
Consensus over Random Networks,
273
10.7
Summary,
274
References
276
Index
280
|
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/2 |
| dewey-search | 519.2/2 |
| dewey-sort | 3519.2 12 |
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| id | DE-604.BV039765717 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:10:58Z |
| institution | BVB |
| isbn | 9781118065679 9781118092972 |
| language | English |
| lccn | 2011007713 |
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| physical | XII, 295 S. graph. Darst. |
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| spelling | Ibe, Oliver C. 1947- Verfasser (DE-588)136641784 aut Fundamentals of stochastic networks Oliver C. Ibe Hoboken, NJ Wiley 2011 XII, 295 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz.: S. 276 - 279 Queuing theory Stochastic analysis Warteschlangennetz (DE-588)4225823-6 gnd rswk-swf Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Stochastische Analysis (DE-588)4132272-1 s Warteschlangennetz (DE-588)4225823-6 s DE-604 Erscheint auch als Online-Ausgabe, EPUB 978-1-118-09298-9 Erscheint auch als Online-Ausgabe, PDF 978-1-118-09299-6 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024626806&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ibe, Oliver C. 1947- Fundamentals of stochastic networks Queuing theory Stochastic analysis Warteschlangennetz (DE-588)4225823-6 gnd Stochastische Analysis (DE-588)4132272-1 gnd |
| subject_GND | (DE-588)4225823-6 (DE-588)4132272-1 |
| title | Fundamentals of stochastic networks |
| title_auth | Fundamentals of stochastic networks |
| title_exact_search | Fundamentals of stochastic networks |
| title_full | Fundamentals of stochastic networks Oliver C. Ibe |
| title_fullStr | Fundamentals of stochastic networks Oliver C. Ibe |
| title_full_unstemmed | Fundamentals of stochastic networks Oliver C. Ibe |
| title_short | Fundamentals of stochastic networks |
| title_sort | fundamentals of stochastic networks |
| topic | Queuing theory Stochastic analysis Warteschlangennetz (DE-588)4225823-6 gnd Stochastische Analysis (DE-588)4132272-1 gnd |
| topic_facet | Queuing theory Stochastic analysis Warteschlangennetz Stochastische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024626806&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ibeoliverc fundamentalsofstochasticnetworks |