Performance analysis of complex networks and systems:
"This rigorous, self-contained book describes mathematical and, in particular, stochastic and graph theoretic methods to assess the performance of complex networks and systems. It comprises three parts: the first is a review of probability theory; Part II covers the classical theory of stochast...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press.
2014
|
| Schlagworte: | |
| Online-Zugang: | Cover Inhaltsverzeichnis Inhaltsverzeichnis |
| Zusammenfassung: | "This rigorous, self-contained book describes mathematical and, in particular, stochastic and graph theoretic methods to assess the performance of complex networks and systems. It comprises three parts: the first is a review of probability theory; Part II covers the classical theory of stochastic processes (Poisson, Markov and queueing theory), which are considered to be the basic building blocks for performance evaluation studies; Part III focuses on the rapidly expanding new field of network science. This part deals with the recently obtained insight that many very different large complex networks - such as the Internet, World Wide Web, metabolic and human brain networks, utility infrastructures, social networks - evolve and behave according to general common scaling laws. This understanding is useful when assessing the end-to-end quality of Internet services and when designing robust and secure networks. Containing problems and solved solutions, the book is ideal for graduate students taking courses in performance analysis"-- |
| Beschreibung: | Frühere Auafl. u.d.T.: Performance analysis of communications networks and systems / Piet Van Mieghem Literaturverz. S. 663 - 672 |
| Beschreibung: | XVI, 675 S. Ill., graph. Darst. |
| ISBN: | 9781107058606 |
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| 100 | 1 | |a Mieghem, Piet van |d 1964- |e Verfasser |0 (DE-588)131444018 |4 aut | |
| 245 | 1 | 0 | |a Performance analysis of complex networks and systems |c Piet Van Mieghem |
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press. |c 2014 | |
| 300 | |a XVI, 675 S. |b Ill., graph. Darst. | ||
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| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Frühere Auafl. u.d.T.: Performance analysis of communications networks and systems / Piet Van Mieghem | ||
| 500 | |a Literaturverz. S. 663 - 672 | ||
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Datensatz im Suchindex
| _version_ | 1804152324970512384 |
|---|---|
| adam_text | Contents
Preface
y^
Symbols xv
1
Introduction
1
Part I Probability theory
5
2
Random variables
7
2.1
Probability theory and set theory
7
2.2
Discrete random variables
12
2.3
Continuous random variables
15
2.4
The conditional probability
22
2.5
Several random variables and independence
24
2.6
Conditional expectation
32
2.7
Problems
33
3
Basic distributions
35
3.1
Discrete random variables
35
3.2
Continuous random variables
40
3.3
Derived distributions
44
3.4
Functions of random variables
54
3.5
Examples of other distributions
57
3.6
Summary tables of probability distributions
64
3.7
Problems
65
1
Correlation
69
4.1
Generation of correlated Gaussian random variables
69
4.2
Generation of correlated random variables
76
4.3
The non-linear transformation method
77
vj Contents
4.4
Examples of the non-linear transformation method
82
4.5
Linear combination of independent auxiliary random variables
86
4.6
Sampling and estimators
90
4.7
Problems 98
5
Inequalities
99
5.1
The minimum (maximum) and infimum (supremuin)
100
5.2
Continuous convex functions
100
5.3
Inequalities deduced from the Mean Value Theorem
102
5.4
The Markov, Chebyshev and Chernoff inequalities
103
5.5
The Holder, Minkowski and Young inequalities
106
5.6
The Gauss inequality
110
5.7
The dominant pole approximation and large deviations
112
5.8
Problems
114
6
Limit laws
115
6.1
General theorems from analysis
115
6.2
Law of Large Numbers
118
6.3
Central Limit Theorem
120
6.4
The Law of Proportionate Effect
121
6.5
Logarithm of a sum of random variables
123
6.6
Extremal distributions
126
6.7
Problem
132
Part II Stochastic processes
133
7
The
Poisson
process I35
7.1
A stochastic process I35
7.2
The
Poisson
process I39
7.3
Properties of the
Poisson
process
141
7.4
The
Poisson
process and the uniform distribution
146
7.5
The non-homogeneous
Poisson
process
150
7.6
The failure rate function
152
7.7
Problems
лгл
8
Renewal theory
-,
r-
8.1
Basic notions
1
ко
8.2
Limit theorems
8.3
The residual waiting time
8.4
The renewal reward process
8.5
Problems
Ί,__
1
ib
Contents
vii
9
Discrete-time Markov chains
179
9.1
Definition
179
9.2
Discrete-time Markov chains
180
9.3
The steady-state of a Markov chain
191
9.4
Example: the two-state Markov chain
197
9.5
A generating function approach
199
9.6
Problems
201
10
Continuous-time Markov chains
205
10.1
Definition
205
10.2
Properties of continuous-
1
ime
Markov processes
206
10.3
Steady-state
212
10.4
The embedded Markov chain
214
10.5
The transitions in a continuous-time Markov chain
219
10.6
Example: the two-state Markov chain in continuous-time
220
10.7
Time reversibility
221
10.8
Problems
224
11
Applications of Markov chains
227
11.1
Discrete Markov chains and independent random variables
227
11.2
The general random walk
228
11.3
Birth and death process
234
11.4
Slotted Aloha
247
11.5
Ranking of webpages
251
11.6
Problems
255
12
Branching processes
257
12.1
The probability generating function
258
12.2
The limit
W
of the scaled random variables Wk
262
12.3
The probability of extinction of a branching process
266
12.4
Conditioning of a supercritical branching process
269
12.5
Asymptotic behavior of
W
273
12.6
A geometric branching process
276
12.7
Time-dependent branching process
278
12.8
Problems 285
13
General queueing theory
287
13.1
A queueing system
287
13.2
The waiting process: Lindley s approach
291
13.3
The
Beneš
approach to the unfinished work
295
13.4
The counting process
302
13.5
Queue observations
viii
Contents
13.6
PASTA
13.7
Little s Law
311
14
Queueing models
14.1
The
M/M/
1
queue 3U
14.2
Variants of the M/M/l queue 316
14.3
The M/G/l queue 322
14.4
The GI/D/m queue 327
14.5
The M/D/l/K queue 334
14.6
The G/M/l queue 337
14.7
The
N*D/D/1
queue 341
14.8
The
AMS
queue
34Г)
14.9
The cell loss ratio
349
14.10
Problems
Part III Network science
357
15
General characteristics of graphs
359
15.1
Introduction
359
15.2
The number of paths with
j
hops
361
15.3
The degree of a node in a graph
362
15.4
The origin of power-law degree distributions in complex net¬
works
364
15.5
Connectivity and robustness
366
15.6
Graph metrics
368
15.7
Random graphs
375
15.8
Interdependent networks
389
15.9
Problems
393
16
The shortest path problem
397
16.1
The shortest path and the link weight structure
398
16.2
The shortest path tree in KN with exponential link weights
399
16.3
The hopcount
h n
in the URT
404
16.4
The weight of the shortest path
409
16.5
Joint distribution of the hopcount and the weight
412
16.6
The flooding time T/v
414
16.7
The degree of a node in the URT
418
16.8
The hopcount in a large, sparse graph
423
16.9
The minimum spanning tree 43I
16.10
Problems
43g
17
Epidemics in networks
44g
Contents ix
17.1
Classical epidemiology
444
17.2
The continuous-time SIS Markov process
446
17.3
The governing
ε—
SIS equations
450
17.4
iV-Intertwined Mean-Field Approximation
(NIMFA)
462
17.5
Heterogeneous iV-intertwined mean-field approximation
471
17.6
Epidemics on the complete graph
Км
473
17.7
Non-Markovian SIS epidemics
477
17.8
Heterogeneous mean-field (HMF) approximation
484
17.9
Problems
486
18
The efficiency of multicast
489
18.1
General results for
длК772)
490
18.2
The random graph Gp (N)
493
18.3
The
/с
-ary
tree
501
18.4
The Chuang Sirbu Law
503
18.5
Stability of a multicast shortest path tree
506
18.6
Proof of
(18.16):
длК772)
for random graphs
509
18.7
Proof of Theorem
18.3.1:
gN(m) for Ar-ary trees
513
18.8
Problems
515
19
The hop count and weight to an any cast group
517
19.1
Introduction
517
19.2
General analysis of the hop count
520
19.3
The fc-ary tree
523
19.4
The uniform recursive tree (URT)
523
19.5
The performance measure
η
in exponentially growing trees
531
19.6
The weight to an anycast group
533
Appendix A A summary of matrix theory
539
Appendix
В
Solutions of problems
575
References
Index
673
|
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| bvnumber | BV041946261 |
| ctrlnum | (OCoLC)884927681 (DE-599)GBV778241726 |
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| id | DE-604.BV041946261 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:08:55Z |
| institution | BVB |
| isbn | 9781107058606 |
| language | English |
| lccn | 2014000241 |
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| physical | XVI, 675 S. Ill., graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Cambridge Univ. Press. |
| record_format | marc |
| spelling | Mieghem, Piet van 1964- Verfasser (DE-588)131444018 aut Performance analysis of complex networks and systems Piet Van Mieghem Cambridge Cambridge Univ. Press. 2014 XVI, 675 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Frühere Auafl. u.d.T.: Performance analysis of communications networks and systems / Piet Van Mieghem Literaturverz. S. 663 - 672 "This rigorous, self-contained book describes mathematical and, in particular, stochastic and graph theoretic methods to assess the performance of complex networks and systems. It comprises three parts: the first is a review of probability theory; Part II covers the classical theory of stochastic processes (Poisson, Markov and queueing theory), which are considered to be the basic building blocks for performance evaluation studies; Part III focuses on the rapidly expanding new field of network science. This part deals with the recently obtained insight that many very different large complex networks - such as the Internet, World Wide Web, metabolic and human brain networks, utility infrastructures, social networks - evolve and behave according to general common scaling laws. This understanding is useful when assessing the end-to-end quality of Internet services and when designing robust and secure networks. Containing problems and solved solutions, the book is ideal for graduate students taking courses in performance analysis"-- Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Leistungsbewertung (DE-588)4167271-9 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Graphentheorie (DE-588)4113782-6 s Leistungsbewertung (DE-588)4167271-9 s DE-604 http://assets.cambridge.org/97811070/58606/cover/9781107058606.jpg Cover DE-601 pdf/application http://www.gbv.de/dms/tib-ub-hannover/778241726.pdf Inhaltsverzeichnis Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027389333&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mieghem, Piet van 1964- Performance analysis of complex networks and systems Stochastischer Prozess (DE-588)4057630-9 gnd Leistungsbewertung (DE-588)4167271-9 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4167271-9 (DE-588)4113782-6 |
| title | Performance analysis of complex networks and systems |
| title_auth | Performance analysis of complex networks and systems |
| title_exact_search | Performance analysis of complex networks and systems |
| title_full | Performance analysis of complex networks and systems Piet Van Mieghem |
| title_fullStr | Performance analysis of complex networks and systems Piet Van Mieghem |
| title_full_unstemmed | Performance analysis of complex networks and systems Piet Van Mieghem |
| title_short | Performance analysis of complex networks and systems |
| title_sort | performance analysis of complex networks and systems |
| topic | Stochastischer Prozess (DE-588)4057630-9 gnd Leistungsbewertung (DE-588)4167271-9 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Stochastischer Prozess Leistungsbewertung Graphentheorie |
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| work_keys_str_mv | AT mieghempietvan performanceanalysisofcomplexnetworksandsystems |
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