Mathematical foundations of computer networking:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Upper Saddle River, NJ
Addison-Wesley
April 2012
|
| Schriftenreihe: | Addison-Wesley professional computing series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 474 Seiten Illustrationen, Diagramme 23 cm |
| ISBN: | 9780321792105 |
Internformat
MARC
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| 245 | 1 | 0 | |a Mathematical foundations of computer networking |c Srinivasan Keshav |
| 264 | 1 | |a Upper Saddle River, NJ |b Addison-Wesley |c April 2012 | |
| 300 | |a XVIII, 474 Seiten |b Illustrationen, Diagramme |c 23 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Addison-Wesley professional computing series | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Computer networks |x Mathematics |v Textbooks | |
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Datensatz im Suchindex
| _version_ | 1804153054324326400 |
|---|---|
| adam_text | Contents
Preface
xv
Chapter
1
Probability
1
1.1
Introduction
1
1.1.1
Outcomes
2
1.1.2
Events
3
1.1.3
Disjunctions and Conjunctions of Events
3
1.1.4
Axioms of Probability
4
1.1.5
Subjective and Objective Probability
5
1.2
Joint and Conditional Probability
7
1.2.1
Joint Probability
7
1.2.2
Conditional Probability
7
1.2.3
Bayes s Rule
11
1.3
Random Variables
14
1.3.1
Distribution
15
1.3.2
Cumulative Density Function
17
1.3.3
Generating Values from an Arbitrary Distribution
17
1.3.4
Expectation of a Random Variable
18
6.3.
б
Variance of a Random Variable
20
Contents
1.4 Moments and Moment
Generating Functions
21
1.4.1 Moments 21
1.4.2 Moment
Generating Functions
22
1.4.3
Properties of
Moment
Generating Functions
24
1.5
Standard Discrete Distributions
25
1.5.1
Bernoulli Distribution
25
1.5.2
Binomial Distribution
25
1.5.3
Geometric Distribution
27
1.5.4
Poisson
Distribution
27
1.6
Standard Continuous Distributions
29
1.6.1
Uniform Distribution
29
1.6.2
Gaussian, or Normal, Distribution
29
1.6.3
Exponential Distribution
32
1.6.4
Power-Law Distribution
34
1.7
Useful Theorems
35
1.7.1
Markov s Inequality
36
1.7.2
Chebyshev s Inequality
36
1.7.3
Chernoff Bound
37
1.7.4
Strong Law of Large Numbers
39
1.7.5
Central Limit Theorem
40
1.8
Jointly Distributed Random Variables
42
1.8.1
Bayesian Networks
44
1.9
Further Reading
47
1.10
Exercises
47
Chapter
2
Statistics
53
2.1
Sampling a Population
53
2.1.1
Types of Sampling
55
2.1.2
Scales
56
2.1.3
Outliers
57
2.2
Describing a Sample Parsimoniously
57
2.2.1
Tables
58
2.2.2
Bar Graphs, Histograms, and Cumulative Histograms
58
2.2.3
The Sample Mean
60
2.2.4
The Sample Median
63
2.2.5
Measures of Variability
64
Contents vii
2.3
Inferring
Population Parameters
from
Sample
Parameters 66
2.4
Testing Hypotheses about Outcomes of
Experiments 70
2.4.1
Hypothesis Testing
71
2.4.2
Errors in Hypothesis Testing
72
2.4.3
Formulating a Hypothesis
73
2.4.4
Comparing an Outcome with a Fixed Quantity
74
2.4.5
Comparing Outcomes from Two Experiments
76
2.4.6
Testing Hypotheses about Quantities Measured on
Ordinal Scales
79
2.4.7
Fitting a Distribution
82
2.4.8
Power
85
2.5
Independence and Dependence: Regression
and Correlation
86
2.5.1
Independence
86
2.5.2
Regression
88
2.5.3
Correlation
90
2.6
Comparing Multiple Outcomes Simultaneously:
Analysis of Variance
95
2.6.1
One-Way Layout
95
2.6.2
Multiway Layouts
98
2.7
Design of Experiments
99
2.8
Dealing with Large Data Sets
100
2.9
Common Mistakes in Statistical Analysis
103
2.9.1
Defining Population
103
2.9.2
Lack of Confidence Intervals in Comparing Results
103
2.9.3
Not Stating the Null Hypothesis
103
2.9.4
Too Small a Sample
104
2.9.5
Too Large a Sample
104
2.9.6
Not Controlling All Variables When Collecting
Observations
104
2.9.7
Converting Ordinal to Interval Scales
104
2.9.8
Ignoring Outliers
105
2.10
Further Reading
105
2.11
Exercises
105
viii Contents
Chapter
3
Linear Algebra
109
3.1
Vectors and Matrices
109
3.2
Vector and Matrix Algebra 111
3.2.1
Addition 111
3.2.2
Transpose 111
3.2.3
Multiplication
112
3.2.4
Square Matrices
113
3.2.5
Exponentiation
113
3.2.6
Matrix Exponential
114
3.3
Linear Combinations, Independence, Basis, and
Dimension
114
3.3.1
Linear Combinations
114
3.3.2
Linear Independence
115
3.3.3
Vector Spaces, Basis, and Dimension
116
3.4
Using Matrix Algebra to Solve Linear Equations
117
3.4.1
Representation
117
3.4.2
Elementary Row Operations and Gaussian
Elimination
118
3.4.3
Rank
120
3.4.4
Determinants
121
3.4.5
Cramer s Theorem
123
3.4.6
The Inverse of a Matrix
124
3.5
Linear Transformations, Eigenvalues, and Eigenvectors
125
3.5.1
A Matrix as a Linear Transformation
125
3.5.2
The Eigenvalue of a Matrix
126
3.5.3
Computing the Eigenvalues of a Matrix
129
3.5.4
The Importance of Eigenvalues
132
3.5.5
The Role of the Principal Eigenvalue
133
3.5.6
Finding Eigenvalues and Eigenvectors
134
3.5.7
Similarity and Diagonalization
137
3.6
Stochastic Matrices
138
3.6.1
Computing State Transitions by Using a
Stochastic Matrix
139
3.6.2
Eigenvalues of a Stochastic Matrix
140
3.7
Exercises
143
Contents
¡χ
Chapter
4
Chapter
5
Optimization
147
4.1
System Modeling and Optimization
147
4.2
Introduction to Optimization
149
4.3
Optimizing Linear Systems
152
4.3.1
Network Flow
156
4.4
Integer Linear Programming
157
4.4.1
Total Unimodularity
160
4.4.2
Weighted Bipartite Matching
161
4.5
Dynamic Programming*
162
4.6
Nonlinear Constrained Optimization
164
4.6.1
Lagrangian Techniques
164
4.6.2
Karush-Kuhn-Tucker Conditions for Nonlinear
Optimization
166
4.7
Heuristic Nonlinear Optimization
167
4.7.1
Hill Climbing
167
4.7.2
Genetic Algorithms
169
4.8
Exercises
170
Signals, Systems, and Transforms
173
5.1
Background
173
5.1.1
Sinusoids
173
Complex Numbers
174
Euler s Formula
176
Discrete-Time Convolution and the Impulse
Function
179
Continuous-Time Convolution and the Dirac
Delta Function
182
5.2
Signals
185
5.2.1
The Complex Exponential Signal
186
5.3
Systems
188
5.4
Analysis of a Linear Time-Invariant System
189
5.4.1
The Effect of an LTI System on a Complex
Exponential Input
189
The Output of an LTI System with a Zero Input
191
The Output of an LTI System for an Arbitrary Input
193
Stability of an LTI System
194
5.1.2
5.1.3
5.1.4
5.1.5
5.4.2
5.4.3
5.4.4
Contents
5.5
Transforms
195
5.6
The Fourier Series
196
5.7
The Fourier Transform and Its Properties
200
5.8
The Laplace Transform
209
5.8.1
Poles, Zeroes, and the Region of Convergence
210
5.8.2
Properties of the Laplace Transform
212
5.9
The Discrete Fourier Transform and Fast Fourier
Transform
216
5.9.1
The Impulse Train
216
5.9.2
The Discrete-Time Fourier Transform
217
5.9.3
Aliasing
219
5.9.4
The Discrete-Time-and-Frequency Fourier
Transform
222
5.9.5
The Fast Fourier Transform
224
5.10
The
Z
Transform
226
5.10.1
Relationship between
Z
and Laplace Transforms
229
5.10.2
Properties of the
Z
Transform
231
5.11
Further Reading
233
5.12
Exercises
234
lhapter
6
Stochastic Processes and Queueing Theory
237
6.1
Overview
237
6.1.1
A General Queueing System
238
6.1.2
Little s Theorem
238
6.2
Stochastic Processes
240
6.2.1
Discrete and Continuous Stochastic Processes
242
6.2.2
Markov Processes
243
6.2.3
Homogeneity, State-Transition Diagrams, and the
Chapman-Kolmogorov Equations
244
6.2.4
Irreducibility
246
6.2.5
Recurrence
247
6.2.6
Periodicity
247
6.2.7
Ergodicity
248
6.2.8
A Fundamental Theorem
249
6.2.9
Stationary (Equilibrium) Probability of a Markov
Chain
250
Contents
6.2.10
A Second
Fundamental Theorem 251
6.2.11
Mean Residence Time in a State
252
6.3
Continuous-Time Markov Chains
252
6.3.1
Markov Property for Continuous-Time Stochastic
Processes
253
6.3.2
Residence Time in a Continuous-Time Markov
Chain
253
6.3.3
Stationary Probability Distribution for a
Continuous-Time Markov Chain
253
6.4
Birth-Death Processes
255
6.4.1
Time-Evolution of a Birth-Death Process
255
6.4.2
Stationary Probability Distribution of a
Birth-Death Process
256
6.4.3
Finding: the Transition-Rate Matrix
257
6.4.4
A Pure-Birth
(Poisson)
Process
259
6.4.5
Stationary Probability Distribution for a
Birth-Death Process
260
6.5
The M/M/l Queue
262
6.6
Two Variations on the M/M/l Queue
266
6.6.1
The
M/M/Ï
Queue: A Responsive Server
266
6.6.2
M/M/l/K: Bounded Buffers
268
6.7
Other Queueing Systems
270
6.7.1
M/D/l: Deterministic Service Times
270
6.7.2
G/G/l
270
6.7.3
Networks of Queues
271
6.8
Further Reading
272
6.9
Exercises
272
Chapter
7
Game Theory
277
7.1
Concepts and Terminology
278
7.1.1
Preferences and Preference Ordering
278
7.1.2
Terminology
281
7.1.3
Strategies
282
7.1.4
Game Representation
283
7.1.5
Response and Best Response
287
7.1.6
Dominant and Dominated Strategy
287
xii Contents
7.1.7 Bayesian Games 288
7.1.8
Repeated
Games 289
7.2
Solving a Game
291
7.2.1
Solution Concept and Equilibrium
291
7.2.2
Dominant-Strategy Equilibria
291
7.2.3
Iterated Removal of Dominated Strategies
293
7.2.4 Maximin
Equilibrium
294
7.2.5
Nash Equilibria
296
7.2.6
Correlated Equilibria
299
7.2.7
Other Solution Concepts
301
7.3
Mechanism Design
301
7.3.1
Practical Mechanisms
302
7.3.2
Three Negative Results
302
7.3.3
Examples of Mechanism Design
304
7.3.4
Formalization
307
7.3.5
Desirable Properties of a Mechanism
308
7.3.6
Revelation Principle
309
7.3.7
Vickrey-Clarke-Groves Mechanism
310
7.3.8
Problems with VCG Mechanisms
313
7.4
Limitations of Game Theory
314
7.5
Further Reading
315
7.6
Exercises
316
Chapter
8
Elements of Control Theory
319
8.1
Overview of a Controlled System
320
8.2
Modeling a System
323
8.2.1
Modeling Approach
323
8.2.2
Mathematical Representation
324
8.3
A First-Order System
329
8.4
A Second-Order System
331
8.4.1
Case
1
(Undamped System):
ς
= 0 331
8.4.2
Case
2
(Underdamped System):
0 <
ς
< 1 332
8.4.3
Case
3
(Critically Damped System):
ς
= 1 334
8.4.4
Case
4
(Overdamped System):
ς
> 1 334
Contents
8.5
В
asics
of Feedb
ack
Control
336
8.5.1
System Goal
338
8.5.2
Constraints
339
8.6 PID
Control
341
8.6.1
Proportional-Mode Control
341
8.6.2
Integral-Mode Control
343
8.6.3
Derivative-Mode Control
344
8.6.4
Combining Modes
345
8.7
Advanced Control Concepts
346
8.7.1
Cascade Control
346
8.7.2
Control Delay
347
8.8
Stability
350
8.8.1
BIBO
Stability Analysis of a Linear Time-Invariant
System
353
8.8.2
Zero-Input Stability Analysis of
a SISO
Linear
Time-Invariant System
356
8.8.3
Placing System Roots
357
8.8.4
Lyapunov Stability
358
8.9
State Space-Based Modeling and Control
360
8.9.1
State Space-Based Analysis
360
8.9.2
Observability and Controllability
361
8.9.3
Controller Design
362
8.10
Digital Control
364
8.11
Partial Fraction Expansion
367
8.11.1
Distinct Roots
367
8.11.2
Complex Conjugate Roots
368
8.11.3
Repeated Roots
369
8.12
Further Reading
370
8.13
Exercises
370
Chapter
9
Information Theory
373
9.1
Introduction
373
9.2
A Mathematical Model for Communication
374
9.3
From Messages to Symbols
378
9.4
Source Coding
379
xiv
Contents
9.5
The
Capacity of a Communication Channel
386
9.5.1
Modeling a Message Source
387
9.5.2
The Capacity of a Noiseless Channel
389
9.5.3
A Noisy Channel
390
9.6
The
Gaussian Channel
399
9.6.1
Modeling a Continuous Message Source
400
9.6.2
A Gaussian Channel
401
9.6.3
The Capacity of a Gaussian Channel
403
9.7
Further Reading
407
9.8
Exercises
407
Solutions to Exercises
411
Index
457
|
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| id | DE-604.BV042399967 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:20:30Z |
| institution | BVB |
| isbn | 9780321792105 |
| language | English |
| lccn | 2011052203 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027835672 |
| oclc_num | 799125311 |
| open_access_boolean | |
| owner | DE-739 DE-11 |
| owner_facet | DE-739 DE-11 |
| physical | XVIII, 474 Seiten Illustrationen, Diagramme 23 cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Addison-Wesley |
| record_format | marc |
| series2 | Addison-Wesley professional computing series |
| spelling | Keshav, Srinivasan Verfasser aut Mathematical foundations of computer networking Srinivasan Keshav Upper Saddle River, NJ Addison-Wesley April 2012 XVIII, 474 Seiten Illustrationen, Diagramme 23 cm txt rdacontent n rdamedia nc rdacarrier Addison-Wesley professional computing series Mathematik Computer networks Mathematics Textbooks Mathematik (DE-588)4037944-9 gnd rswk-swf Rechnernetz (DE-588)4070085-9 gnd rswk-swf Rechnernetz (DE-588)4070085-9 s Mathematik (DE-588)4037944-9 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027835672&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Keshav, Srinivasan Mathematical foundations of computer networking Mathematik Computer networks Mathematics Textbooks Mathematik (DE-588)4037944-9 gnd Rechnernetz (DE-588)4070085-9 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4070085-9 |
| title | Mathematical foundations of computer networking |
| title_auth | Mathematical foundations of computer networking |
| title_exact_search | Mathematical foundations of computer networking |
| title_full | Mathematical foundations of computer networking Srinivasan Keshav |
| title_fullStr | Mathematical foundations of computer networking Srinivasan Keshav |
| title_full_unstemmed | Mathematical foundations of computer networking Srinivasan Keshav |
| title_short | Mathematical foundations of computer networking |
| title_sort | mathematical foundations of computer networking |
| topic | Mathematik Computer networks Mathematics Textbooks Mathematik (DE-588)4037944-9 gnd Rechnernetz (DE-588)4070085-9 gnd |
| topic_facet | Mathematik Computer networks Mathematics Textbooks Rechnernetz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027835672&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT keshavsrinivasan mathematicalfoundationsofcomputernetworking |