Probability, Markov chains, queues, and simulation: the mathematical basis of performance modeling
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton [u.a.]
Princeton Univ. Press
2009
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 758 S. graph. Darst. |
| ISBN: | 9780691140629 |
Internformat
MARC
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| 100 | 1 | |a Stewart, William J. |d 1946- |e Verfasser |0 (DE-588)124089143 |4 aut | |
| 245 | 1 | 0 | |a Probability, Markov chains, queues, and simulation |b the mathematical basis of performance modeling |c William J. Stewart |
| 264 | 1 | |a Princeton [u.a.] |b Princeton Univ. Press |c 2009 | |
| 300 | |a XVIII, 758 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Probabilities |x Computer simulation | |
| 650 | 4 | |a Markov processes | |
| 650 | 4 | |a Queuing theory | |
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| 650 | 0 | 7 | |a Mathematische Methode |0 (DE-588)4155620-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Wahrscheinlichkeitsrechnung |0 (DE-588)4064324-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Markov-Prozess |0 (DE-588)4134948-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Warteschlangentheorie |0 (DE-588)4255044-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Datenverarbeitungssystem |0 (DE-588)4125229-9 |2 gnd |9 rswk-swf |
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| 689 | 1 | |5 DE-604 | |
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Datensatz im Suchindex
| _version_ | 1804140021537570816 |
|---|---|
| adam_text | Contents
Preface
and Acknowledgments
xv
I PROBABILITY
1
1
Probability
3
. 1
Trials, Sample Spaces, and Events
3
.2
Probability Axioms and Probability Space
9
.3
Conditional Probability
12
.4
Independent Events
15
.5
Law of Total Probability
18
1.6
Bayes
Rule
20
1.7
Exercises
21
2
Combinatorics
—
The Art of Counting
25
2.1
Permutations
25
2.2
Permutations with Replacements
26
2.3
Permutations without Replacement
27
2.4
Combinations without Replacement
29
2.5
Combinations with Replacements
31
2.6
Bernoulli (Independent) Trials
33
2.7
Exercises
36
3
Random Variables and Distribution Functions
40
3.1
Discrete and Continuous Random Variables
40
3.2
The Probability Mass Function for a Discrete Random Variable
43
3.3
The Cumulative Distribution Function
46
3.4
The Probability Density Function for a Continuous Random Variable
51
3.5
Functions of a Random Variable
53
3.6
Conditioned Random Variables
58
3.7
Exercises
60
4
Joint and Conditional Distributions
64
4.1
Joint Distributions
64
4.2
Joint Cumulative Distribution Functions
64
4.3
Joint Probability Mass Functions
68
4.4
Joint Probability Density Functions
71
4.5
Conditional Distributions
77
4.6
Convolutions and the Sum of Two Random Variables
80
4.7
Exercises
82
5
Expectations and More
87
5.1
Definitions
87
5.2
Expectation of Functions and Joint Random Variables
92
5.3
Probability Generating Functions for Discrete Random Variables
100
viii Contents
5.4
Moment
Generating Functions
103
5.5
Maxima and Minima of Independent Random Variables
108
5.6
Exercises
110
6
Discrete Distribution Functions
115
6.1
The Discrete Uniform Distribution
115
6.2
The Bernoulli Distribution
116
6.3
The Binomial Distribution
117
6.4
Geometric and Negative Binomial Distributions
120
6.5
The
Poisson
Distribution
124
6.6
The Hypergeometric Distribution
127
6.7
The Multinomial Distribution
128
6.8
Exercises
130
7
Continuous Distribution Functions
134
7.1
The Uniform Distribution
134
7.2
The Exponential Distribution
136
7.3
The Normal or Gaussian Distribution
141
7.4
The Gamma Distribution
145
7.5
Reliability Modeling and the Weibull Distribution
149
7.6
Phase-Type Distributions
155
7.6.1
The Erlang-2 Distribution
155
7.6.2
The Erlang-r Distribution
158
7.6.3
The Hypoexponential Distribution
162
7.6.4
The Hyperexponential Distribution
164
7.6.5
The Coxian Distribution
166
7.6.6
General Phase-Type Distributions
168
7.6.7
Fitting Phase-Type Distributions to Means and Variances
171
7.7
Exercises
176
8
Bounds and Limit Theorems
180
8.1
The Markov Inequality
180
8.2
The Chebychev Inequality
181
8.3
The Chernoff Bound
182
8.4
The Laws of Large Numbers
182
8.5
The Central Limit Theorem
184
8.6
Exercises
187
Π
MARKOV CHAINS
191
9
Discrete-and Continuous-Time Markov Chains
193
9.1
Stochastic Processes and Markov Chains
193
9.2
Discrete-Time Markov Chains: Definitions
195
9.3
The Chapman-Kolmogorov Equations
202
9.4
Classification of States
206
9.5
Irreducibility
214
9.6
The Potential, Fundamental, and Reachability Matrices
218
9.6.1
Potential and Fundamental Matrices and Mean Time to Absorption
219
9.6.2
The Reachability Matrix and Absorption Probabilities
223
Contents ix
9.7
Random Walk Problems
228
9.8
Probability Distributions
235
9.9
Reversibility
248
9.10
Continuous-Time Markov Chains
253
9.10.1
Transition Probabilities and Transition Rates
254
9.10.2
The Chapman-Kolmogorov Equations
257
9.10.3
The Embedded Markov Chain and State Properties
259
9.10.4
Probability Distributions
262
9.10.5
Reversibility
265
9.11
Semi-Markov Processes
265
9.12
Renewal Processes
267
9.13
Exercises
275
10
Numerical Solution of Markov Chains
285
10.1
Introduction
285
10.1.1
Setting the Stage
285
10.1.2
Stochastic Matrices
287
10.1.3
The Effect of Discretization
289
10.2
Direct Methods for Stationary Distributions
290
10.2.1
Iterative versus Direct Solution Methods
290
10.2.2
Gaussian Elimination and
LU
Factorizations
291
10.3
Basic Iterative Methods for Stationary Distributions
301
10.3.1
The Power Method
301
10.3.2
The Iterative Methods of Jacobi and Gauss-Seidel
305
10.3.3
The Method of Successive Overrelaxation
311
10.3.4
Data Structures for Large Sparse Matrices
313
10.3.5
Initial Approximations, Normalization, and Convergence
316
10.4
Block Iterative Methods
319
10.5
Decomposition and Aggregation Methods
324
10.6
The Matrix Geometric/Analytic Methods for Structured Markov Chains
332
10.6.1
The Quasi-Birth-Death Case
333
10.6.2
Block Lower
Hessenberg
Markov Chains
340
10.6.3
Block Upper
Hessenberg
Markov Chains
345
10.7
Transient Distributions
354
10.7.1
Matrix Scaling and Powering Methods for Small State Spaces
357
10.7.2
The Uniformization Method for Large State Spaces
361
10.7.3
Ordinary Differential Equation Solvers
365
10.8
Exercises
375
Ш
QUEUEING MODELS
383
11
Elementary Queueing Theory
385
11.1
Introduction and Basic Definitions
385
11.1.1
Arrivals and Service
386
11.1.2
Scheduling Disciplines
395
11.1.3
Kendall s Notation
396
11.1.4
Graphical Representations of Queues
397
11.1.5
Performance Measures
—
Measures of Effectiveness
398
11.1.6
Little s Law
400
Contents
11.2
Birth-Death Processes: The
M/M fl
Queue
402
11.2.1
Description and Steady-State Solution
402
11.2.2
Performance Measures
406
11.2.3
Transient Behavior
412
11.3
General Birth-Death Processes
413
11.3.1
Derivation of the State Equations
413
11.3.2
Steady-State Solution
415
11.4
Multiserver Systems
419
11.4.1
The M/M/c Queue
419
11.4.2
The M/M/oo Queue
425
11.5
Finite-Capacity Systems—The M/Mfl/K Queue
425
11.6
Multiserver, Finite-Capacity Systems
—
The M/M/c/K Queue
432
11.7
Finite-Source Systems—The M/M/cf/M Queue
434
11.8
State-Dependent Service
437
11.9
Exercises
438
12
Queues with Phase-Type Laws: Neuts Matrix-Geometric Method
444
12.1
The Erlang-r Service Model—The M/Erfl Queue
444
12.2
The Erlang-r Arrival Model—The Er/Mfl Queue
450
12.3
The
М/Нф.
and H-JMfl Queues
454
12.4
Automating the Analysis of Single-Server Phase-Type Queues
458
12.5
The
Яу^з/І
Queue and General Ph/Phfl Queues
460
12.6
Stability Results for Ph/Phfl Queues
466
12.7
Performance Measures for Ph/Phfl Queues
468
12.8
Matlab
code for Ph/Phfl Queues
469
12.9
Exercises
471
13
The z-Transform Approach to Solving Markovian Queues
475
13.1
The z-Transform
475
13.2
The Inversion Process
478
13.3
Solving Markovian Queues using z-Transforms
484
13.3.1
The z-Transform Procedure
484
13.3.2
The M/Mfl Queue Solved using z-Transforms
484
13.3.3
The M/Mfl Queue with Arrivals in Pairs
486
13.3.4
The M/Erfl Queue Solved using z-Transforms
488
13.3.5
The Er/Mfl Queue Solved using z-Transforms
496
13.3.6
Bulk Queueing Systems
503
13.4
Exercises
506
14
The M/G/l and G/MIl Queues
509
14.1
Introduction to the M/G/l Queue
509
14.2
Solution via an Embedded Markov Chain
510
14.3
Performance Measures for the M/Gfl Queue
515
14.3.1
The Pollaczek-Khintchine Mean Value Formula
515
14.3.2
The Pollaczek-Khintchine Transform Equations
518
14.4
The M/Gfl Residual Time: Remaining Service Time
523
14.5
The M/Gfl Busy Period
526
14.6
Priority Scheduling
531
14.6.1
М/МД:
Priority Queue with Two Customer Classes
531
14.6.2
M/G/l :Nonpreemptive Priority Scheduling
533
Contents xi
14.6.3 M/G/l : Preempt-Resume
Priority Scheduling
536
14.6.4
A Conservation Law and SPTF Scheduling
538
14.7
The M/G/l/K Queue
542
14.8
The G/M/l Queue
546
14.9
The G/M/l/K Queue
551
14.10
Exercises
553
15
Queueing Networks
559
15.1
Introduction
559
15.1.1
Basic Definitions
559
15.1.2
The Departure Process
—
Burke
s
Theorem
560
15.1.3
Two M/M/l Queues in Tandem
562
15.2
Open Queueing Networks
563
15.2.1
Feedforward Networks
563
15.2.2
Jackson Networks
563
15.2.3
Performance Measures for Jackson Networks
567
15.3
Closed Queueing Networks
568
15.3.1
Definitions
568
15.3.2
Computation of the Normalization Constant: Buzen s Algorithm
570
15.3.3
Performance Measures
577
15.4
Mean Value Analysis for Closed Queueing Networks
582
15.5
The Flow-Equivalent Server Method
591
15.6
Multiclass Queueing Networks and the BCMP Theorem
594
15.6.1
Product-Form Queueing Networks
595
15.6.2
The BCMP Theorem for Open, Closed, and Mixed Queueing
Networks
598
15.7
Java Code
602
15.8
Exercises
607
IV SIMULATION
611
16
Some Probabilistic and Deterministic Applications of Random Numbers
613
16.1
Simulating Basic Probability Scenarios
613
16.2
Simulating Conditional Probabilities, Means, and Variances
618
16.3
The Computation of Definite Integrals
620
16.4
Exercises
623
17
Uniformly Distributed Random Numbers
625
17.1
Linear Recurrence Methods
626
17.2
Validating Sequences of Random Numbers
630
17.2.1
The Chi-Square Goodness-of-Fit Test
630
17.2.2
The Kolmogorov-Smirnov Test
633
17.2.3
Run Tests
634
17.2.4
The Gap Test
640
17.2.5
The Poker Test
641
17.2.6
Statistical Test Suites
644
17.3
Exercises
644
xii Contents
18 Nonuniformly
Distributed Random Numbers
647
18.1
The Inverse Transformation Method
647
18.1.1
The Continuous Uniform Distribution
649
18.1.2
Wedge-Shaped Density Functions
649
18.1.3
Triangular Density Functions
650
18.1.4
The Exponential Distribution
652
18.1.5
The Bernoulli Distribution
653
18.1.6
An Arbitrary Discrete Distribution
653
18.2
Discrete Random
Variâtes
by Mimicry
654
18.2.1
The Binomial Distribution
654
18.2.2
The Geometric Distribution
655
18.2.3
The
Poisson
Distribution
656
18.3
The Accept-Reject Method
657
18.3.1
The
Lognormal
Distribution
660
18.4
The Composition Method
662
18.4.1
The Erlang-r Distribution
662
18.4.2
The Hyperexponential Distribution
663
18.4.3
Partitioning of the Density Function
664
18.5
Normally Distributed Random Numbers
670
18.5.1
Normal
Variâtes
via the Central Limit Theorem
670
18.5.2
Normal
Variâtes
via Accept-Reject and Exponential
Bounding Function
670
18.5.3
Normal
Variâtes
via Polar Coordinates
672
18.5.4
Normal
Variâtes
via Partitioning of the Density Function
673
18.6
The Ziggurat Method
673
18.7
Exercises
676
19
Implementing Discrete-Event Simulations
680
19.1
The Structure of a Simulation Model
680
19.2
Some Common Simulation Examples
682
19.2.1
Simulating the
Μ/Μβ
Queue and Some Extensions
682
19.2.2
Simulating Closed Networks of Queues
686
19.2.3
The Machine Repairman Problem
689
19.2.4
Simulating an Inventory Problem
692
19.3
Programming Projects
695
20
Simulation Measurements and Accuracy
697
20.1
Sampling
697
20.1.1
Point Estimators
698
20.1.2
Interval Estimators/Confidence Intervals
704
20.2
Simulation and the Independence Criteria
707
20.3
Variance Reduction Methods
711
20.3.1
Antithetic Variables
711
20.3.2
Control Variables
713
20.4
Exercises
716
Appendix A: The Greek Alphabet
719
Appendix B: Elements of Linear Algebra
721
В
. 1
Vectors and Matrices
721
B.2 Arithmetic on Matrices
721
Contents xiii
8.
3
Vector
and Matrix
Norms
723
8.
4
Vector Spaces
724
8.
5
Determinants
726
B.6 Systems of Linear Equations
728
B.6.1 Gaussian Elimination and
L U
Decompositions
730
В.
7
Eigenvalues and Eigenvectors
734
B.8 Eigenproperties of Decomposable, Nearly Decomposable, and Cyclic
Stochastic Matrices
738
B.8.1 Normal Form
738
B.8.2 Eigenvalues of Decomposable Stochastic Matrices
739
B.8.3 Eigenvectors of Decomposable Stochastic Matrices
741
B.8.
4
Nearly Decomposable Stochastic Matrices
743
B.8.
5
Cyclic Stochastic Matrices
744
Bibliography
745
Index
749
|
| any_adam_object | 1 |
| author | Stewart, William J. 1946- |
| author_GND | (DE-588)124089143 |
| author_facet | Stewart, William J. 1946- |
| author_role | aut |
| author_sort | Stewart, William J. 1946- |
| author_variant | w j s wj wjs |
| building | Verbundindex |
| bvnumber | BV035737621 |
| callnumber-first | Q - Science |
| callnumber-label | QA273 |
| callnumber-raw | QA273 |
| callnumber-search | QA273 |
| callnumber-sort | QA 3273 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 444 SK 820 |
| ctrlnum | (OCoLC)255018592 (DE-599)BVBBV035737621 |
| dewey-full | 519.201/13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.201/13 |
| dewey-search | 519.201/13 |
| dewey-sort | 3519.201 213 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV035737621 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:53:21Z |
| institution | BVB |
| isbn | 9780691140629 |
| language | English |
| lccn | 2008041122 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018014089 |
| oclc_num | 255018592 |
| open_access_boolean | |
| owner | DE-29T DE-634 DE-703 DE-384 DE-824 DE-188 DE-11 DE-473 DE-BY-UBG |
| owner_facet | DE-29T DE-634 DE-703 DE-384 DE-824 DE-188 DE-11 DE-473 DE-BY-UBG |
| physical | XVIII, 758 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| spelling | Stewart, William J. 1946- Verfasser (DE-588)124089143 aut Probability, Markov chains, queues, and simulation the mathematical basis of performance modeling William J. Stewart Princeton [u.a.] Princeton Univ. Press 2009 XVIII, 758 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Probabilities Computer simulation Markov processes Queuing theory Computersimulation (DE-588)4148259-1 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf Datenverarbeitungssystem (DE-588)4125229-9 gnd rswk-swf Leistungsbewertung (DE-588)4167271-9 gnd rswk-swf Datenverarbeitungssystem (DE-588)4125229-9 s Leistungsbewertung (DE-588)4167271-9 s Mathematische Methode (DE-588)4155620-3 s DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Markov-Prozess (DE-588)4134948-9 s Warteschlangentheorie (DE-588)4255044-0 s Computersimulation (DE-588)4148259-1 s Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018014089&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stewart, William J. 1946- Probability, Markov chains, queues, and simulation the mathematical basis of performance modeling Probabilities Computer simulation Markov processes Queuing theory Computersimulation (DE-588)4148259-1 gnd Mathematische Methode (DE-588)4155620-3 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Markov-Prozess (DE-588)4134948-9 gnd Warteschlangentheorie (DE-588)4255044-0 gnd Datenverarbeitungssystem (DE-588)4125229-9 gnd Leistungsbewertung (DE-588)4167271-9 gnd |
| subject_GND | (DE-588)4148259-1 (DE-588)4155620-3 (DE-588)4064324-4 (DE-588)4134948-9 (DE-588)4255044-0 (DE-588)4125229-9 (DE-588)4167271-9 |
| title | Probability, Markov chains, queues, and simulation the mathematical basis of performance modeling |
| title_auth | Probability, Markov chains, queues, and simulation the mathematical basis of performance modeling |
| title_exact_search | Probability, Markov chains, queues, and simulation the mathematical basis of performance modeling |
| title_full | Probability, Markov chains, queues, and simulation the mathematical basis of performance modeling William J. Stewart |
| title_fullStr | Probability, Markov chains, queues, and simulation the mathematical basis of performance modeling William J. Stewart |
| title_full_unstemmed | Probability, Markov chains, queues, and simulation the mathematical basis of performance modeling William J. Stewart |
| title_short | Probability, Markov chains, queues, and simulation |
| title_sort | probability markov chains queues and simulation the mathematical basis of performance modeling |
| title_sub | the mathematical basis of performance modeling |
| topic | Probabilities Computer simulation Markov processes Queuing theory Computersimulation (DE-588)4148259-1 gnd Mathematische Methode (DE-588)4155620-3 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Markov-Prozess (DE-588)4134948-9 gnd Warteschlangentheorie (DE-588)4255044-0 gnd Datenverarbeitungssystem (DE-588)4125229-9 gnd Leistungsbewertung (DE-588)4167271-9 gnd |
| topic_facet | Probabilities Computer simulation Markov processes Queuing theory Computersimulation Mathematische Methode Wahrscheinlichkeitsrechnung Markov-Prozess Warteschlangentheorie Datenverarbeitungssystem Leistungsbewertung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018014089&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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