Allen Probability, Statistics, and Queueing Theory

2. Auflage 2014
ISBN: 978-0-08-057105-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 768 Seiten, Web PDF

Reihe: Computer Science and Scientific Computing

This is a textbook on applied probability and statistics with computer science applications for students at the upper undergraduate level. It may also be used as a self study book for the practicing computer science professional. The successful first edition of this book proved extremely useful to students who need to use probability, statistics and queueing theory to solve problems in other fields, such as engineering, physics, operations research, and management science. The book has also been successfully used for courses in queueing theory for operations research students. This second edition includes a new chapter on regression as well as more than twice as many exercises at the end of each chapter. While the emphasis is the same as in the first edition, this new book makes more extensive use of available personal computer software, such as Minitab and Mathematica.

Arnold O. Allen is a member of the technical staff of the Performance Technology Center at Hewlett-Packard. He received his Ph.D. in mathematics from UCLA. Much of the material in the book was developed for classes in probability, statistics, queueing theory, and computer modeling that he taught as UCLA, IBM, and Hewlett-Packard. Dr. Allen has been active in teaching conference tutorials on computer modeling and was the keynote speaker at two international conferences.

Autoren/Hrsg.

Allen, Arnold O.

Inhaltsverzeichnis

1;Front Cover;1
2;Probability, Statistics, and Queueing Theory: With Computer Science Applications;4
3;Copyright Page;5
4;Table of Contents;8
5;Deditcation;6
6;Preface;12
7;Acknowledgments;20
8;Chapter 1. Introduction;26
9;Part One: Probability;30
9.1;Preface to Part One: Probability;32
9.2;Chapter 2. Probability and Random Variables;34
9.2.1;2.0 Introduction;34
9.2.2;2.1 Sample Spaces and Events;35
9.2.3;2.2 Probability Measures;40
9.2.4;2.3 Combinatorial Analysis;45
9.2.5;2.4 Conditional Probability;49
9.2.6;2.5 Random Variables;59
9.2.7;2.6 Parameters of Random Variables;65
9.2.8;2.7 Jointly Distributed Random Variables;71
9.2.9;2.8 Conditional Expectation;85
9.2.10;2.9 Transform Methods;92
9.2.11;2.10 Inequalities;101
9.2.12;2.11 Exercises;111
9.2.13;References;131
9.3;Chapter 3. Probability Distributions;134
9.3.1;3.0 Introduction;134
9.3.2;3.1 Discrete Random Variables;135
9.3.3;3.2 Continuous Random Variables;146
9.3.4;3.3 Central Limit Theorem;183
9.3.5;3.4 Applied Transforms;189
9.3.6;3.5 Summary;202
9.3.7;3.6 Exercises;204
9.3.8;References;221
9.4;Chapter 4. Stochastic Processes;224
9.4.1;4.0 Introduction;224
9.4.2;4.1 Definitions;225
9.4.3;4.2 The Poisson Process;229
9.4.4;4.3 Birth-and-Death Process;234
9.4.5;4.4 Markov Chains;244
9.4.6;4.5 Renewal Theory;259
9.4.7;4.6 Exercises;263
9.4.8;References;265
10;Part Two: Queueing Models;268
10.1;Preface to Part Two: Queueing Models;270
10.2;Chapter 5. Queueing Theory;272
10.2.1;5.0 Introduction;272
10.2.2;5.1 Describing a Queueing System;276
10.2.3;5.2 Birth-and-Death Process Models;286
10.2.4;5.3 Embedded Markov Chain Systems;326
10.2.5;5.4 Priority Queueing Systems;349
10.2.6;5.5 Bounds and Approximations;361
10.2.7;5.6 Summary;367
10.2.8;5.7 Exercises;367
10.2.9;References;395
10.3;Chapter 6. Queueing Models of Computer Systems;402
10.3.1;6.0 Introduction;402
10.3.2;6.1 Finite Population Models;406
10.3.3;6.2 Jackson Networks;411
10.3.4;6.3 BCMP Queueing Networks;425
10.3.5;6.4 Summary;442
10.3.6;6.5 Exercises;442
10.3.7;References;445
11;Part Three: Statistical Inference;448
11.1;Preface to Part Three: Statistical Inference;450
11.2;Chapter 7. Estimation and Data Analysis;454
11.2.1;7.0 Introduction;454
11.2.2;7.1 Estimators;456
11.2.3;7.2 Confidence Intervals;467
11.2.4;7.3 Exploratory Data Analysis;475
11.2.5;7.4 Exercises;502
11.2.6;References;505
11.3;Chapter 8. Hypothesis Testing;508
11.3.1;8.0 Introduction;508
11.3.2;8.1 Hypothesis Test Procedure;509
11.3.3;8.2 Tests of Means;514
11.3.4;8.3 Tests of Variances;526
11.3.5;8-4 Bernoulli Tests;531
11.3.6;8.5 Chi-Square Tests;540
11.3.7;8.6 EDF Tests;549
11.3.8;8.7 Analysis of Variance;559
11.3.9;8.8 Nonparametric Tests;564
11.3.10;8.9 Summary Table;571
11.3.11;8.10 Exercises;573
11.3.12;References;576
11.4;Chapter 9. Regression and Correlation Analysis;580
11.4.1;9.0 Introduction;580
11.4.2;9.1 Simple Linear Regression;582
11.4.3;9.2 Nonlinear Regression;609
11.4.4;9.3 Multiple Linear Regression;613
11.4.5;9.4 Exercises;635
11.4.6;References;641
12;Appendix A: Statistical Tables;644
12.1;A.1 Discrete Random Variables;644
12.2;A.2 Continuous Random Variables;647
12.3;..3 Statistical Tables;649
12.4;A.4 The Laplace—Stieltjes Transform;661
13;Appendix .: APL Programs;664
13.1;Cited References;664
13.2;B.1 APL Programs;666
13.3;..2 APL Programs;667
13.4;B.3 APL Programs;668
13.5;..4 APL Programs;669
13.6;..5 APL Programs;670
13.7;B.6 APL Programs;671
13.8;..7 APL Programs;672
13.9;B.8 APL Programs;673
13.10;.·9 APL Programs;674
13.11;..10 APL Programs;675
13.12;B.11 APL Programs;676
13.13;..12 APL Programs;677
13.14;B.13 APL Programs;678
13.15;B.14 APL Programs;679
13.16;..15 APL Programs;680
13.17;..16 APL Programs;681
13.18;B.17 APL Programs;682
13.19;..18 APL Programs;683
13.20;B.19 APL Programs;684
13.21;B.20 APL Programs;685
13.22;B.21 APL Programs;686
13.23;B.22 APL Programs;687
13.24;B.23 APL Programs;688
13.25;B.24 APL Programs;689
14;Appendix C: Queueing Theory Formulas;690
14.1;C.1 Notation and Definitions;691
14.2;C.2 Relationships between Random Variables;694
14.3;C.3 M/M/1 Queueing Formulas;695
14.4;C.4 M/M/1/K Queueing Formulas;696
14.5;C.5 M/M/c Queueing Formulas;697
14.6;C.6 M/M/2 Queueing Formulas;700
14.7;C.7 M/M/c/c Queueing Formulas;703
14.8;C.8 M/M/c/K/K Queueing Formulas;704
14.9;C.9 M/M/8 Queueing Formulas;706
14.10;C.10 M/M/1/K/K Queueing Formulas;707
14.11;C.11 M/G/1/K/K Queueing Formulas;709
14.12;C.12 M/M/c/K/K Queueing Formulas;710
14.13;C.13 D/D/c/K/K Queueing Formulas;712
14.14;C.14 M/G/1 Queueing Formulas;713
14.15;C.15 GI/M/1 Queueing Formulas;722
14.16;C.16 GI/M/c Queueing Formulas;723
14.17;C.17 M/G/1 Priority Queueing;725
14.18;C.18 M/M/c Priority Queueing;732
14.19;C.19 Queueing Networks;733
14.20;C.20 Graph of C[c, a];737
14.21;C.21 Graph of B[c, a];738
14.22;C.22 Graph of . for Machine Repair;739
15;Appendix D: Mathematica Programs;740
15.1;Cited References;740
15.2;D.1 Mathematica Programs;740
16;Appendix .: Answers to Exercises;746
16.1;E.1 Answers to Exercises;746
17;Index;756