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E-grāmata: Applied Probability and Stochastic Processes

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  • Formāts: PDF+DRM
  • Izdošanas datums: 27-Nov-2009
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Valoda: eng
  • ISBN-13: 9783642051586
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Applied Probability and Stochastic ProcessesPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 27-Nov-2009
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Valoda: eng
  • ISBN-13: 9783642051586
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This book is a result of teaching stochastic processes to junior and senior undergr- uates and beginning graduate students over many years. In teaching such a course, we have realized a need to furnish students with material that gives a mathematical presentation while at the same time providing proper foundations to allow students to build an intuitive feel for probabilistic reasoning. We have tried to maintain a b- ance in presenting advanced but understandable material that sparks an interest and challenges students, without the discouragement that often comes as a consequence of not understanding the material. Our intent in this text is to develop stochastic p- cesses in an elementary but mathematically precise style and to provide suf cient examples and homework exercises that will permit students to understand the range of application areas for stochastic processes. We also practice active learning in the classroom. In other words, we believe that the traditional practice of lecturing continuously for 50 to 75 minutes is not a very effective method for teaching. Students should somehow engage in the subject m- ter during the teaching session. One effective method for active learning is, after at most 20 minutes of lecture, to assign a small example problem for the students to work and one important tool that the instructor can utilize is the computer. So- times we are fortunate to lecture students in a classroom containing computers with a spreadsheet program, usually Microsofts Excel.

Recenzijas

amazon.con Customer Reviews on 1st edition:



5.0 out of 5 stars It's worth at least six stars!, February 19, 2000 By Lisa Ann Ball (Seattle, WA United States) - See all my reviews



I randomly ran across this book in my math library trying to find an extra book to help with the difficult Stochastics Process class I was taking. Little did I know I would find a book I value as much as Douglas Kelly's Introduction to Probability. This book has applied problems and examples! It is not the dry, endless pages of confusing equations we have come to expect from Stochastics Processes books. There is something better out there! This book saved me as an undergraduate, and am now looking forward to it living up to my God like expectations as a post grad. If you are a professor, please use this book for you students. It ties together and lets you appreciate many fields such as linear analysis and even graph theory from computer science. This book will not disappoint.



5.0 out of 5 stars Best introductory book, February 22, 2001 By Brad (Austin, TX USA) - See all my reviews



Extremely clear, and easy to understand. It is the best introductory book on stochastic processes for non-mathematics major. After you read this book (one month is enough, how amazing it is!), it becomes easier to read "the first course in stochastic processes". The book focuses on the concept and intuition, instead of proof, and I find it is extremely useful for me -- CS major. Strong recommend this great book



5.0 out of 5 stars Good book! , August 13, 2007 By Yuan J. Son (sunnyvale, CA) - See all my reviews A lot of examples, easy to read. A lot of stochastic and queuing books are usually full of notations and theorems, thus hard to understand. However, the author of this book presented the materials in a way that we can actually understand the stochastic processes. If you want to learn queuing and do not have much background, this is the book!!!!

1 Basic Probability Review 1
1.1 Basic Definitions
1
1.2 Random Variables and Distribution Functions
4
1.3 Mean and Variance
10
1.4 Important Distributions
13
1.5 Multivariate Distributions
23
1.6 Combinations of Random Variables
31
1.6.1 Fixed Sum of Random Variables
32
1.6.2 Random Sum of Random Variables
32
1.6.3 Mixtures of Random Variables
34
Appendix
35
Problems
37
References
43
2 Basics of Monte Carlo Simulation 45
2.1 Simulation by Hand
46
2.2 Generation of Random Numbers
49
2.2.1 Multiplicative Linear Congruential Generators
50
2.2.2 A Multiple Recursive Generator
52
2.2.3 Composite Generators
53
2.3 Generation of Random Variates
55
2.3.1 Discrete Random Variates
55
2.3.2 Continuous Random Variates
61
2.3.3 Bivariate Continuous Random Variates
64
2.3.4 Random Variates from Empirical Distributions
66
Appendix
67
Problems
69
References
72
3 Basic Statistical Review 73
3.1 Collection of Data
73
3.1.1 Preliminary Definitions
74
3.1.2 Graphical Representations
75
3.2 Parameter Estimation
78
3.2.1 Method of Moments
80
3.2.2 Maximum Likelihood Estimation
81
3.3 Confidence Intervals
82
3.3.1 Means
83
3.3.2 Proportions
87
3.3.3 Variances
87
3.3.4 Correlation Coefficient
89
3.4 Fitting Distributions
90
3.4.1 The Chi-Square Test
91
3.4.2 The Kolmogorov-Smirnov Test
95
3.5 Fitting Models
99
3.5.1 Ordinary Least Squares Regression
100
3.5.2 Maximum Likelihood Estimates for Linear Models
105
Appendix
105
Problems
109
References
113
4 Poisson Processes 115
4.1 Basic Definitions
115
4.2 Properties and Computations
118
4.3 Extensions of a Poisson Process
121
4.3.1 Compound Poisson Processes
121
4.3.2 Non-stationary Poisson Process
123
4.4 Poisson Regression
124
4.4.1 Poisson Regression with One Independent Variable
124
4.4.2 Poisson Regression with Several Independent Variables
128
Appendix
133
Problems
136
References
139
5 Markov Chains 141
5.1 Basic Definitions
142
5.2 Multistep Transitions
145
5.3 Classification of States
149
5.4 Steady-State Behavior
157
5.5 Computations
162
Appendix
169
Problems
171
References
178
6 Markov Processes 181
6.1 Basic Definitions
181
6.2 Steady-State Properties
184
6.3 Revenues and Costs
188
6.4 lime-Dependent Probabilities
191
Appendix
195
Problems
196
7 Queueing Processes 201
7.1 Basic Definitions and Notation
201
7.2 Single Server Systems
203
7.2.1 Infinite Capacity Single-Server Systems
203
7.2.2 Finite Capacity Single Server Systems
210
7.3 Multiple Server Queues
213
7.4 Approximations
217
Appendix
219
Problems
220
References
225
8 Queueing Networks 227
8.1 Jackson Networks
227
8.1.1 Open Jackson Networks
228
8.1.2 Closed Jackson Networks
232
8.2 Network Approximations
235
8.2.1 Deterministic Routing with Poisson Input
236
8.2.2 Deterministic Routing with non-Poisson Input
242
Appendix
245
Problems
246
References
249
9 Event-Driven Simulation and Output Analyses 251
9.1 Event-Driven Simulations
251
9.2 Statistical Analysis of Output
262
9.2.1 Terminating Simulations
263
9.2.2 Steady-State Simulations
266
9.2.3 Comparing Systems
275
Problems
279
References
284
10 Inventory Theory 285
10.1 The News-Vendor Problem
286
10.2 Single-Period Inventory
289
10.2.1 No Setup Costs
289
10.2.2 Setup Costs
292
10.3 Multi-Period Inventory
295
Problems
299
References
303
11 Replacement Theory 305
11.1 Age Replacement
305
11.1.1 Discrete Life limes
306
11.1.2 Continuous Life limes
309
11.2 Minimal Repair
312
11.2.1 Minimal Repairs without Early Replacements
313
11.2.2 Minimal Repairs with Early Replacements
314
11.3 Block Replacement
316
Problems
319
12 Markov Decision Processes 323
12.1 Basic Definitions
324
12.1.1 Expected Total Discounted Cost Criterion
326
12.1.2 Average Long-Run Cost Criterion
327
12.2 Stationary Policies
327
12.3 Discounted Cost Algorithms
329
12.3.1 Value Improvement for Discounted Costs
331
12.3.2 Policy Improvement for Discounted Costs
332
12.3.3 Linear Programming for Discounted Costs
336
12.4 Average Cost Algorithms
337
12.4.1 Policy Improvement for Average Costs
340
12.4.2 Linear Programming for Average Costs
344
12.5 The Optimal Stopping Problem
346
Problems
349
13 Advanced Queues 355
13.1 Difference Equations
356
13.2 Batch Arrivals
358
13.2.1 Quasi-Birth-Death Processes
360
13.2.2 Batch Arrivals (continued)
362
13.3 Phase-Type Distributions
364
13.4 Systems with Phase-Type Service
368
13.4.1 The M/Ph/1 Queueing System
368
13.4.2 The M/Ph/c Queueing System
372
13.5 Systems with Phase-Type Arrivals
374
Problems
375
References
379
A Matrix Review 381
A.1 Matrix Addition and Subtraction
382
A.2 Matrix Multiplication
382
A.3 Determinants
383
A.4 Determinants by Cofactor Expansion
385
A.5 Nonsingular Matrices
386
A.6 Inversion-in-Place
387
A.7 Derivatives
390
References
392
Index 393
Richard M. Feldman is a Professor of Industrial and Systems Engineering at Texas A&M University. He received a B.A. degree in mathematics from Hope College, an M.S. degree in mathematics from Michigan State University, an M.S. degree in Industrial and Systems Engineering from Ohio University, and a Ph.D. in Industrial Engineering from Northwestern University. His teaching interests include simulation, applied probability, and queueing theory. His consulting and funded research activities have involved modeling and simulation within manufacturing, transportation, and biological contexts. He has received several teaching awards, published papers in applied probability and queueing theory, and co-authored four books.



Ciriaco Valdez-Flores is senior risk assessment consultant at Sielken & Associates Consulting, Inc. He received a bachelors degree from the Tecnológico at Cd. Victoria in México and masters and Ph.D. degrees from Texas A&M University, all in Industrial Engineering. He has taught graduate courses at Texas A&M University focusing in the areas of operations research and applied stochastic processes. As a consultant, he applies his background to the development of new methods of quantitative health risk assessment that incorporate simulation and decision tree theory. He has published in health risk assessment and stochastic processes, co-authored one book and has contributed to books in engineering economy and risk assessment.
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