Probability Models in Operations Research

by Cassady; C. Richard

• ISBN13: 9781420054897
• ISBN10: 1420054899
• Edition: 1st
• Format: Hardcover
• Copyright: 2008-08-05
• Publisher: CRC Press

Summary

Balancing applications with mathematical rigor, Probability Models in Operations Researchprovides an introduction to the use of probability to define models that have applications in industrial engineering and operations research. With a concise review of the key components of probability theory, this book offers coverage of all basic model forms, probability modeling fundamentals, random variables analysis, multiple random variables analysis, Bernoulli processes, discrete-time Markov chains, Poisson processes, renewal processes, continuous-time Markov chains, and queueing theory. The text serves as a practical reference for those who use probability to model system behaviors.

Table of Contents

Preface	p. xi
Authors	p. xiii
Probability Modeling Fundamentals	p. 1
Random Experiments and Events	p. 2
Probability	p. 8
Conditional Probability	p. 11
Homework Problems	p. 15
Random Experiments and Events	p. 15
Probability	p. 16
Conditional Probability	p. 17
Application: Basic Reliability Theory	p. 19
Analysis of Random Variables	p. 23
Introduction to Random Variables	p. 23
Discrete Random Variables	p. 25
Continuous Random Variables	p. 26
Expectation	p. 29
Generating Functions	p. 33
Common Applications of Random Variables	p. 35
Equally Likely Alternatives	p. 35
Random Sampling	p. 39
Normal Random Variables	p. 41
Homework Problems	p. 42
Discrete Random Variables	p. 42
Continuous Random Variables	p. 43
Expectation	p. 43
Generating Functions	p. 44
Common Applications of Random Variables	p. 45
Application: Basic Warranty Modeling	p. 45
Analysis of Multiple Random Variables	p. 49
Two Random Variables	p. 49
Two Discrete Random Variables	p. 50
Two Continuous Random Variables	p. 52
Expectation	p. 55
Common Applications of Multiple Random Variables	p. 61
The Multinomial Distribution	p. 61
The Bivariate Normal Distribution	p. 62
Analyzing Discrete Random Variables Using Conditional Probability	p. 62
Analyzing Continuous Random Variables Using Conditional Probability	p. 67
Computing Expectations by Conditioning	p. 70
Computing Probabilities by Conditioning	p. 75
Homework Problems	p. 77
Two Random Variables	p. 77
Common Applications of Multiple Random Variables	p. 79
Analyzing Discrete Random Variables Using Conditional Probability	p. 79
Analyzing Continuous Random Variables Using Conditional Probability	p. 80
Computing Expectations by Conditioning	p. 81
Computing Probabilities by Conditioning	p. 83
Application: Bivariate Warranty Modeling	p. 84
Introduction to Stochastic Processes	p. 89
Introduction to Stochastic Processes	p. 89
Introduction to Counting Processes	p. 90
Introduction to Renewal Processes	p. 91
Renewal-Reward Processes	p. 94
Alternating Renewal Processes	p. 95
Bernoulli Processes	p. 97
Homework Problems	p. 102
Introduction to Stochastic Processes	p. 102
Introduction to Counting Processes	p. 102
Introduction to Renewal Processes	p. 102
Bernoulli Processes	p. 104
Application: Acceptance Sampling	p. 105
Poisson Processes	p. 111
Introduction to Poisson Processes	p. 111
Interarrival Times	p. 114
Arrival Times	p. 118
Decomposition and Superposition of Poisson Processes	p. 121
Competing Poisson Processes	p. 124
Nonhomogeneous Poisson Processes	p. 125
Homework Problems	p. 126
Introduction to Poisson Processes	p. 126
Interarrival Times	p. 128
Arrival Times	p. 130
Decomposition and Superposition of Poisson Processes	p. 131
Competing Poisson Processes	p. 133
Nonhomogeneous Poisson Processes	p. 133
Application: Repairable Equipment	p. 134
Discrete-Time Markov Chains	p. 137
Introduction	p. 137
Manipulating the Transition Probability Matrix	p. 141
Classification of States	p. 147
Limiting Behavior	p. 149
Absorbing States	p. 152
Homework Problems	p. 157
Introduction	p. 157
Manipulating the Transition Probability Matrix	p. 159
Classification of States	p. 161
Limiting Behavior	p. 161
Absorbing States	p. 162
Application: Inventory Management	p. 163
Continuous-Time Markov Chains	p. 165
Introduction	p. 165
Birth and Death Processes	p. 168
Limiting Probabilities	p. 170
Time-Dependent Behavior	p. 173
Semi-Markov Processes	p. 176
Homework Problems	p. 177
Birth and Death Processes	p. 177
Limiting Probabilities	p. 177
Semi-Markov Processes	p. 179
Markovian Queueing Systems	p. 181
Queueing Basics	p. 181
The M/M/1 Queue	p. 184
The M/M/1/c Queue	p. 186
The M/M/s Queue	p. 188
The M/M/s/c Queue	p. 191
The M/G/1 Queue	p. 193
Networks of Queues	p. 194
Homework Problems	p. 196
Queueing Basics	p. 196
The M/M/1 Queue	p. 197
The M/M/1/c Queue	p. 197
The M/M/s Queue	p. 198
The M/M/s/c Queue	p. 198
The M/G/1 Queue	p. 198
Networks of Queues	p. 199
Bibliography	p. 201
Index	p. 203
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