Probability models in operations research:
Abstract:. - http://www3.openu.ac.il/ouweb/owal/new_books1.book_desc?in_mis_cat=128683.
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press Taylor & Francis
2009
|
| Series: | The operations research series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | Abstract:. - http://www3.openu.ac.il/ouweb/owal/new_books1.book_desc?in_mis_cat=128683. |
| Item Description: | Includes bibliographical references and index Erscheint: Juli 2008 |
| Physical Description: | XIV, 208 S. |
| ISBN: | 9781420054897 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface
..........................................................................................................xi
Authors
......................................................................................................xiii
1
Probability Modeling Fundamentals
...............................................1
1.1
Random Experiments and Events
......................................................2
1.2
Probability
..............................................................................................8
1.3
Conditional Probability
......................................................................11
Homework Problems
..................................................................................15
1.1
Random Experiments and Events
.........................................15
1.2
Probability
................................................................................16
1.3
Conditional Probability
..........................................................17
Application: Basic Reliability Theory
.......................................................19
2
Analysis of Random Variables
.......................................................23
2.1
Introduction to Random Variables
...................................................23
2.2
Discrete Random Variables
...............................................................25
2.3
Continuous Random Variables
.........................................................26
2.4
Expectation
...........................................................................................29
2.5
Generating Functions
.........................................................................33
2.6
Common Applications of Random Variables
.................................35
2.6.1
Equally Likely Alternatives
...................................................35
2.6.2
Random Sampling
...................................................................39
2.6.3
Normal Random Variables
.....................................................41
Homework Problems
..................................................................................42
2.2
Discrete Random Variables
...............................................................42
2.3
Continuous Random Variables
.........................................................43
2.4
Expectation
...........................................................................................43
2.5
Generating Functions
.........................................................................44
2.6
Common Applications of Random Variables
.................................45
Application: Basic Warranty Modeling
....................................................45
3
Analysis of Multiple Random Variables
.......................................49
3.1
Two Random Variables
.......................................................................49
3.1.1
Two Discrete Random Variables
...........................................50
3.1.2
Two Continuous Random Variables
.....................................52
3.1.3
Expectation
...............................................................................55
3.2
Common Applications of Multiple Random Variables
.................61
3.2.1
The Multinomial Distribution
...............................................61
3.2.2
The Bivariate Normal Distribution
.......................................62
3.3
Analyzing Discrete Random Variables Using Conditional
Probability
............................................................................................62
Ό
vi
Contents
3.4
Analyzing Continuous Random Variables Using
Conditional Probability
......................................................................67
3.5
Computing Expectations by Conditioning
.....................................70
3.6
Computing Probabilities by Conditioning
......................................75
Homework Problems
..................................................................................77
3.1
Two Random Variables
...........................................................77
3.2
Common Applications of Multiple Random Variables
......79
3.3
Analyzing Discrete Random Variables Using
Conditional Probability
..........................................................79
3.4
Analyzing Continuous Random Variables Using
Conditional Probability
..........................................................80
3.5
Computing Expectations by Conditioning
..........................81
3.6
Computing Probabilities by Conditioning
..........................83
Application: Bivariate Warranty Modeling
.............................................84
4
Introduction to Stochastic Processes
.............................................89
4.1
Introduction to Stochastic Processes
................................................89
4.2
Introduction to Counting Processes
.................................................90
4.3
Introduction to Renewal Processes
..................................................91
4.3.1
Renewal-Reward Processes
....................................................94
4.3.2
Alternating Renewal Processes
.............................................95
4.4
Bernoulli Processes
.............................................................................97
Homework Problems
................................................................................102
4.1
Introduction to Stochastic Processes
..................................102
4.2
Introduction to Counting Processes
...................................102
4.3
Introduction to Renewal Processes
.....................................102
4.4
Bernoulli Processes
...............................................................104
Application: Acceptance Sampling
.........................................................105
5
Poisson
Processes
............................................................................
Ill
5.1
Introduction to
Poisson
Processes
..................................................
Ill
5.2
Interarrivai
Times
.............................................................................114
5.3
Arrival Times
.....................................................................................118
5.4
Decomposition and Superposition of
Poisson
Processes
............121
5.5
Competing
Poisson
Processes
.........................................................124
5.6
Nonhomogeneous
Poisson
Processes
............................................125
Homework Problems
................................................................................126
5.1
Introduction to
Poisson
Processes
......................................126
5.2
Interarrivai
Times
..................................................................128
5.3
Arrival Times
.........................................................................130
5.4
Decomposition and Superposition of
Poisson
Processes
.................................................................................131
5.5
Competing
Poisson
Processes
.............................................133
5.6
Nonhomogeneous
Poisson
Processes
.................................133
Application: Repairable Equipment
........................................................134
Contents
vii
6
Discrete-Time Markov Chains
.....................................................137
6.1
Introduction
.......................................................................................137
6.2
Manipulating the Transition Probability Matrix
..........................141
6.3
Classification of States
......................................................................147
6.4
Limiting Behavior
.............................................................................149
6.5
Absorbing States
................................................................................152
Homework Problems
................................................................................157
6.1
Introduction
............................................................................157
6.2
Manipulating the Transition Probability Matrix
..............159
6.3
Classification of States
..........................................................161
6.4
Limiting Behavior
.................................................................161
6.5
Absorbing States
....................................................................162
Application: Inventory Management
......................................................163
7
Continuous-Time Markov Chains
................................................165
7.1
Introduction
.......................................................................................165
7.2
Birth and Death Processes
...............................................................168
7.3
Limiting Probabilities
.......................................................................170
7.4
Time-Dependent Behavior
...............................................................173
7.5
Semi-Markov Processes
...................................................................176
Homework Problems
................................................................................177
7.2
Birth and Death Processes
...................................................177
7.3
Limiting Probabilities
...........................................................177
7.5
Semi-Markov Processes
........................................................179
8
Markovian Queueing Systems
......................................................181
8.1
Queueing Basics
................................................................................181
8.2
The M/M/l Queue
...........................................................................184
8.3
The M/M/l/c Queue
........................................................................186
8.4
The M/M/s Queue
............................................................................188
8.5
The M/M/s/c Queue
.........................................................................191
8.6
The M/G/l Queue
............................................................................193
8.7
Networks of Queues
.........................................................................194
Homework Problems
................................................................................196
8.1
Queueing Basics
.....................................................................196
8.2
The M/M/l Queue
................................................................197
8.3
The M/M/l/c Queue
............................................................197
8.4
The M/M/s Queue
................................................................198
8.5
The M/M/s/c Queue
.............................................................198
8.6
The M/G/l Queue
.................................................................198
8.7
Networks of Queues
.............................................................199
Bibliography
.............................................................................................201
Index
..........................................................................................................203
|
| adam_txt |
Contents
Preface
.xi
Authors
.xiii
1
Probability Modeling Fundamentals
.1
1.1
Random Experiments and Events
.2
1.2
Probability
.8
1.3
Conditional Probability
.11
Homework Problems
.15
1.1
Random Experiments and Events
.15
1.2
Probability
.16
1.3
Conditional Probability
.17
Application: Basic Reliability Theory
.19
2
Analysis of Random Variables
.23
2.1
Introduction to Random Variables
.23
2.2
Discrete Random Variables
.25
2.3
Continuous Random Variables
.26
2.4
Expectation
.29
2.5
Generating Functions
.33
2.6
Common Applications of Random Variables
.35
2.6.1
Equally Likely Alternatives
.35
2.6.2
Random Sampling
.39
2.6.3
Normal Random Variables
.41
Homework Problems
.42
2.2
Discrete Random Variables
.42
2.3
Continuous Random Variables
.43
2.4
Expectation
.43
2.5
Generating Functions
.44
2.6
Common Applications of Random Variables
.45
Application: Basic Warranty Modeling
.45
3
Analysis of Multiple Random Variables
.49
3.1
Two Random Variables
.49
3.1.1
Two Discrete Random Variables
.50
3.1.2
Two Continuous Random Variables
.52
3.1.3
Expectation
.55
3.2
Common Applications of Multiple Random Variables
.61
3.2.1
The Multinomial Distribution
.61
3.2.2
The Bivariate Normal Distribution
.62
3.3
Analyzing Discrete Random Variables Using Conditional
Probability
.62
Ό
vi
Contents
3.4
Analyzing Continuous Random Variables Using
Conditional Probability
.67
3.5
Computing Expectations by Conditioning
.70
3.6
Computing Probabilities by Conditioning
.75
Homework Problems
.77
3.1
Two Random Variables
.77
3.2
Common Applications of Multiple Random Variables
.79
3.3
Analyzing Discrete Random Variables Using
Conditional Probability
.79
3.4
Analyzing Continuous Random Variables Using
Conditional Probability
.80
3.5
Computing Expectations by Conditioning
.81
3.6
Computing Probabilities by Conditioning
.83
Application: Bivariate Warranty Modeling
.84
4
Introduction to Stochastic Processes
.89
4.1
Introduction to Stochastic Processes
.89
4.2
Introduction to Counting Processes
.90
4.3
Introduction to Renewal Processes
.91
4.3.1
Renewal-Reward Processes
.94
4.3.2
Alternating Renewal Processes
.95
4.4
Bernoulli Processes
.97
Homework Problems
.102
4.1
Introduction to Stochastic Processes
.102
4.2
Introduction to Counting Processes
.102
4.3
Introduction to Renewal Processes
.102
4.4
Bernoulli Processes
.104
Application: Acceptance Sampling
.105
5
Poisson
Processes
.
Ill
5.1
Introduction to
Poisson
Processes
.
Ill
5.2
Interarrivai
Times
.114
5.3
Arrival Times
.118
5.4
Decomposition and Superposition of
Poisson
Processes
.121
5.5
Competing
Poisson
Processes
.124
5.6
Nonhomogeneous
Poisson
Processes
.125
Homework Problems
.126
5.1
Introduction to
Poisson
Processes
.126
5.2
Interarrivai
Times
.128
5.3
Arrival Times
.130
5.4
Decomposition and Superposition of
Poisson
Processes
.131
5.5
Competing
Poisson
Processes
.133
5.6
Nonhomogeneous
Poisson
Processes
.133
Application: Repairable Equipment
.134
Contents
vii
6
Discrete-Time Markov Chains
.137
6.1
Introduction
.137
6.2
Manipulating the Transition Probability Matrix
.141
6.3
Classification of States
.147
6.4
Limiting Behavior
.149
6.5
Absorbing States
.152
Homework Problems
.157
6.1
Introduction
.157
6.2
Manipulating the Transition Probability Matrix
.159
6.3
Classification of States
.161
6.4
Limiting Behavior
.161
6.5
Absorbing States
.162
Application: Inventory Management
.163
7
Continuous-Time Markov Chains
.165
7.1
Introduction
.165
7.2
Birth and Death Processes
.168
7.3
Limiting Probabilities
.170
7.4
Time-Dependent Behavior
.173
7.5
Semi-Markov Processes
.176
Homework Problems
.177
7.2
Birth and Death Processes
.177
7.3
Limiting Probabilities
.177
7.5
Semi-Markov Processes
.179
8
Markovian Queueing Systems
.181
8.1
Queueing Basics
.181
8.2
The M/M/l Queue
.184
8.3
The M/M/l/c Queue
.186
8.4
The M/M/s Queue
.188
8.5
The M/M/s/c Queue
.191
8.6
The M/G/l Queue
.193
8.7
Networks of Queues
.194
Homework Problems
.196
8.1
Queueing Basics
.196
8.2
The M/M/l Queue
.197
8.3
The M/M/l/c Queue
.197
8.4
The M/M/s Queue
.198
8.5
The M/M/s/c Queue
.198
8.6
The M/G/l Queue
.198
8.7
Networks of Queues
.199
Bibliography
.201
Index
.203 |
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| id | DE-604.BV035188075 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T23:00:41Z |
| indexdate | 2024-07-09T21:27:01Z |
| institution | BVB |
| isbn | 9781420054897 |
| language | English |
| lccn | 2008023731 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016994734 |
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| physical | XIV, 208 S. |
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| publisher | CRC Press Taylor & Francis |
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| spelling | Cassady, C. Richard Verfasser aut Probability models in operations research C. Richard Cassady ; Joel A. Nachlas Boca Raton [u.a.] CRC Press Taylor & Francis 2009 XIV, 208 S. txt rdacontent n rdamedia nc rdacarrier The operations research series Includes bibliographical references and index Erscheint: Juli 2008 Abstract:. - http://www3.openu.ac.il/ouweb/owal/new_books1.book_desc?in_mis_cat=128683. Mathematik Operations research Mathematics Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Operations Research (DE-588)4043586-6 gnd rswk-swf Operations Research (DE-588)4043586-6 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Nachlas, Joel A. Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016994734&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cassady, C. Richard Nachlas, Joel A. Probability models in operations research Mathematik Operations research Mathematics Stochastisches Modell (DE-588)4057633-4 gnd Operations Research (DE-588)4043586-6 gnd |
| subject_GND | (DE-588)4057633-4 (DE-588)4043586-6 |
| title | Probability models in operations research |
| title_auth | Probability models in operations research |
| title_exact_search | Probability models in operations research |
| title_exact_search_txtP | Probability models in operations research |
| title_full | Probability models in operations research C. Richard Cassady ; Joel A. Nachlas |
| title_fullStr | Probability models in operations research C. Richard Cassady ; Joel A. Nachlas |
| title_full_unstemmed | Probability models in operations research C. Richard Cassady ; Joel A. Nachlas |
| title_short | Probability models in operations research |
| title_sort | probability models in operations research |
| topic | Mathematik Operations research Mathematics Stochastisches Modell (DE-588)4057633-4 gnd Operations Research (DE-588)4043586-6 gnd |
| topic_facet | Mathematik Operations research Mathematics Stochastisches Modell Operations Research |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016994734&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT cassadycrichard probabilitymodelsinoperationsresearch AT nachlasjoela probabilitymodelsinoperationsresearch |