Traffic processes in queueing networks: a Markov renewal approach
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Baltimore [u.a.]
Johns Hopkins Univ. Pr.
1987
|
| Series: | Johns Hopkins series in the mathematical sciences
4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 251 S. Illustrationen |
| ISBN: | 0801834546 |
Staff View
MARC
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| 245 | 1 | 0 | |a Traffic processes in queueing networks |b a Markov renewal approach |c Ralph L. Disney and Peter C. Kiessler |
| 264 | 1 | |a Baltimore [u.a.] |b Johns Hopkins Univ. Pr. |c 1987 | |
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Record in the Search Index
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| adam_text | Contents
List of Figures and Tables ix
Preface xi
Acknowledgments xvii
Chapter 1. Introduction 1
1. Introduction 1
2. Queueing Networks 2
3. An Important Special Case 3
4. Three Examples of Traffic Properties 6
4.1. Burke s Output Traffic Problem 6
4.2. Palm s Overflow Traffic Problem 7
4.3. Traffic in the Queue with Instantaneous Bernoulli
Feedback 8
5. Point Processes and Queueing Networks 10
5.7. Point Processes 11
5.2. Marked Point Processes 12
6. Probability Structures 12
6.1. Point Process Structures 13
6.2. Marked Point Process Structures 15
Chapter 2. Background 19
1. Introduction 19
2. Markov Renewal Process Structure 20
3. m Step Transition Functions 22
4. Markov Renewal Kernel 25
5. The Classification of States 27
6. Markov Renewal Equations 29
7. Limit Theorems 32
8. Semi Markov Processes 33
9. Markov Chains, Markov Renewal Processes,
and Stationarity 34
10. Examples 36
11. Equivalence 46
12. Lumpability 53
13. Reversibility and Dynamic Reversibility 55
13.1. Reversing Markov Chains 56
v
vi Contents
13.2. Reversing Markov Processes 57
13.3. Dynamically Reversible Markov Processes 57
13.4. Reversing Markov Renewal Processes 57
14. Bibliographic Notes 59
Chapter 3. Examples of Traffic Processes 60
1. Introduction 60
2. A Simulation Analysis of Simple Networks 61
2.1. A Three Node Cyclic Closed Network 62
2.2. Delayed Feedback—Closed Network 63
2.3. Delayed Feedback—Open Network 63
2.4. Positive Autocorrelations in Closed Networks 65
3. Outputs from the Ml Mil Queue 67
4. The MIM/l Overflow Queue with L = 0 70
5. Output from the MIMIML Queue 76
6. A Queue with Delayed Feedback 79
7. Crosscorrelations in Traffic Processes in the Overflow
Queue 81
8. Bibliographic Notes 85
Chapter 4. Traffic Processes in Markov Networks 86
1. Introduction 86
2. Preliminaries 87
3. The Embedded Markov Renewal Process 89
4. Open Jackson Networks 95
5. The Reversibility of Jackson Networks 97
6. Traffic in Reversible Jackson Networks 97
7. Jackson Networks with Instantaneous Feedback 100
8. Closed Jackson Networks 103
9. Traffic in Closed Jackson Networks 105
10. Symmetric Queueing Networks 109
11. Extensions to Networks Where the State Process Is Not
Dynamically Reversible 114
12. Some Implications 118
12.1. The Reversibility of Queue Length Processes and
Traffic Processes 118
12.2. The Reversibility of Point Processes 119
12.3. Reversibility and Operations on Random Processes 119
12.4. Reversible Traffic Processes in Nonreversible
Networks 120
12.5. Implications 121
13. Special Cases 122
14. Bibliographic Notes 123
14.1. State Processes 123
Contents vii
14.2. Traffic Processes in Queueing Networks 124
Chapter 5. Tbe Decomposition of Traffic Processes 126
1. Introduction 126
2. Overflow Queueing Networks 127
3. Semi Markov Switches 132
4. The Classification of States 133
5. A Special Case 136
6. The cth Output Process 141
7. Examples 149
7.1. Decomposing a Compound Poisson Process 149
7.2. Decomposing a Markov Jump Process Whose Jumps
Are Independent of the Point Process 151
8. A Generalization for Traffic Processes 153
9. Two Approaches Compared 159
10. An Example 160
11. Bibliographic Notes 166
Chapter 6. Output Processes 167
1. Introduction 167
2. Outputs from Birth Death Queues 167
3. Outputs from MIGIIIIL oo Queues 171
4. Second Order Statistical Properties of M/GI/1IL , oo
Output Processes—Covariances, Lag 1 177
5. The Ml Mil Queue with Instantaneous Bernoulli Feedback 182
5.7. The Arrival Process 185
5.2. The Output Process 186
5.3. The Input Process 188
5.4. The Feedback Process 188
5.5. Comparisons 189
6. The Queue with Delayed Feedback 190
7. General Delay 196
8. Bibliographic Notes 198
Chapter 7. Decomposing Point and Marked Point Processes:
Crosscovariance and Crosscorrelation Analysis 200
1. Introduction 200
2. Crosscorrelation and Crosscovariance 201
2.1. Decomposing a Point Process 201
2.2. Decomposing a Marked Point Process 202
3. Crosscovariance: A Point Process Decomposed by a
Bernoulli Process 203
4. Decomposing Stationary Renewal Processes 205
5. Decomposing Synchronous Renewal Processes 207
viii Contents
6. Interval Count Relations 209
7. State Dependent Decomposing of a Markov Renewal Process 211
8. Two Examples 214
9. Variances of NA(t), and NB(t) 217
10. Bernoulli Decomposing of Alternating Markov Processes 219
11. Markov Chain Decomposing of Renewal Processes 221
12. Bibliographic Notes 223
Appendix. Point Processes and Reversibility 224
1. Introduction 224
2. Point Processes 225
3. Marked Point Processes 228
4. Stationarity 229
5. Palm Distributions 229
6. Markov Renewal Processes 231
7. Reversing Random Marked Point Processes 232
8. Dynamic Reversibility and Dynamically Reversed
Processes 237
9. Bibliographic Notes 240
References 241
Index 245
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:18:20Z |
| institution | BVB |
| isbn | 0801834546 |
| language | English |
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| publishDate | 1987 |
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| spelling | Disney, Ralph L. 1928- Verfasser (DE-588)131679716 aut Traffic processes in queueing networks a Markov renewal approach Ralph L. Disney and Peter C. Kiessler Baltimore [u.a.] Johns Hopkins Univ. Pr. 1987 XIX, 251 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Johns Hopkins series in the mathematical sciences 4 Files d'attente, Théorie des Markov, Processus de Markov processes Queuing theory Erneuerungsprozess (DE-588)4152833-5 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Warteschlangennetz (DE-588)4225823-6 gnd rswk-swf Wartesystem (DE-588)4251734-5 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 s Warteschlangennetz (DE-588)4225823-6 s DE-604 Wartesystem (DE-588)4251734-5 s Erneuerungsprozess (DE-588)4152833-5 s Kiessler, Peter C. 1955- Verfasser (DE-588)131679740 aut Johns Hopkins series in the mathematical sciences 4 (DE-604)BV000016231 4 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000449547&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Disney, Ralph L. 1928- Kiessler, Peter C. 1955- Traffic processes in queueing networks a Markov renewal approach Johns Hopkins series in the mathematical sciences Files d'attente, Théorie des Markov, Processus de Markov processes Queuing theory Erneuerungsprozess (DE-588)4152833-5 gnd Markov-Prozess (DE-588)4134948-9 gnd Warteschlangennetz (DE-588)4225823-6 gnd Wartesystem (DE-588)4251734-5 gnd |
| subject_GND | (DE-588)4152833-5 (DE-588)4134948-9 (DE-588)4225823-6 (DE-588)4251734-5 |
| title | Traffic processes in queueing networks a Markov renewal approach |
| title_auth | Traffic processes in queueing networks a Markov renewal approach |
| title_exact_search | Traffic processes in queueing networks a Markov renewal approach |
| title_full | Traffic processes in queueing networks a Markov renewal approach Ralph L. Disney and Peter C. Kiessler |
| title_fullStr | Traffic processes in queueing networks a Markov renewal approach Ralph L. Disney and Peter C. Kiessler |
| title_full_unstemmed | Traffic processes in queueing networks a Markov renewal approach Ralph L. Disney and Peter C. Kiessler |
| title_short | Traffic processes in queueing networks |
| title_sort | traffic processes in queueing networks a markov renewal approach |
| title_sub | a Markov renewal approach |
| topic | Files d'attente, Théorie des Markov, Processus de Markov processes Queuing theory Erneuerungsprozess (DE-588)4152833-5 gnd Markov-Prozess (DE-588)4134948-9 gnd Warteschlangennetz (DE-588)4225823-6 gnd Wartesystem (DE-588)4251734-5 gnd |
| topic_facet | Files d'attente, Théorie des Markov, Processus de Markov processes Queuing theory Erneuerungsprozess Markov-Prozess Warteschlangennetz Wartesystem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000449547&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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