Stochastic storage processes: queues, insurance risk, dams, and data communication
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Springer
1998
|
| Edition: | 2. ed. |
| Series: | Applications of mathematics
15 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 206 S. |
| ISBN: | 0387982485 3540905227 |
Staff View
MARC
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| 245 | 1 | 0 | |a Stochastic storage processes |b queues, insurance risk, dams, and data communication |c N. U. Prabhu |
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Record in the Search Index
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| adam_text | Contents
Preface to the Second Edition vii
Preface to the First Edition ix
Abbreviations and Notation xv
Introduction 1
1. A Class of Stochastic Models 1
1.1 The Single Server Queueing System 1
1.2 Inventory Models 2
1.3 Storage Models 4
1.4 Insurance Risk 4
1.5 Continuous Time Inventory and Storage Models 5
2. Problems Arising from the Models 6
3. The Scope of This Book 7
4. Further Remarks 8
4.1 Queues 8
4.2 Inventory Models 8
4.3 Models for Dams 9
4.4 Insurance Risk 9
4.5 Data Communication Models 9
Problems 10
Selected Bibliography 14
Parti. The Single Server Queue 17
1. The Queue GI/G/1 19
1. Orientation 19
2. Ladder Processes 21
3. Two Renewal Functions 23
4. Maximum and Minimum 24
xi
xii Contents
5. Application to the Queue GI/G/1 27
6. The Principle of Duality 30
7. The Queue M/M/l 31
8. The Queues GI/M/1 and M/G/l 33
8.1 The Queue GI/M/1 33
8.2 The Queue M/G/l 36
9. Transforms 37
10. The Queues GI/Et/l and E^/G/l 42
10.1 The Queue GI/Efc/1 42
10.2 The Queue E^/G/l 44
11. Further Problems in the Queue GI/G/1 44
12. A Random Walk on the Half Plane 45
13. Applications to the Queue GI/G/1 48
13.1 The Queue GI/M/1 49
13.2 The Queue M/G/l 50
14. The Busy and Idle Periods 50
15. Compound Renewal Processes 52
16. Further Remarks 56
Problems 57
2. Further Results for the Queue GI/G/1 61
1. Orientation 61
2. The Workload and Idle Time 61
3. The Workload and Idle Time in GI/M/1 64
4. The Workload and Idle Time in M/G/l 66
5. The Queue Length in GI/M/1 67
6. The Queue Length in M/G/l 71
7. The Queue M/D/l 75
8. The Queue D/M/l 78
9. Bulk Queues 81
10. The Queue M(X)/G(y)/l 83
11. The Queue G(X)/M(y)/l 86
12. The Queue Length in E4/G/l and GI/E^/1 88
Problems 89
3. The Queue M/M/l 91
1. Introduction 91
2. The Net Input Process X(t) 92
3. The Busy Period 94
4. The Distribution of Q(t) 95
5. The Output 98
Problems 100
References 101
Contents xiii
Part II. Continuous Time Storage Models 103
4. The Basic Storage Model 105
1. Orientation 105
2. Levy Processes 107
2.1 A Continuous Time Model for a Dam 110
3. A Generalized Storage Model 113
4. A First Passage Time 120
5. Applications to M/G/l and Related Models 121
6. The Process {T(x), x 0} in M/G/l 122
7. The Process {T(x), x 0} in Dam Models 125
8. Limit Theorems for {T{x), x 0} 127
9. Insurance Risk: Two Special Cases 128
10. The Ladder Process {T*, Y(J£} 129
11. Limit Theorems for the Storage Process 132
12. Dams of Infinite Depth 135
13. The Insurance Risk Problem: General Case 138
14. A Storage Model with Random Output 141
15. Queues with Static Priorities 142
16. Queues with Dynamic Priorities 145
Problems 147
References 150
Partm. Markov Modulated Storage Models 153
5. The Markov Modulated Single Server Queue 155
1. Introduction 155
2. The Adjoint Queue 156
3. Wiener Hopf Factorization; Fluctuation Theory 157
4. The Waiting Time and Idle Time 160
5. The Markov Modulated M/M/l Queue 161
6. Further Remarks 164
Problems 165
6. A Fluid Model for Data Communication 166
1. Introductory Examples 166
2. The Storage Model 168
3. The Net Input Process 170
4. TheMRW{rn,5n Jn) 172
5. The Busy Period 176
6. The Storage Process {Z(r), / (t), J(t)} 176
7. Further Remarks 179
xiv Contents
7. A Data Communication Model with Packets 180
1. Introduction 180
2. The Model 182
3. The Busy Period Process 184
4. The Unsatisfied Demand / (r) 187
5. The Storage Process {Z(t), lit), J(t)} 188
6. Further Remarks 192
Problems 192
References 193
Appendix 195
Appendix A 195
Appendix B 197
Appendix C 199
|
| any_adam_object | 1 |
| author | Prabhu, Narahari U. 1924- |
| author_GND | (DE-588)118076183 |
| author_facet | Prabhu, Narahari U. 1924- |
| author_role | aut |
| author_sort | Prabhu, Narahari U. 1924- |
| author_variant | n u p nu nup |
| building | Verbundindex |
| bvnumber | BV011692514 |
| callnumber-first | T - Technology |
| callnumber-label | T57 |
| callnumber-raw | T57.9.P63 1998 |
| callnumber-search | T57.9.P63 1998 |
| callnumber-sort | T 257.9 P63 41998 |
| callnumber-subject | T - General Technology |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)37748477 (DE-599)BVBBV011692514 |
| dewey-full | 519.8/221 519.8/2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.8/2 21 519.8/2 |
| dewey-search | 519.8/2 21 519.8/2 |
| dewey-sort | 3519.8 12 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| physical | XVI, 206 S. |
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| series | Applications of mathematics |
| series2 | Applications of mathematics |
| spelling | Prabhu, Narahari U. 1924- Verfasser (DE-588)118076183 aut Stochastic storage processes queues, insurance risk, dams, and data communication N. U. Prabhu 2. ed. New York Springer 1998 XVI, 206 S. txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 15 Files d'attente, Théorie des ram PROCESSOS ESTOCASTICOS larpcal Stochastische processen gtt TEORIA DAS FILAS larpcal Wachttijdproblemen gtt file attente inriac modèle file attente inriac processus stochastique inriac stockage inriac Queuing theory Stochastic processes Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Applications of mathematics 15 (DE-604)BV000895226 15 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007884331&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Prabhu, Narahari U. 1924- Stochastic storage processes queues, insurance risk, dams, and data communication Applications of mathematics Files d'attente, Théorie des ram PROCESSOS ESTOCASTICOS larpcal Stochastische processen gtt TEORIA DAS FILAS larpcal Wachttijdproblemen gtt file attente inriac modèle file attente inriac processus stochastique inriac stockage inriac Queuing theory Stochastic processes Warteschlangentheorie (DE-588)4255044-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4255044-0 (DE-588)4057630-9 |
| title | Stochastic storage processes queues, insurance risk, dams, and data communication |
| title_auth | Stochastic storage processes queues, insurance risk, dams, and data communication |
| title_exact_search | Stochastic storage processes queues, insurance risk, dams, and data communication |
| title_full | Stochastic storage processes queues, insurance risk, dams, and data communication N. U. Prabhu |
| title_fullStr | Stochastic storage processes queues, insurance risk, dams, and data communication N. U. Prabhu |
| title_full_unstemmed | Stochastic storage processes queues, insurance risk, dams, and data communication N. U. Prabhu |
| title_short | Stochastic storage processes |
| title_sort | stochastic storage processes queues insurance risk dams and data communication |
| title_sub | queues, insurance risk, dams, and data communication |
| topic | Files d'attente, Théorie des ram PROCESSOS ESTOCASTICOS larpcal Stochastische processen gtt TEORIA DAS FILAS larpcal Wachttijdproblemen gtt file attente inriac modèle file attente inriac processus stochastique inriac stockage inriac Queuing theory Stochastic processes Warteschlangentheorie (DE-588)4255044-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Files d'attente, Théorie des PROCESSOS ESTOCASTICOS Stochastische processen TEORIA DAS FILAS Wachttijdproblemen file attente modèle file attente processus stochastique stockage Queuing theory Stochastic processes Warteschlangentheorie Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007884331&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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