Asymptotic methods in queuing theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Chichester [u.a.]
Wiley
1984
|
| Series: | Wiley series in probability and mathematical statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | EST: Asimptotičeskie metodi v teorii massovogo obsluživanija (engl.) |
| Physical Description: | XI, 292 S. |
| ISBN: | 0471902861 |
Staff View
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| 100 | 1 | |a Borovkov, Aleksandr A. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Asimptotičeskie metody v teorii massovogo obsluživanija |
| 245 | 1 | 0 | |a Asymptotic methods in queuing theory |c Alexander A. Borovkov |
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 1984 | |
| 300 | |a XI, 292 S. | ||
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Record in the Search Index
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| adam_text | Contents
FOREWORD vii
CHAPTER 1: ON THE CONVERGENCE OF RANDOM
PROCESSES 1
1.1. General definitions and theorems 1
1.2. Fundamental aspects of convergence of processes 5
1.3. The fundamental types of limit processes 9
1.4. Conditions for convergence to degenerate processes 26
1.5. Conditions for convergence to a process of unbounded diffusion 35
1.6. The proof of theorem 1 of section 1.5 39
1.7. The proof of theorem 2 of section 1.5 48
1.8. Conditions for mean convergence to an unbounded diffusion 52
1.9. Convergence to diffusion processes with reflection at a
boundary 54
1.10. Conditions for convergence to a diffusion with two reflecting
boundaries 64
1.11. Examples 64
1.12. The connection between the conditions of theorem 1 of section
1.5 and strong mixing conditions 72
CHAPTER 2: LIMIT THEOREMS FOR SYSTEMS WITH
INTENSIVE INPUT STREAM AND
A LARGE NUMBER OF SERVICE CHANNELS 83
2.1. Description of the systems. Rough theorems for the number of
busy lines and for the probability of refusal 85
2.2. Limit theorems for the number of busy lines for underloaded
systems 102
2.3. Convergence to a stationary process 112
2.4.* The connection with branching processes with intensive
immigration 119
v
vi CONTENTS
2.5.* On limit processes for loaded systems with refusals and with
queues 124
2.6.* Generalization of the basic results of sections 2.2 and 2.3 to
the case of dependent waiting times 128
2.7. The distribution of the number of free channels for overloaded
systems 138
CHAPTER 3: THE DESCRIPTION OF SERVICE
SYSTEMS BY DIFFUSION PROCESSES 142
3.1. The notions of independence of input and output streams and
stochastic control 145
3.2. Preliminary remarks on approximation by diffusion processes 153
3.3. General theorems on convergence of the normalized
occupation1 q(t) to a diffusion process 157
3.4. Multichannel systems with intensive input streams 172
3.5. Independent input stream and stochastic control of refusals 182
3.6. Properties of systems with independent output. Loaded systems 192
3.7. A numerical example 200
CHAPTER 4: STABILITY THEOREMS 204
4.1. Subsidiary results on the distribution of the maximum of sequences of
sums of stationarily related variables 207
4.2. Stability theorems for single channel systems with waiting and
systems with autonomous service 218
4.3. Some estimates for the speed of convergence 226
4.4. Ergodicity and stability theorems for random walks in a strip
and their application to single channel systems with constraints 240
4.5. Stability theorems for systems with an infinite number of
service channels 251
4.6. General ergodic theorems and stability theorems for sequences
wn + 1 =/(wB, tb) 258
4.7. Ergodic theorems and stability theorems for multichannel
systems with refusals and with queues 266
REFERENCES 285
SUBJECT INDEX 291
|
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| ctrlnum | (OCoLC)9731893 (DE-599)BVBBV002035753 |
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| dewey-search | 519.8/2 |
| dewey-sort | 3519.8 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV002035753 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:39:16Z |
| institution | BVB |
| isbn | 0471902861 |
| language | English Russian |
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| physical | XI, 292 S. |
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| publishDate | 1984 |
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| publisher | Wiley |
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| series2 | Wiley series in probability and mathematical statistics |
| spelling | Borovkov, Aleksandr A. Verfasser aut Asimptotičeskie metody v teorii massovogo obsluživanija Asymptotic methods in queuing theory Alexander A. Borovkov Chichester [u.a.] Wiley 1984 XI, 292 S. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics EST: Asimptotičeskie metodi v teorii massovogo obsluživanija (engl.) Wachttijdproblemen gtt Asymptotic expansions Queuing theory Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 s Asymptotische Methode (DE-588)4287476-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001331030&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Borovkov, Aleksandr A. Asymptotic methods in queuing theory Wachttijdproblemen gtt Asymptotic expansions Queuing theory Asymptotische Methode (DE-588)4287476-2 gnd Warteschlangentheorie (DE-588)4255044-0 gnd |
| subject_GND | (DE-588)4287476-2 (DE-588)4255044-0 |
| title | Asymptotic methods in queuing theory |
| title_alt | Asimptotičeskie metody v teorii massovogo obsluživanija |
| title_auth | Asymptotic methods in queuing theory |
| title_exact_search | Asymptotic methods in queuing theory |
| title_full | Asymptotic methods in queuing theory Alexander A. Borovkov |
| title_fullStr | Asymptotic methods in queuing theory Alexander A. Borovkov |
| title_full_unstemmed | Asymptotic methods in queuing theory Alexander A. Borovkov |
| title_short | Asymptotic methods in queuing theory |
| title_sort | asymptotic methods in queuing theory |
| topic | Wachttijdproblemen gtt Asymptotic expansions Queuing theory Asymptotische Methode (DE-588)4287476-2 gnd Warteschlangentheorie (DE-588)4255044-0 gnd |
| topic_facet | Wachttijdproblemen Asymptotic expansions Queuing theory Asymptotische Methode Warteschlangentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001331030&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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