Mathematical methods in the theory of queueing:
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | , |
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
London
Griffin
1969
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Griffin's statistical monographs and courses
7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 120 Seiten |
Internformat
MARC
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| 240 | 1 | 0 | |a Matematičeskie metody teorii massovogo obsluživanija |
| 245 | 1 | 0 | |a Mathematical methods in the theory of queueing |c A.Y. Khintchine ; translated by. D.M. Andrews and M.H. Quenouille ; additional notes by Eric Wolman |
| 250 | |a Second edition | ||
| 264 | 1 | |a London |b Griffin |c 1969 | |
| 300 | |a 120 Seiten | ||
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| 700 | 1 | |a Quenouille, M.H. |4 trl | |
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Datensatz im Suchindex
| _version_ | 1804118357717286912 |
|---|---|
| adam_text | CONTENTS
PREFACE
PART I
THE INCOMING STREAM OF CALLS
Chapter Page
1 THEORY OF THE SIMPLE STREAM
1 Definition and statement of the problem ... ... ... ... 11
2 Elementary solution ... ... ... ... ... ... ... 12
3 Method of differential equations ... ... ... ... ... IS
4 Intensity of a simple stream ... ... ... ... ... ... 17
5 A stream with a variable parameter ... ... ... ... ... 18
2 GENERAL PROPERTIES OF STATIONARY STREAMS
6 The stream of demands as a random process ... ... ... ... 23
7 Fundamental properties of stationary streams ... ... ... ... 26
8 General form of a stationary stream without after effects ... ... 30
3 PALM S FUNCTIONS
9 Definition and proof of existence ... ... ... ... ... 37
10 Palm s formulae 39
11 The intensity of a stationary stream — Korolyuk s theorem ... ... 41
4 STREAMS WITH LIMITED AFTER EFFECTS
12 Another method of describing a stream of calls ... ... ... 43
13 Streams with limited after effects ... ... ... ... ... 44
5 LIMIT THEOREM
14 Statement of the problem — Palm s theorem ... ... ... ... 49
15 Limiting behaviour of functions ... ... ... ... ... 51
16 Limit theorem ... ... ... ... ... ... ... ... 55
PART II
SYSTEMS WITH LOSSES
17 Introductory remarks ... ... ... ... ... ... ... 57
(
6 ERLANG S PROBLEM FOR A FINITE COLLECTION
18 Statement of the problem 60
19 Markoff s theorem 63
20 Erlang s formulae and equations ... ... ... ... ... 65
21 The ergodic theorem 69
10
CONTENTS
Chapter Pag
7 ERLANG S PROBLEM FOR AN INFINITE COLLECTION
22 Equations for the generating function 73
23 Solution of the problem 75
24 Stream with a variable parameter ... ... ... ... ¦¦• 77
25 The infinite collection with an arbitrary distribution function for
the lengths of conversation 79
8 PALM S PROBLEM ^
26 Statement of the problem 82
27 Elementary calculations ... ... ... ... ... ... ... 84
28 Palm s fundamental theorem ... ... ... ... ... ... 87
29 Deduction from the basic system of equations ... ... ... 88
30 Laplace s transformation 90
31 Determination of functions ? (*) ... ¦¦¦ ••• ... ••• 91
32 Expansion of functions y iii) in partial fractions ... ... ... 93
33 Conclusion 94
PART III
SYSTEMS ALLOWING DELAY
9 THE CASE OF AN EXPONENTIAL DISTRIBUTION FOR
THE LENGTH OF CONVERSATIONS
34 Probabilities of different states 96
35 The distribution function of the waiting time... ... ... ... 99
10 SINGLE LINE SYSTEMS WITH A FIXED LENGTH OF
CONVERSATION
36 Difference differential equations for the problem ... ... ... 102
37 Distribution function of the waiting time ... ¦¦• ... ••• 104
11 GENERAL THEORY OF SINGLE LINE SYSTEMS
38 Statement of the problem and definitions 106
39 Subsidiary hypotheses 107
40 The characteristic function of the waiting time 114
SECTION NOTES AND REFERENCES 119
BIBLIOGRAPHY 120
ADDITIONAL NOTES 121
|
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| author | Chinčin, Aleksandr Ja. 1894-1959 |
| author2 | Andrews, D.M Quenouille, M.H |
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| indexdate | 2024-07-09T16:09:01Z |
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| language | English Russian |
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| publishDate | 1969 |
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| publisher | Griffin |
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| series | Griffin's statistical monographs and courses |
| series2 | Griffin's statistical monographs and courses |
| spelling | Chinčin, Aleksandr Ja. 1894-1959 Verfasser (DE-588)124080634 aut Matematičeskie metody teorii massovogo obsluživanija Mathematical methods in the theory of queueing A.Y. Khintchine ; translated by. D.M. Andrews and M.H. Quenouille ; additional notes by Eric Wolman Second edition London Griffin 1969 120 Seiten txt rdacontent n rdamedia nc rdacarrier Griffin's statistical monographs and courses 7 Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 s DE-604 Andrews, D.M. trl Quenouille, M.H. trl Wolman, Eric oth Griffin's statistical monographs and courses 7 (DE-604)BV000725110 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002584922&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chinčin, Aleksandr Ja. 1894-1959 Mathematical methods in the theory of queueing Griffin's statistical monographs and courses Warteschlangentheorie (DE-588)4255044-0 gnd |
| subject_GND | (DE-588)4255044-0 |
| title | Mathematical methods in the theory of queueing |
| title_alt | Matematičeskie metody teorii massovogo obsluživanija |
| title_auth | Mathematical methods in the theory of queueing |
| title_exact_search | Mathematical methods in the theory of queueing |
| title_full | Mathematical methods in the theory of queueing A.Y. Khintchine ; translated by. D.M. Andrews and M.H. Quenouille ; additional notes by Eric Wolman |
| title_fullStr | Mathematical methods in the theory of queueing A.Y. Khintchine ; translated by. D.M. Andrews and M.H. Quenouille ; additional notes by Eric Wolman |
| title_full_unstemmed | Mathematical methods in the theory of queueing A.Y. Khintchine ; translated by. D.M. Andrews and M.H. Quenouille ; additional notes by Eric Wolman |
| title_short | Mathematical methods in the theory of queueing |
| title_sort | mathematical methods in the theory of queueing |
| topic | Warteschlangentheorie (DE-588)4255044-0 gnd |
| topic_facet | Warteschlangentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002584922&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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