On Regenerative Processes in Queueing Theory:
I. The single server queue GIIG/1 1 1. 1 Definitions 1 1. 2 Regenerative processes 2 1. 3 The sequence n 1,2, . . . 4 = !::!n' 1. 4 The process t dO,co)} 11 {~t' The process t dO,co)} 1. 5 15 {~t' Applications to the GIIG/1 queue 1. 6 16 The average virtual waiting time during a busy...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1976
|
| Ausgabe: | 1st ed. 1976 |
| Schriftenreihe: | Lecture Notes in Economics and Mathematical Systems
121 |
| Schlagworte: | |
| Online-Zugang: | BTU01 Volltext |
| Zusammenfassung: | I. The single server queue GIIG/1 1 1. 1 Definitions 1 1. 2 Regenerative processes 2 1. 3 The sequence n 1,2, . . . 4 = !::!n' 1. 4 The process t dO,co)} 11 {~t' The process t dO,co)} 1. 5 15 {~t' Applications to the GIIG/1 queue 1. 6 16 The average virtual waiting time during a busy 17 cycle ii. Little's formula 17 iii. The relation between the stationary distributions 18 of the virtual and actual waiting time iv. The relation between the distribution of the idle 20 period and the stationary distribution of the actual waiting time v. The limiting distribution of the residual service 24 time £. , -pw vi. The relation for ~ rn E{e -n} 25 n=O 1. 7 Some notes on chapter I 27 II. The M/G/K system 31 2. 1 On the stationary distribution of the actual and virtua131 waiting time for the M/G/K queueing system 2. 2 The M/G/K loss system 36 2. 3 Proof of Erlang's formula for the M/G/K loss system 43 i. Proof for the system MIMI'" 45 ii. Proof for the system M/G/co 47 VI iii. Proof fol' the MIG IK los s system III. The M/G/1 system 3. 1 Introduction 71 (K) 3. 2 Downcrossings of the ~t -process 74 3. 3 The distribution of the supremum of the virtual waiting 75 • (00) d' b 1 tlme ~t urlng a usy cyc e i. The exit probability 76 ii |
| Beschreibung: | 1 Online-Ressource (IX, 93 p) |
| ISBN: | 9783642952814 |
| DOI: | 10.1007/978-3-642-95281-4 |
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| 245 | 1 | 0 | |a On Regenerative Processes in Queueing Theory |c by Jacob W. Cohen |
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| 490 | 0 | |a Lecture Notes in Economics and Mathematical Systems |v 121 | |
| 520 | |a I. The single server queue GIIG/1 1 1. 1 Definitions 1 1. 2 Regenerative processes 2 1. 3 The sequence n 1,2, . . . 4 = !::!n' 1. 4 The process t dO,co)} 11 {~t' The process t dO,co)} 1. 5 15 {~t' Applications to the GIIG/1 queue 1. 6 16 The average virtual waiting time during a busy 17 cycle ii. Little's formula 17 iii. The relation between the stationary distributions 18 of the virtual and actual waiting time iv. The relation between the distribution of the idle 20 period and the stationary distribution of the actual waiting time v. The limiting distribution of the residual service 24 time £. , -pw vi. The relation for ~ rn E{e -n} 25 n=O 1. 7 Some notes on chapter I 27 II. The M/G/K system 31 2. 1 On the stationary distribution of the actual and virtua131 waiting time for the M/G/K queueing system 2. 2 The M/G/K loss system 36 2. 3 Proof of Erlang's formula for the M/G/K loss system 43 i. Proof for the system MIMI'" 45 ii. Proof for the system M/G/co 47 VI iii. Proof fol' the MIG IK los s system III. The M/G/1 system 3. 1 Introduction 71 (K) 3. 2 Downcrossings of the ~t -process 74 3. 3 The distribution of the supremum of the virtual waiting 75 • (00) d' b 1 tlme ~t urlng a usy cyc e i. The exit probability 76 ii | ||
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Datensatz im Suchindex
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| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 658 - General management |
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| dewey-tens | 650 - Management and auxiliary services |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| doi_str_mv | 10.1007/978-3-642-95281-4 |
| edition | 1st ed. 1976 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T08:56:07Z |
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| isbn | 9783642952814 |
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| series2 | Lecture Notes in Economics and Mathematical Systems |
| spelling | Cohen, Jacob W. Verfasser aut On Regenerative Processes in Queueing Theory by Jacob W. Cohen 1st ed. 1976 Berlin, Heidelberg Springer Berlin Heidelberg 1976 1 Online-Ressource (IX, 93 p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Economics and Mathematical Systems 121 I. The single server queue GIIG/1 1 1. 1 Definitions 1 1. 2 Regenerative processes 2 1. 3 The sequence n 1,2, . . . 4 = !::!n' 1. 4 The process t dO,co)} 11 {~t' The process t dO,co)} 1. 5 15 {~t' Applications to the GIIG/1 queue 1. 6 16 The average virtual waiting time during a busy 17 cycle ii. Little's formula 17 iii. The relation between the stationary distributions 18 of the virtual and actual waiting time iv. The relation between the distribution of the idle 20 period and the stationary distribution of the actual waiting time v. The limiting distribution of the residual service 24 time £. , -pw vi. The relation for ~ rn E{e -n} 25 n=O 1. 7 Some notes on chapter I 27 II. The M/G/K system 31 2. 1 On the stationary distribution of the actual and virtua131 waiting time for the M/G/K queueing system 2. 2 The M/G/K loss system 36 2. 3 Proof of Erlang's formula for the M/G/K loss system 43 i. Proof for the system MIMI'" 45 ii. Proof for the system M/G/co 47 VI iii. Proof fol' the MIG IK los s system III. The M/G/1 system 3. 1 Introduction 71 (K) 3. 2 Downcrossings of the ~t -process 74 3. 3 The distribution of the supremum of the virtual waiting 75 • (00) d' b 1 tlme ~t urlng a usy cyc e i. The exit probability 76 ii Operations Research/Decision Theory Operations research Decision making Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf Regenerativer Prozess (DE-588)4183384-3 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 s Regenerativer Prozess (DE-588)4183384-3 s DE-604 Erscheint auch als Druck-Ausgabe 9783540076278 Erscheint auch als Druck-Ausgabe 9783642952821 https://doi.org/10.1007/978-3-642-95281-4 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Cohen, Jacob W. On Regenerative Processes in Queueing Theory Operations Research/Decision Theory Operations research Decision making Warteschlangentheorie (DE-588)4255044-0 gnd Regenerativer Prozess (DE-588)4183384-3 gnd |
| subject_GND | (DE-588)4255044-0 (DE-588)4183384-3 |
| title | On Regenerative Processes in Queueing Theory |
| title_auth | On Regenerative Processes in Queueing Theory |
| title_exact_search | On Regenerative Processes in Queueing Theory |
| title_exact_search_txtP | On Regenerative Processes in Queueing Theory |
| title_full | On Regenerative Processes in Queueing Theory by Jacob W. Cohen |
| title_fullStr | On Regenerative Processes in Queueing Theory by Jacob W. Cohen |
| title_full_unstemmed | On Regenerative Processes in Queueing Theory by Jacob W. Cohen |
| title_short | On Regenerative Processes in Queueing Theory |
| title_sort | on regenerative processes in queueing theory |
| topic | Operations Research/Decision Theory Operations research Decision making Warteschlangentheorie (DE-588)4255044-0 gnd Regenerativer Prozess (DE-588)4183384-3 gnd |
| topic_facet | Operations Research/Decision Theory Operations research Decision making Warteschlangentheorie Regenerativer Prozess |
| url | https://doi.org/10.1007/978-3-642-95281-4 |
| work_keys_str_mv | AT cohenjacobw onregenerativeprocessesinqueueingtheory |