| Title:
|
Joint distribution of the busy and idle periods of a discrete modified $GI/GI/c/\infty$ queue (English) |
| Author:
|
Dvurečenskij, Anatolij |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
33 |
| Issue:
|
1 |
| Year:
|
1988 |
| Pages:
|
68-76 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Slovak |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a discrete modified $GI/GI/c/\infty$ queue, $1\leq c < \infty$, where the service times of all customers served during any busy period are independent random variables with not necessarily identical distribution functions, the joint distribution of the busy period, the subsequent idle period and the number of customers served during the busy period is derived. The formulae presented are in a convenient form for practical use. The paper is a continuation of [5], where the $M/GI/c/\infty$ discrete modified queue has been studied. (English) |
| Keyword:
|
distribution of the busy period |
| Keyword:
|
idle period |
| Keyword:
|
number of customers |
| MSC:
|
60K25 |
| MSC:
|
90B22 |
| idZBL:
|
Zbl 0658.60126 |
| idMR:
|
MR0934375 |
| DOI:
|
10.21136/AM.1988.104287 |
| . |
| Date available:
|
2008-05-20T18:33:56Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104287 |
| . |
| Reference:
|
[1] A. A. Borovkov: On discrete queueing systems.Teorija veroj. i prim., 8, 251 - 263 (1963) (in Russian). MR 0154344 |
| Reference:
|
[2] A. A. Borovkov: Stochastic Process in Queueing Theory.Nauka, Moscow (1972) (in Russian). MR 0315800 |
| Reference:
|
[3] A. Dvurečenskij, al.: On a problem of the busy-period determination in queues with infinitely many servers.J. Appl. Prob. 21, 201 - 206 (1984). MR 0732687, 10.2307/3213680 |
| Reference:
|
[4] A. Dvurečenskij G. A. Ososkov: On a modified counter with prolonging dead time.J. Appl. Prob., 22, 678-687(1985). MR 0799290, 10.1017/S0021900200029429 |
| Reference:
|
[5] A. Dvurečenskij: On a discrete modified $M/GI/c/\infty$ queue.Aplikace mat., 32, 214 - 223 (1987). MR 0895879 |
| Reference:
|
[6] V. V. Kalashnikov: On joint distribution of the busy and idle periods of queueing systems.Izv. AN SSSR, Tekh. kiber. no. 6, 106-109 (1917) (in Russian). |
| Reference:
|
[7] A. G. Pakes: A GI/M/1 queue with a modified service mechanism.Ann. Inst. Statis. Math., 24, 589-597 (1972). Zbl 0311.60054, MR 0336844, 10.1007/BF02479785 |
| Reference:
|
[8] A. G. Pakes: On the busy period of the modified GI/GI/1 queue.J. Appl. Prob., 10, 192-197 (1973). MR 0350902, 10.2307/3212506 |
| Reference:
|
[9] J. G. Shanthikumar: Level crossing of some variants of GI/M/1 queues.Opsearch., 19, 148-159 (1982). MR 0696148 |
| Reference:
|
[10] P. D. Welch: On a generalized M/G/1 queueing process in which the first customer of each busy period receives exceptional service.Oper. res., 12, 736-752 (1964). MR 0176544, 10.1287/opre.12.5.736 |
| Reference:
|
[11] G. F. Yeo: Single server queues with modified service mechanisms.J. Austral. Math. Soc., 3, 491-502( 1962). Zbl 0134.35302, MR 0181026 |
| . |
