# Joint distribution of the busy and idle periods of a discrete modified $GI/GI/c/\infty $ queue

Aplikace matematiky (1988)

- Volume: 33, Issue: 1, page 68-76
- ISSN: 0862-7940

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topDvurečenskij, Anatolij. "Joint distribution of the busy and idle periods of a discrete modified $GI/GI/c/\infty $ queue." Aplikace matematiky 33.1 (1988): 68-76. <http://eudml.org/doc/15524>.

@article{Dvurečenskij1988,

abstract = {For a discrete modified $GI/GI/c/\infty $ queue, $1\le 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.},

author = {Dvurečenskij, Anatolij},

journal = {Aplikace matematiky},

keywords = {distribution of the busy period; idle period; number of customers; distribution of the busy period; idle period; number of customers},

language = {eng},

number = {1},

pages = {68-76},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Joint distribution of the busy and idle periods of a discrete modified $GI/GI/c/\infty $ queue},

url = {http://eudml.org/doc/15524},

volume = {33},

year = {1988},

}

TY - JOUR

AU - Dvurečenskij, Anatolij

TI - Joint distribution of the busy and idle periods of a discrete modified $GI/GI/c/\infty $ queue

JO - Aplikace matematiky

PY - 1988

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 33

IS - 1

SP - 68

EP - 76

AB - For a discrete modified $GI/GI/c/\infty $ queue, $1\le 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.

LA - eng

KW - distribution of the busy period; idle period; number of customers; distribution of the busy period; idle period; number of customers

UR - http://eudml.org/doc/15524

ER -

## References

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- 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). (1917)
- A. G. Pakes, 10.1007/BF02479785, Ann. Inst. Statis. Math., 24, 589-597 (1972). (1972) Zbl0311.60054MR0336844DOI10.1007/BF02479785
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- J. G. Shanthikumar, Level crossing of some variants of GI/M/1 queues, Opsearch., 19, 148-159 (1982). (1982) MR0696148
- P. D. Welch, 10.1287/opre.12.5.736, Oper. res., 12, 736-752 (1964). (1964) MR0176544DOI10.1287/opre.12.5.736
- G. F. Yeo, Single server queues with modified service mechanisms, J. Austral. Math. Soc., 3, 491-502( 1962). (1962) Zbl0134.35302MR0181026

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