Joint distribution of the busy and idle periods of a discrete modified G I / G I / c / queue

Anatolij Dvurečenskij

Aplikace matematiky (1988)

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

Abstract

top
For a discrete modified G I / G I / c / queue, 1 c < , 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 / G I / c / discrete modified queue has been studied.

How to cite

top

Dvurečenskij, 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

top
  1. A. A. Borovkov, On discrete queueing systems, Teorija veroj. i prim., 8, 251 - 263 (1963) (in Russian). (1963) MR0154344
  2. A. A. Borovkov, Stochastic Process in Queueing Theory, Nauka, Moscow (1972) (in Russian). (1972) MR0315800
  3. A. Dvurečenskij, al., 10.2307/3213680, J. Appl. Prob. 21, 201 - 206 (1984). (1984) MR0732687DOI10.2307/3213680
  4. A. Dvurečenskij G. A. Ososkov, 10.2307/3213870, J. Appl. Prob., 22, 678-687(1985). (1985) MR0799290DOI10.2307/3213870
  5. A. Dvurečenskij, On a discrete modified M / G I / c / queue, Aplikace mat., 32, 214 - 223 (1987). (1987) MR0895879
  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). (1917) 
  7. A. G. Pakes, 10.1007/BF02479785, Ann. Inst. Statis. Math., 24, 589-597 (1972). (1972) Zbl0311.60054MR0336844DOI10.1007/BF02479785
  8. A. G. Pakes, 10.2307/3212506, J. Appl. Prob., 10, 192-197 (1973). (197) MR0350902DOI10.2307/3212506
  9. J. G. Shanthikumar, Level crossing of some variants of GI/M/1 queues, Opsearch., 19, 148-159 (1982). (1982) MR0696148
  10. P. D. Welch, 10.1287/opre.12.5.736, Oper. res., 12, 736-752 (1964). (1964) MR0176544DOI10.1287/opre.12.5.736
  11. G. F. Yeo, Single server queues with modified service mechanisms, J. Austral. Math. Soc., 3, 491-502( 1962). (1962) Zbl0134.35302MR0181026

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.