A discrete-time Geo[X]/G/1 retrial queue with general retrial time and M-additional options for service

Muthukrishnan Senthil Kumar

RAIRO - Operations Research (2011)

  • Volume: 45, Issue: 2, page 131-152
  • ISSN: 0399-0559

Abstract

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This paper concerns a discrete time Geo[X]/G/1 retrial queue with general retrial time in which all the arriving customers require first essential service with probability α 0 while only some of them demand one of other optional services: type − r (r = 1, 2, 3,...M) service with probability α r . The system state distribution, the orbit size and the system size distributions are obtained in terms of generating functions. The stochastic decomposition law holds for the proposed model. Performance measures of the system in steady state are obtained.  Finally, some numerical illustrations are presented to justify the influence of parameters on several performance characteristics.

How to cite

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Senthil Kumar, Muthukrishnan. "A discrete-time Geo[X]/G/1 retrial queue with general retrial time and M-additional options for service." RAIRO - Operations Research 45.2 (2011): 131-152. <http://eudml.org/doc/276358>.

@article{SenthilKumar2011,
abstract = { This paper concerns a discrete time Geo[X]/G/1 retrial queue with general retrial time in which all the arriving customers require first essential service with probability $\alpha_\{0\}$ while only some of them demand one of other optional services: type − r (r = 1, 2, 3,...M) service with probability $\alpha_\{r\}$. The system state distribution, the orbit size and the system size distributions are obtained in terms of generating functions. The stochastic decomposition law holds for the proposed model. Performance measures of the system in steady state are obtained.  Finally, some numerical illustrations are presented to justify the influence of parameters on several performance characteristics. },
author = {Senthil Kumar, Muthukrishnan},
journal = {RAIRO - Operations Research},
keywords = {Discrete-time queue; first essential service (FES); multi- optional service; retrial queue ; discrete-time queue; retrial queue},
language = {eng},
month = {9},
number = {2},
pages = {131-152},
publisher = {EDP Sciences},
title = {A discrete-time Geo[X]/G/1 retrial queue with general retrial time and M-additional options for service},
url = {http://eudml.org/doc/276358},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Senthil Kumar, Muthukrishnan
TI - A discrete-time Geo[X]/G/1 retrial queue with general retrial time and M-additional options for service
JO - RAIRO - Operations Research
DA - 2011/9//
PB - EDP Sciences
VL - 45
IS - 2
SP - 131
EP - 152
AB - This paper concerns a discrete time Geo[X]/G/1 retrial queue with general retrial time in which all the arriving customers require first essential service with probability $\alpha_{0}$ while only some of them demand one of other optional services: type − r (r = 1, 2, 3,...M) service with probability $\alpha_{r}$. The system state distribution, the orbit size and the system size distributions are obtained in terms of generating functions. The stochastic decomposition law holds for the proposed model. Performance measures of the system in steady state are obtained.  Finally, some numerical illustrations are presented to justify the influence of parameters on several performance characteristics.
LA - eng
KW - Discrete-time queue; first essential service (FES); multi- optional service; retrial queue ; discrete-time queue; retrial queue
UR - http://eudml.org/doc/276358
ER -

References

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