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

RAIRO - Operations Research (2011)

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

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topSenthil 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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