A discrete-time Geo [X] /G/1 retrial queue with general retrial time and M-additional options for service
RAIRO - Operations Research - Recherche Opérationnelle, Tome 45 (2011) no. 2, pp. 131-152.

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.

DOI : https://doi.org/10.1051/ro/2011109
Classification : 60K25,  90B22
Mots clés : discrete-time queue, first essential service (FES), multi optional service, retrial queue
@article{RO_2011__45_2_131_0,
     author = {Senthil Kumar, Muthukrishnan},
     title = {A discrete-time Geo$^{[X]}/G/1$ retrial queue with general retrial time and M-additional options for service},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {131--152},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {2},
     year = {2011},
     doi = {10.1051/ro/2011109},
     zbl = {1262.90046},
     language = {en},
     url = {http://www.numdam.org/item/RO_2011__45_2_131_0/}
}
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 - Recherche Opérationnelle, Tome 45 (2011) no. 2, pp. 131-152. doi : 10.1051/ro/2011109. http://www.numdam.org/item/RO_2011__45_2_131_0/

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