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.

Keywords: 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://archive.numdam.org/articles/10.1051/ro/2011109/} }

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 - Recherche Opérationnelle PY - 2011 SP - 131 EP - 152 VL - 45 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2011109/ DO - 10.1051/ro/2011109 LA - en ID - RO_2011__45_2_131_0 ER -

%0 Journal Article %A Senthil Kumar, Muthukrishnan %T A discrete-time Geo$^{[X]}/G/1$ retrial queue with general retrial time and M-additional options for service %J RAIRO - Operations Research - Recherche Opérationnelle %D 2011 %P 131-152 %V 45 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2011109/ %R 10.1051/ro/2011109 %G en %F 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, Volume 45 (2011) no. 2, pp. 131-152. doi : 10.1051/ro/2011109. http://archive.numdam.org/articles/10.1051/ro/2011109/

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