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

Published online by Cambridge University Press:  22 September 2011

Muthukrishnan Senthil Kumar*
Affiliation:
Department of Nanobio Materials and Electronics, WCU, Gwangju Institute of Science and Technology, 500 712 – Gwangju, Republic of Korea. [email protected]
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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: typer (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.

Type
Research Article
Copyright
© EDP Sciences, ROADEF, SMAI, 2011

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