An Analysis of Discrete Time Geo/G/1 Retrial Queue with Second Optional Service with A Vacation
P. Gunasekaran1, S. Jeyakumar2

1P. Gunasekaran, Assistant Professor, J.C.T. College of Engineering and Technology, Coimbatore (Tamil Nadu), India.
2S. Jeyakumar, Assistant Professor, Government Arts College, Coimbatore (Tamil Nadu), India.
Manuscript received on 28 March 2019 | Revised Manuscript received on 07 April 2019 | Manuscript Published on 27 April 2019 | PP: 814-822 | Volume-7 Issue-6S2 April 2019 | Retrieval Number: F10810476S219/2019©BEIESP
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Abstract: In this paper we discussed a discrete time Geo/G/1 retrial queuing model with single vacation and second discretionary service. In this model the system gives primary vital service to every customers exhaustively and the customers appearing at the time of busy period becomes non persistent. After completion of this service only few customers ask for second optional service. Also, the system have idle of unsystematic distance and afterward this vacation the server starts its work only if customer available in the server otherwise the server is idle until minimum a single customer available in the server. In this model arrival times are geometrically distributed and service times and vacation times are commonly distributed. By creating function technique we obtain PGF and also we derived an analytical expression for mean queue length.
Keywords: Arrival and Service Time, Essential and Optional Service, Geo/G/1 Retrial Queue, Mean Queue Length, Non Persistent Customers.
Scope of the Article: Service Oriented Architectures