An Analysis of Randomized Threshold Discrete Geo/G/1 Retrial Queue with Impatient Customers and Single Vacation
P Gunasekaran1, S. Jeyakumar2

1P Gunasekaran, Assistant Professor, J.C.T. College of Engineering and Technology, Coimbatore (Tamil Nadu), India.
2Dr. S. 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: 832-838 | Volume-7 Issue-6S2 April 2019 | Retrieval Number: F10830476S219/2019©BEIESP
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Abstract: It is discussed in brief about randomized threshold discrete queue Geo/G/1 queue with impatient customers and single vacation in this article. Consider systems with server vacation where customers impatience are due to the absence of servers upon arrival the server begins its service, here the probability is p, this is possible if N (N- fixed count ) number of customers are come together in the queue else the server will not give any service for the probability 1-p. Server will again start its service with probability p only if the length of the queue reaches N. In this model customers arrive according to geometric distribution and the service times, vacation times are generally distributed. In this article we derived PGF of the orbit by generating function technique and in the performance measure is derived an analytical expression for mean queue length. Numerical results are presented in order to illustrate the effectiveness of performance of the mean queue length.
Keywords: Arrival, Time, Geo/G/1 Queue, Impatient Customer, and Mean Queue Length, Service Time, Threshold Policy, Vacation Time.
Scope of the Article: Discrete Optimization