This paper analyses the steady state behaviour of an M/G/1 retrial queue with impatient subscribers, two phases of essential service, general retrial time and general vacation time. If the primary call, on arrival finds the server busy, becomes impatient and leaves the system with probability (1-) and with probability, it enters into an orbit. The server provides preliminary first essential service (FES) and second essential service (SES) to the primary arriving calls or calls from the retrial group. As soon as the SES of a call is completed, the server may terminate call connection (vacation of random length of time) with probability ‘p’(0< p < 1) or may remain in the system to serve the next call, if any, with probability ‘q’ (=1-p). The steady state queue size distribution of number of customers in retrial group, expected number of customers in retrial group and expected waiting time of the customers in the orbit are obtained. The application of the proposed model is also discussed to analyze a communication protocol with the numerical illustration.
Keywords: Retrial Queues, Steady State Distribution, Essential Service, Vacation Time, Impatient Subscribers, SMTP Protocol
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