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Analysis of a Discrete- Time Geo/G/1 Retrial Queue with Starting Failures, Second Optional Service and Single Vacation

N. Kalpana, R. Arumuganathan


This paper analyses a discrete time Geo/G/1 retrial queue with starting failures, second optional service and single vacation. The arriving customers who find the server busy leave the service area and join the orbit to try again for their request later. The retrial time follows a general distribution. The server provides a first essential service to all the arriving customers either from orbit or from main pool. After the completion of first essential service (FES), the customer may request for second optional service (SES) with probability ‘ ’ or leaves the system with the complementary probability ‘ ’. At a service completion of FES without request for SOS, or at a service completion of SOS, if the orbit is empty, then the server avails a single vacation; otherwise the server remains in the system to serve the customer from the orbit or new arrivals. The Markov chain underlying the considered queueing system, and system state probabilities are derived. Some performance measures based on the generating functions are obtained. Stochastic decomposition of the system size is obtained without vacation and the additional system size due to vacation. Numerical results with graphs are provided to illustrate the effect of parameters on main performance measures of the system. 

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