Performance prediction of a discrete-time batch arrival retrial queue with Bernoulli feedback

Abstract

This paper examines a discrete-time GeoX/G/1 retrial queue wherein the customer is feedback again to the head of the queue with some probability in case when he is unsatisfied with his service. This phenomenon is called as Bernoulli feedback. We consider that if the server is busy at the arrival epoch, the arriving customer either interrupts the customer in service to receive his own service with probability pα or joins the orbit with probability pα¯=p(1−α) or departs from the system completely with probability p¯=1−p. A customer under the above defined three situations is called as either preferred customer or repeated customer or impatient customer, respectively. On the other hand if the incoming customer finds the server idle, he starts his service immediately. The service time and retrial time are general distributed whereas batch size is geometric distributed. We use generating function method to derive expressions for system size, orbit size and other performance measures. Further we provide the continuous time equivalent of our model. Finally numerical results are given to show the effect of some critical system parameters on various performance measures.