Performance Analysis of Queueing Model with Two types of Vacations and Single Service with Feedback

Consider two types of service patterns and two types of vacations for a bulk arrival queuing model. In this model, the bulk service is supplied only when queue length is greater than or equal to the smallest batch size, when server either goes to single service or departs for vacation (fast or slow). Then service will not be stopped during service time expect the vacation time. After completing bulk or single service, if a customer decides to leave or a customer is unsatisfied with it, they may select to rejoin the queue (feedback) with probability p. Also, this type of queuing model was presented to determine the Probability Generating Function (PGF). Finally, various performance measures and numerical illustrations are provided.