Quality control for feedback M/M/1/N queue with balking and retention of reneged customers

In this paper, we provide a simple and direct approach to determine quality control policy and optimization of the Markovian feedback customers that has single-server and limited system capacity under steady-state situation adding the concepts of balking and retention of reneged customers. We use the iterative method to obtain the probability that there are n customers in the system, the probability of empty system and some performance measures. Some important queueing systems are derived as special cases and the optimization of the model is performed.