Optimal threshold control of a retrial queueing system with finite buffer

In this paper, we analyze the optimal control of a retrial queueing system with finite buffer K. At any decision epoch, if the buffer is full, the controller have to make two decisions: one is for the new arrivals, to decide whether they are allowed to join the orbit or not (admission control); the other one is for the repeated customers, to decide whether they are allowed to get back to the orbit or not (retrial control). The problems are constructed as a Markov decision process. We show that the optimal policy has a threshold-type structure and the thresholds are monotonic in operating parameters and various cost parameters. Furthermore, based on the structure of the optimal policy, we construct a performance evaluation model for computing efficiently the thresholds. The expression of the expected cost is given by solving the quasi birth-and-death (QBD) process. Finally, we provide some numerical results to illustrate the impact of different parameters on the optimal policy and average cost.