Optimal admission and price control in a retrial queueing system

In this paper, we analyze the optimal control policy to minimize the average costs in a retrial queueing system. At any decision epoch, the manager uses admission probabilities a's to control the arriving customers and determines a cancellation price c for the unsuccessful retrial customer, which will lead to him out of system with the probability of G(c) otherwise back to the orbit. We cast the problem as a Markov decision process and derive that the optimal policy has a pure threshold form. We also show that the two thresholds are monotonic in system parameters. Furthermore, based on the structure of the optimal policy, we construct a performance evaluation model for computing efficiently the optimal thresholds. The expression of the average cost is given by solving the quasi-birth-death (QBD) process. Finally, some numerical experiments are presented to illustrate the effect of the system parameters on the optimal policy.