Optimal admission control in queues with abandonments

We consider a multi-sever Markovian queueing system with abandonments where admitted customers pay a reward either at the time of arrival or service completion. There is a cost associated with abandonments and a holding cost associated with customers in the system. We prove that the policy that maximizes the long-run average reward is of threshold type and completely characterize the optimal thresholds. We conclude with a comparison of various characteristics of the two variants of the model.