A monotonic property of the optimal admission control to an M/M/1 queue under periodic observations with average cost criterion

We consider the problem of admission control to an M/M/1 queue under periodic observations with average cost criterion. The admission controller receives the system state information every ø :th second and can accordingly adjust the acceptance probability for customers who arrive before the next state information update instance. For a period of ø seconds, the cost is a linear function of the time average of customer populations and the total number of served customers in that period. The objective is to Ønd a stationary deterministic control policy that minimizes the long run average cost. The problem is formulated as a discrete time Markov decision process whose states are fully observable. By taking the control period ø to 0 or to 1, the model in question generalizes two classical queueing control problems: the open and the closed loop admission control to an M/M/1 queue. We show that the optimal policy is to admit customers with a non-increasing probability with respect to the observed number of customers in the system. Numerical examples are also given