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

Författare

Jianhua Cao
Christian Nyberg

Summary, in English

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.

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