An approximating diffusion control problem for dynamic admission and service rate control in a G∕M∕N+G queue

We study a diffusion control problem that is motivated by the dynamic admission and service rate control problem for a G∕M∕N+G queue. The objective is to minimize long run average cost. Because the original queueing control problem is not tractable, we solve the approximating diffusion control problem that arises under the QED heavy traffic regime and show that its optimal solution has two components: (1) a threshold control that regulates the diffusion and (2) a feedback-type drift rate control.