Max-Min Optimality of Service Rate Control in Closed Queueing Networks
In this paper, the authors discuss the optimality properties of service rate control in closed Jackson networks. They prove that when the cost function is linear to a particular service rate, the system performance is monotonic w.r.t. (with respect to) that service rate and the optimal value of that service rate can be either maximum or minimum (they call it Max-Min optimality); When the second-order derivative of the cost function w.r.t. a particular service rate is always positive (negative), which makes the cost function strictly convex (concave), the optimal value of such service rate for the performance maximization (minimization) problem can be either maximum or minimum.