Numerical investigation of optimal control policies of service rates

A single-server system with controllable service rates in relation to the discount factor and the average cost criterion is considered. It is known that in the absence of holding (waiting or sojourn) costs, the optimal control policies display the monotonicity property, in this work, numerical methods are used for establishing other qualitative properties of optimal policies, such as a continuous dependence of the sets of the policy optimality on the discount factor down to its aero and a weal; dependence of the service time on the I;ind of its distribution. It is shown that at nonzero holding costs, the monotonicity properly breaks down.