Extension of the optimality of the threshold policy in heterogeneous multiserver queueing systems

The authors extend the validity of some results on the optimal control of two-server queueing models with service times of unequal distribution, operating in continuous or discrete time. The distribution of arrivals can be arbitrary subject to some conditions. Both discounted and long-run average costs are considered. Dynamic programming and probabilistic arguments are used to establish the assertion that the optimal policy is of threshold type, i.e. the slower server should be utilized only when the queue length exceeds a certain threshold value