  This paper studies optimal switching on and o? of the entire service capacity
of an M/M/Infinity queue with holding, running and switching costs where the
running costs depend only on whether the system is running or not. The goal is
to minimize average costs per unit time. The main result is that an
average-optimal policy either always runs the system or is an (M, N)-policy
defined by two thresholds M and N, such that the system is switched on upon an
arrival epoch when the system size accumulates to N and is switched off upon a
departure epoch when the system size decreases to M. It is shown that this
optimization problem can be reduced to a problem with a finite number of states
and actions, and an average-optimal policy can be computed via linear
programming. An example, in which the optimal (M, N)-policy outperforms the
best (0, N)-policy, is provided. Thus, unlike the case of single-server queues
studied in the literature, (0, N)-policies may not be average-optimal.
