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This paper studies optimal switching on and o? of the entire service capacityof an M/M/Infinity queue with holding, running and switching costs where therunning costs depend only on whether the system is running or not. The goal isto minimize average costs per unit time. The main result is that anaverage-optimal policy either always runs the system or is an (M, N)-policydefined by two thresholds M and N, such that the system is switched on upon anarrival epoch when the system size accumulates to N and is switched off upon adeparture epoch when the system size decreases to M. It is shown that thisoptimization problem can be reduced to a problem with a finite number of statesand actions, and an average-optimal policy can be computed via linearprogramming. An example, in which the optimal (M, N)-policy outperforms thebest (0, N)-policy, is provided. Thus, unlike the case of single-server queuesstudied in the literature, (0, N)-policies may not be average-optimal.

Optimal Switching On and Off the Entire Service Capacity of a Parallel Queue