The optimal strategy structure of an intermittently operated service channel

An analysis is made of the policy space structure for an intermittently operated M/M/1 queuing system. When the queue length builds up to limit N, the service channel is opened and service rendered until the queue length is reduced to some lower number, v, whereupon the channel is closed. Certain costs, namely these of lost customers, of giving service and of opening and closing the channel are imposed. A technique for dividing the policy space into regions of optimal {v, N} is developed so that the best strategy for any combination of costs is immediately visible to the decision maker.