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Customers arrive in a Poisson stream into a network consisting of two service stations in tandem. The service rate at station 1 is to be selected as a function of the state ( ) where x _i is the number of customers at station so as to minimize the expected total discounted or average cost corresponding to the instantaneous cost . The optimal policy is of the form or according as and is a switching function. For the case of discounted cost, the optimal process can be nonergodic, but it is ergodic for the case of average cost.