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This work investigates a problem of scheduling tasks on a single server in which the rate at which the server can complete its tasks is not fixed but can be varied- a higher service rate resulting in correspondingly less reliable service. This is a prevalent trade-off in many practical systems including wireless communication systems. Introducing the idea of mode of service, we formulate the rate-reliability problem as a Markov control problem. We obtain existence results and show that the optimal policy has a threshold mode. The optimal policy is also shown to provide average delay guarantee while maximizing goodput. We provide numerical results supporting our analysis and showing advantage of the optimal policy over fixed rate policies.