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The authors investigate flow rate optimization on a wireless link with randomly varying channel gain using techniques from adaptive modulation and network utility maximization. They consider the problem of choosing the data flow rate to optimally trade off average transmit power and the average utility of the smoothed data flow rate. The smoothing allows one to model the demands of an application that can tolerate variations in flow over a certain time interval; they will see that this smoothing leads to a substantially different optimal data flow rate policy than without smoothing. They pose the problem as a convex stochastic control problem. For the case of a single flow, the optimal data flow rate policy can be numerically computed using stochastic dynamic programming.
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