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We consider a single source transmitting data to one or more receivers/usersover a shared wireless channel. Due to random fading, the wireless channelconditions vary with time and from user to user. Each user has a buffer tostore received packets before they are drained. At each time step, the sourcedetermines how much power to use for transmission to each user. The source'sobjective is to allocate power in a manner that minimizes an expected costmeasure, while satisfying strict buffer underflow constraints and a total powerconstraint in each slot. The expected cost measure is composed of costsassociated with power consumption from transmission and packet holding costs.The primary application motivating this problem is wireless media streaming.For this application, the buffer underflow constraints prevent the user buffersfrom emptying, so as to maintain playout quality. In the case of a single userwith linear power-rate curves, we show that a modified base-stock policy isoptimal under the finite horizon, infinite horizon discounted, and infinitehorizon average expected cost criteria. For a single user with piecewise-linearconvex power-rate curves, we show that a finite generalized base-stock policyis optimal under all three expected cost criteria. We also present thesequences of critical numbers that complete the characterization of the optimalcontrol laws in each of these cases when some additional technical conditionsare satisfied. We then analyze the structure of the optimal policy for the caseof two users. We conclude with a discussion of methods to identifyimplementable near-optimal policies for the most general case of M users.

Energy-Efficient Transmission Scheduling with Strict Underflow Constraints