Consider the forward link of a system with K remote units and a single base transmitter with time varying connecting channels. Data to be transmitted to the remote units arrives according to some random process, and is queued according to its destination. Power is to be allocated to the K channels in a queue and channel state dependent way to minimize some cost criterion. The channel fading rate is fast and the bandwidth and data arrival rates are high. Owing to the high speed the fading, arrival, and service rates, an asymptotic or averaging of the heavy traffic type method is promising. By heavy traffic, we mean that on the average there is little server idle time and spare power over the "average" requirements. Heavy traffic analysis has been very helpful in simplifying control problems in queueing and communications networks. It eliminates inessential detail and focuses on the fundamental issues of scaling and parametric dependencies. To illustrate the scope of the method, several models are considered. The basic model assumes that the channel state is known, and that given the channel state there is a well defined rate of transmission per unit power. Then, convergence of the controlled scaled queue lengths is shown. The scaling is different from the usual in heavy traffic work. The appropriate orders of reserve power and buffer size are given as well as suggested policies. The approximating process is a controlled reflected diffusion which is simpler than the original problem and facilitates understanding parametric dependencies, solutions and stability. The averaging is robust and can be done under a great variety of conditions. To illustrate the scope of the method, more complicated systems are also treated, e.g., power scheduling Is done at prescribed intervals only, knowledge of the channel might be subject to random errors, retransmissions might be needed due to excessive errors at the receiver, or the system might be of the time division multiple access (TDMA) type. The methods and approximating control problems are similar.