  We consider a utility maximization problem over partially observable Markov
ON/OFF channels. In this network instantaneous channel states are never known,
and at most one user is selected for service in every slot according to the
partial channel information provided by past observations. Solving the utility
maximization problem directly is difficult because it involves solving
partially observable Markov decision processes. Instead, we construct an
approximate solution by optimizing the network utility only over a good
constrained network capacity region rendered by stationary policies. Using a
novel frame-based Lyapunov drift argument, we design a policy of admission
control and user selection that stabilizes the network with utility that can be
made arbitrarily close to the optimal in the constrained region. Equivalently,
we are dealing with a high-dimensional restless bandit problem with a general
functional objective over Markov ON/OFF restless bandits. Thus the network
control algorithm developed in this paper serves as a new approximation
methodology to attack such complex restless bandit problems.
