Network Utility Maximization over Partially Observable Markovian Channels

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.