Whittle index approach to opportunistic scheduling with partial channel information

Opportunistic scheduling in wireless cellular systems utilizes random channel quality variations in time by favoring the users with good channel conditions. However, the success of such schedulers is heavily depending on the accuracy of the available information on the channel states of users. In this paper, we consider the opportunistic scheduling problem of downlink data traffic with partial channel information, where the target is to minimize the flow-level holding costs. In earlier works, the Whittle index approach has successfully been utilized to develop near-optimal scheduling policies for the corresponding problems, however, typically with exact channel information. Using the same approach, we complement and extend the results found thus far. More specifically said, our novel contributions are (i) proving that the flow-level opportunistic scheduling problem with partial channel information is indexable at least in certain parts of the parameter space; (ii) deriving an explicit formula for the corresponding Whittle index; (iii) proving that, in these parts of the parameter space, the optimal policy for the relaxed optimization problem is of threshold type; and (iv) demonstrating that, in the remaining parts of the parameter space, it is possible that the optimal policy for the relaxed problem is not of threshold type. In addition, we evaluate the performance of the derived Whittle index policies and compare them with some greedy policies by numerical simulations.