Indexability of Restless Bandit Problems and Optimality of Index Policies for Dynamic Multichannel Access

We consider an opportunistic communication system consisting of multiple independent channels with time-varying states. With limited sensing, a user can only sense and access a subset of channels and accrue rewards determined by the states of the sensed channels. We formulate the problem of optimal sequential channel selection as a restless multi-armed bandit process. We establish the indexability and obtain Whittle’s index in closed-form for both discounted and average reward criteria. These results lead to the direct implementation of Whittle’s index policy with remarkably low complexity. When channels are stochastically identical, we show that Whittle’s index policy is optimal under certain conditions. Furthermore, it has a semi-universal structure that obviates the need to know the channel transition probabilities. The optimality and the semi-universal structure result from the equivalency between Whittle’s index policy and the myopic policy established in this work. For non-identical channels, we develop efficient algorithms for computing a performance upper bound resulting from Lagrangian relaxation. The tightness of the upper bound and the near-optimal performance of Whittle’s index policy are illustrated with simulation examples. Index Terms Opportunistic access, dynamic channel selection, restless multi-armed bandit, Whittle’s index, indexability, myopic policy. This work was supported by the Army Research Laboratory CTA on Communication and Networks under Grant DAAD1901-2-0011 and by the National Science Foundation under Grants ECS-0622200 and CCF-0830685. Part of this work was presented at the 5th IEEE Conference on Sensor, Mesh and Ad Hoc Communications and Networks (SECON) Workshops (June, 2008) and the IEEE Asilomar Conference on Signals, Systems, and Computers (October, 2008).