Spot Pricing of Secondary Spectrum Access in Wireless Cellular Networks

Recent deregulation initiatives enable cellular providers to sell excess spectrum for secondary usage. In this paper, we investigate the problem of optimal spot pricing of spectrum by a provider in the presence of both nonelastic primary users, with long-term commitments, and opportunistic, elastic secondary users. We first show that optimal pricing can be formulated as an infinite horizon average reward problem and solved using stochastic dynamic programming. Next, we investigate the design of efficient single pricing policies. We provide numerical and analytical evidences that static pricing policies do not perform well in such settings (in sharp contrast to settings where all the users are elastic). On the other hand, we prove that deterministic threshold pricing achieves optimal profit amongst all single-price policies and performs close to global optimal pricing. We characterize the profit regions of different pricing policies, as a function of the arrival rate of primary users. Under certain reasonable assumptions on the demand function, we prove that the profit region of threshold pricing is optimal and independent of the specific form of the demand function, and that it includes the profit region of static pricing. In addition, we show that the profit function of threshold pricing is unimodal in price. We determine a restricted interval in which the optimal threshold lies. These properties enable very efficient computation of the optimal threshold policy, which is far faster than that of the global optimal policy.