Online Pricing of Secondary Spectrum Access with Unknown Demand Function

We consider a wireless provider who caters to two classes of customers, namely primary users (PUs) and secondary users (SUs). PUs have long term contracts while SUs are admitted and priced according to current availability of excess spectrum. The average rate at which SUs attempt to access the spectrum is a function on the currently advertised price, referred to as the demand function. We analyze the problem of maximizing the average profit gained by admissions of SUs, when the demand function is unknown. We introduce a new on-line algorithm, called Measurement-based Threshold Pricing (MTP), that requires the optimization of only two parameters, a price and a threshold, whereby SU calls are admitted and charged a fixed price when the channel occupancy is lower than the threshold and rejected otherwise. At each iteration, MTP measures the average arrival rate of SUs corresponding to a certain test price. We prove that these measurements of the secondary demand are sufficient for MTP to converge to a local optimal price and corresponding optimal threshold, within a number of measurements that is logarithmic in the total number of possible prices. We further provide an adaptive version of MTP that adjusts to time-varying demand and establish its convergence properties. We conduct numerical studies showing the convergence of MTP to near-optimal online profit and its superior performance over a traditional reinforcement learning approach.