Pricing mechanisms and equilibrium behaviors of noncooperative users in cognitive radio networks

We study the pricing mechanisms and their effects on equilibrium behaviors of self-optimizing secondary users (SUs) sharing a single channel of primary users (PUs) operated by a service provider (SP) in cognitive radio networks. From SUs´ point of view, a spectrum access decision on whether to join a queue or not is characterized through an individual optimal strategy. With this strategy, we show that there exists a unique equilibrium in terms of SUs´ joining probability. This strategy also requires each SU to know its average queueing delay, which is a non-trivial problem because of multiple SUs service´s interruptions from the returns of PUs; we, however, can analyze this queueing delay based on the general distribution of SUs´s service time and PUs´ traffic model by using renewal theory. We also provide a sufficient condition and iterative algorithms for the convergence of equilibrium points. From the SP´s point of view, two pricing mechanisms are proposed with different goals: revenue maximization and social welfare maximization. And the optimal price can be solved efficiently using numerical methods.