Optimal Pricing Strategies in Cognitive Radio Networks With Heterogeneous Secondary Users and Retrials

In a cognitive radio (CR) system, excessive access services for secondary users (SUs) lead to a substantial increase in congestion and the retrial phenomenon, both of which degrade the performance of CR networks, especially in overload conditions. This paper investigates the price-based spectrum access control policy that characterizes the network operator's provision to heterogeneous and delay-sensitive SUs through pricing strategies. Based on shared-use dynamic spectrum access (DSA), the SUs can occupy the dedicated spectrum without degrading the operations of primary users (PUs). The service to transmission of SUs can be interrupted by an arriving PU, while the interrupted SUs join a retrial pool called an orbit, later trying to use the spectrum to complete the service. In the retrial orbit, the interrupted SU competes fairly with other SUs in the orbit. Such a DSA mechanism is formulated as a retrial queue with service interruptions and general service times. Regarding the heterogeneity of delay-sensitive SUs, we consider two cases: the delay-sensitive parameter follows a discrete distribution and a continuous distribution, respectively. In equilibrium, we find that the revenue-optimal price is unique, while there may exist a continuum of equilibria for the socially optimal price. In addition, the socially optimal price is always not greater than the revenue-optimal price, and thus the socially optimal arrival rate is not less than the revenue-optimal one, which is contrary with the conclusion, i.e., the socially optimal and revenue-optimal arrival rates are consistent, drawn in the literature for homogeneous SUs. Finally, we present numerical examples to show the effect of various parameters on the operator's pricing strategies and SUs' behavior.