Socially Optimal Queuing Control in Cognitive Radio Systems: Pricing and Learning

A cognitive radio system is modeled as a queue with a server subject to interruptions from primary users. Each customer (packet) arriving at the queue has choices of balking or joining the queue. The individual decision of each customer is optimized based on the reward for the completion of service and the penalty for the waiting time (delay). A socially optimal strategy is also found to maximize the average reward of all customers. Numerical results show that these two strategies, individual and social, generally do not coincide, i.e. an individually optimal strategy does not imply social optimality. To oblige the coincidence of the two optimal strategies, an admission fee to the queue is proposed and the optimal price is found by numerical approaches. To tackle the problem of unknown environments, a learning procedure is proposed to learn the pricing strategy without explicitly modeling the primary users' behavior.