Socially Optimal Queuing Control in Cognitive Radio Networks Subject to Service Interruptions: To Queue or Not to Queue?

The main challenge to cognitive radio is the emergence of primary users, which can be considered as the service interruptions in a queuing system. The service interruption can incur significant delays for secondary users' data packets which are considered as secondary customers. Therefore, a secondary customer needs to decide whether to join the queue or leave for other means of transmission. It is shown that the individually optimal strategy for joining the queue is characterized by a threshold of queue length. When the current queue length is above this threshold, the secondary customer should leave; otherwise it should join the queue. The socially optimal threshold of queue length is also obtained and is numerically shown to be smaller than the individually optimal one, which implies that the individually optimal strategy does not yield the socially optimal one. To bridge the gap between the individually and socially optimal strategies, a pricing mechanism is proposed to toll the service of each secondary customer, thus equalizing the two optimal strategies. When the channel statistics are unknown, an online learning procedure, based on the Kiefer-Wolfowitz algorithm, is proposed. The proposed algorithms are then demonstrated using numerical simulations.