A priority queue model for competition with shared spectrum

Spectrum sharing has been put forward as a way to more efficiently use limited spectrum and thus increase wireless network capacity. This paper considers a scenario where a primary Service Provider (SP) shares spectrum with secondary SPs and competes for a common pool of customers. We study such a scenario using a model for price competition in which customers select a SP based on the sum of the SP´s announced service price and the congestion incurred when using their service. Here, we assume that the primary has strict priority over the secondary and model the resulting congestion via a preemptive priority queue. We characterize the equilibrium of the resulting pricing game. In particular we find that when the service time has a small variance, secondary users can be excluded from the system, while the primary has to offer a lower price than it would if it were a monopolist due to the threat of entry. As the amount of available bandwidth increases, the primary SP´s profit will decrease asymptotically to zero. In addition, for some scenarios, we show that social welfare may decrease with additional bandwidth and be less than that obtained without sharing.