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.