We introduce a private commons model that consists of network providers who serve a fixed primary demand and price strate-gically to improve their revenues from an additional secondary demand. For general forms of secondary demand, we establish the existence and uniqueness of two characteristic prices: the break-even price and the market sharing price. We show that the market sharing price is always greater than the break-even price, leading to a price interval in which a provider is both profitable and willing to share the demand. Making use of this result, we give insight into the nature of market outcomes.

Abstract—A recent policy ruling by the Federal Com-munications Commission (FCC) set aside a fixed amount of cleared spectrum for smaller network providers. Thanks to this ruling, smaller providers can improve their quality of service using carrier aggregation. In this paper, we determine the optimal (minimum) level of carrier aggre-gation that a smaller provider needs in order to bring its service in line with a larger provider in the same market. Toward this end, we provide an asymptotically exact formula for the loss (blocking) probability of flows under a quality-driven (QD) regime. Using this formula, we establish an efficient way of numerically calculating the optimal level of carrier aggregation and derive scaling laws. Specifically, we show that the optimal level of carrier aggregation scales sub-linearly with respect to the scaling factor, i.e., the ratio between the network capacities of the two providers, and decreases with the initial traffic load of the providers. We derive a closed-form linear upper bound on the optimal level of carrier aggregation and prove that it is the tightest possible. We provide numerical results, showing the accuracy of our methods and illustrating their use. We also discuss the extension of our results to delay-related metrics as well as their application to profitable pricing in secondary spectrum markets. I.

New regulations grant network service providers with the right to lease their spectrum to short-term leased secondary users (SUs) for opportunistic usage. In this work, we tackle the challenge of determining admission control and pricing policies on SUs that guarantee profitability under general secondary demand and general traffic models, and accu-rately reflect the operation of modern cellular data networks (e.g., LTE) in which resources are shared rather than rigidly partitioned. We first analyze the joint problem of bandwidth allocation and admission control of elastic secondary users. We assume Poisson session arrivals, where each session is composed of arbitrarily distributed, and possibly correlated, on and off periods. Under balanced bandwidth allocation, we show that the steady state distribution of the number of active users in the network is insensitive to traffic charac-teristics beyond their means. This result holds for arbitrary occupancy-based admission control policies on SUs. Next, we prove that the optimal occupancy-based admission con-trol policy is of threshold type, which means that secondary user arrivals are accepted when the total number of active users in the network is below a certain threshold; otherwise, they are rejected. Finally, we identify a price, referred to as the break-even price, and an admission control policy which, together, ensure profitability for any price greater than the break-even price, irrespective of the shape of the secondary demand function.