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Abstract

Selling spectrum resources to mobile virtual network operators (MVNOs) is popular among primary network operators (POs) for increasing licensed spectrum utilization. An MVNO seeks transmission opportunities (TXOPs) on the PO’s licensed spectrum channel(s) by spectrum sensing. Since licensed primary users (PUs) often have higher transmission priority, TXOPs available to the MVNO are directly determined by PUs’ transmission behaviors. In this paper, we present the first study that uses a pricing scheme to regulate PUs’ transmission behaviors so that TXOPs for an MVNO are improved, meanwhile quality-of-service (QoS) of PUs can be guaranteed as well. Our idea is to design a non-uniform pricing scheme that regulates PUs to transmit based on a time-varying non-uniform transmission cost. We model the optimal pricing problem as a hierarchical game where the interaction between the PO and PUs is modeled as a Stackelberg game and the spectrum random access among PUs is modeled as a non-cooperative game. We first solve the non-cooperative game among PUs, as a building block, then we embed its outcome to a Markov Chain Monte Carlo (MCMC) framework to solve the whole optimal pricing problem. We strictly shows that there could be multiple optimal pricing schemes for a PO. Comprehensive simulations confirm the theoretical analysis, and valid the effectiveness of our proposed scheme.

7. Conclusions

Emergence of secondary operators motivated us to study the influence of PUs’ behaviors to TXOPs for MVNOs. In this paper, we proposed a non-uniform pricing scheme applied on PUs to improve TXOPs for MVNOs subject to the QoS constraint for PUs and the SLA constraint for an MVNO. We formulated the optimal pricing problem as a hierarchical game consisting of a PO-PUs Stackelberg game and a spectrum random access game among PUs, which is a challenging BPEC black-box optimization problem. To solve it, we thoroughly studied the property of the problem, and based on the understandings, we designed efficient solver based on an MCMC-based framework, which has not been used in game-theoretical analysis. Finally, we have also conducted extensive simulation experiments, which confirm the effectiveness of the proposed scheme. In future, multiple MVNOs scenarios can be also considered and studied under the general framework here.