Wireless network virtualization enables mobile virtual network operators (MVNOs) to develop new services on a low-cost platform by leasing virtual resources from mobile network owners. In this paper, we investigate a two-stage spectrum leasing framework, where an MVNO acquires radio spectrum through both advance reservation and on-demand request. To maximize its surplus, the MVNO jointly optimizes the amount of spectrum to lease in each stage by taking into account the traffic distribution, random user locations, wireless channel statistics, quality-of-service requirements, and the prices differences. Meanwhile, the MVNO dynamically allocates the acquired spectrum resources to its mobile subscribers (users) according to fast channel fading in order to maximize the utilization of the resources. The MVNO's surplus maximization problem is formulated as a tri-level nested optimization problem consisting of dynamic resource allocation (DRA), on-demand request, and advance reservation subproblems. To solve the problem efficiently, we first analyze the DRA problem, and then use the optimal solution to find the optimal leasing decisions in the two stages. In particular, we derive a closed-form expression of the optimal on-demand request, and develop a stochastic gradient descent algorithm to find the optimal advance reservation. For a special case when the proportional fairness utility is adopted, we show that the optimal two-stage leasing scheme is related to the number of users and is irrelevant to user locations. Simulation results show that the two-stage spectrum leasing scheme can adapt to different levels of traffic and on-demand price variations, and achieve higher surplus than conventional one-stage leasing schemes.
Index Termsradio spectrum management, mobile virtual network operator, stochastic optimization This work has been presented in part in 2016 IEEE ICCS,