Joint Scheduling of Proactive Pushing and On-Demand Transmission Over Shared Spectrum for Profit Maximization

Proactive pushing has emerged as a promising solution to scale the service capacity by utilizing idle spectrum resources when on-demand transmission cannot fully exploit the spectrum resources during off-peak times. How to schedule both pushing and on-demand transmission jointly to meet a higher spectrum efficiency becomes a critical issue. Moreover, efficient and fair spectrum sharing among multiple resource schedulers remains open. In this paper, we introduce virtual network operators (VNOs) as schedulers that pay for consumed bandwidth and jointly schedule pushing and on-demand services. We adopt nonlinear spectrum pricing schemes with a convex and increasing price function enabling each VNO to share spectrum resources appropriately and independently. Considering the revenue from users and the cost for spectrum, we formulate a Markov decision process (MDP) to maximize the profit of VNO. A modified value iteration algorithm is applied to solve the MDP with reduced computational complexity. Furthermore, we show the structure of the optimal policy and provide the upper and lower bounds for the optimal performance. We present a low-complexity heuristic policy that can scale in practice with large state spaces and action spaces.