# Joint Spectrum Reservation and On-demand Request for Mobile Virtual Network Operators

## TL;DR

This paper proposes a two-stage spectrum leasing framework for MVNOs that optimizes resource acquisition and allocation to maximize surplus, leveraging both advance reservation and on-demand requests.

## Contribution

It introduces a joint optimization model for spectrum leasing and resource allocation, deriving closed-form solutions and a stochastic gradient descent algorithm for general utility functions.

## Key findings

- Two-stage leasing improves spectrum utilization and surplus.
- Optimal leasing strategies adapt to traffic and price variations.
- Simulation confirms effectiveness of the proposed framework.

## Abstract

With wireless network virtualization, Mobile Virtual Network Operators (MVNOs) can 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 the two stages by taking into account the traffic distribution, random user locations, wireless channel statistics, Quality of Service (QoS) requirements, and the prices differences. Meanwhile, the acquired spectrum resources are dynamically allocated to the MVNO's mobile subscribers (users) according to fast channel fadings in order to maximize the utilization of the resources. The MVNO's surplus maximization problem is naturally formulated as a tri-level nested optimization problem that consists of Dynamic Resource Allocation (DRA), on-demand request, and advance reservation subproblems. To solve the problem efficiently, we rigorously analyze the structure of the optimal solution in the DRA problem, and the optimal value is used to find the optimal leasing decisions in the two stages. In particular, we derive closed-form expressions of the optimal advance reservation and on-demand requests when the proportional fair utility function is adopted. We further extend the analysis to general utility functions and derive a Stochastic Gradient Decent (SGD) algorithm to find the optimal leasing decisions. Simulation results show that the two-stage spectrum leasing strategy can take advantage of both the price discount of advance reservation and the flexibility of on-demand request to deal with traffic variations.