Wireless network virtualization is a promising avenue of research for next-generation 5G cellular networks. This work investigates the problem of selecting base stations to construct virtual networks for a set of service providers, and adaptive slicing of the resources between the service providers to satisfy service provider demands. A two-stage stochastic optimization framework is introduced to solve this problem, and two methods are presented for approximating the stochastic model. The first method uses a sampling approach applied to the deterministic equivalent program of the stochastic model. The second method uses a genetic algorithm for base station selection and adaptively slicing via a single-stage linear optimization problem. A number of scenarios are simulated using a log-normal model designed to emulate demand from real world cellular networks. Simulations indicate that the first approach can provide a reasonably tight solution, but is constrained as the time expense grows exponentially with the number of parameters. The second approach provides a significant improvement in run time with the introduction of marginal error. / Master of Science / 5G, the next generation cellular network standard, promises to provide significant improvements over current generation standards. For 5G to be successful, this must be accompanied by similarly significant efficiency improvements. Wireless network virtualization is a promising technology that has been shown to improve the cost efficiency of current generation cellular networks. By abstracting the physical resource—such as cell tower base stations— from the use of the resource, virtual resources are formed. This work investigates the problem of selecting virtual resources (e.g., base stations) to construct virtual wireless networks with minimal cost and slicing the selected resources to individual networks to optimally satisfy individual network demands. This problem is framed in a stochastic optimization framework and two approaches are presented for approximation. The first approach converts the framework into a deterministic equivalent and reduces it to a tractable form. The second approach uses a genetic algorithm to approximate resource selection. Approaches are simulated and evaluated utilizing a demand model constructed to emulate the statistics of an observed real world urban network. Simulations indicate that the first approach can provide a reasonably tight solution with significant time expense, and that the second approach provides a solution in significantly less time with the introduction of marginal error.

Wireless network virtualization (WNV) and millimeter wave (mmW) communications are emerging as two key technologies for cellular networks. Virtualization in cellular networks enables wireless services to be decoupled from network resources (e.g., infrastructure and spectrum) so that multiple virtual networks can be built using a shared pool of network resources. At the same time, utilization of the large bandwidth available in mmW frequency band would help to overcome ongoing spectrum scarcity issues. In this context, this dissertation presents efficient frameworks for building virtual networks in sub-6 GHz and mmW bands. Towards developing the frameworks, first, we derive a closed-form expression for the downlink rate coverage probability of a typical sub-6 GHz cellular network with known base station (BS) locations and stochastic user equipment (UE) locations and channel conditions. Then, using the closed-form expression, we develop a sub-6 GHz virtual resource allocation framework that aggregates, slices, and allocates the sub-6 Ghz network resources to the virtual networks in such a way that the virtual networks' sub-6 GHz downlink coverage and rate demands are probabilistically satisfied while resource over-provisioning is minimized in the presence of uncertainty in UE locations and channel conditions. Furthermore, considering the possibility of lack of sufficient sub-6 GHz resources to satisfy the rate coverage demands of all virtual networks, we design a prioritized sub-6 GHz virtual resource allocation scheme where virtual networks are built sequentially based on their given priorities. To this end, we develop static frameworks that allocate sub-6 GHz resources in the presence of uncertainty in UE locations and channel conditions, i.e., before the UE locations and channel conditions are revealed. As a result, when a slice of a BS serves its associated UEs, it can be over-satisfied (i.e., resources left after satisfying the rate demands of all UEs) or under-satisfied (i.e., lack of resources to satisfy the rate demands of all UEs). On the other hand, it is extremely challenging to execute the entire virtual resource allocation process in real time due to the small transmission time intervals (TTIs) of cellular technologies. Taking this into consideration, we develop an efficient scheme that performs the virtual resource allocation in two phases, i.e., virtual network deployment phase (static) and statistical multiplexing phase (adaptive). In the virtual network deployment phase, sub-6 GHz resources are aggregated, sliced, and allocated to the virtual networks considering the presence of uncertainty in UE locations and channel conditions, without knowing which realization of UE locations and channel conditions will occur. Once the virtual networks are deployed, each of the aggregated BSs performs statistical multiplexing, i.e., allocates excess resources from the over-satisfied slices to the under-satisfied slices, according to the realized channel conditions of associated UEs. In this way, we further improve the sub-6 GHz resource utilization. Next, we steer our focus on the mmW virtual resource allocation process. MmW systems typically use beamforming techniques to compensate for the high pathloss. The directional communication in the presence of uncertainty in UE locations and channel conditions, make maintaining connectivity and performing initial access and cell discovery challenging. To address these challenges, we develop an efficient framework for mmW virtual network deployment and UE assignment. The deployment decisions (i.e., the required set of mmW BSs and their optimal beam directions) are taken in the presence of uncertainty in UE locations and channel conditions, i.e., before the UE locations and channel conditions are revealed. Once the virtual networks are deployed, an optimal mmW link (or a fallback sub-6 GHz link) is assigned to each UE according to the realized UE locations and channel conditions. Our numerical results demonstrate the gains brought by our proposed scheme in terms of minimizing resource over-provisioning while probabilistically satisfying virtual networks' sub-6 GHz and mmW demands in the presence of uncertainty in UE locations and channel conditions. / Doctor of Philosophy / In cellular networks, mobile network operators (MNOs) have been sharing resources (e.g., infrastructure and spectrum) as a solution to extend coverage, increase capacity, and decrease expenditures. Recently, due to the advent of 5G wireless services with enormous coverage and capacity demands and potential revenue losses due to over-provisioning to serve peak demands, the motivation for sharing and virtualization has significantly increased in cellular networks. Through wireless network virtualization (WNV), wireless services can be decoupled from the network resources so that various services can efficiently share the resources. At the same time, utilization of the large bandwidth available in millimeter wave (mmW) frequency band would help to overcome ongoing spectrum scarcity issues. However, due to the inherent features of cellular networks, i.e., the uncertainty in user equipment (UE) locations and channel conditions, enabling WNV and mmW communications in cellular networks is a challenging task. Specifically, we need to build the virtual networks in such a way that UE demands are satisfied, isolation among the virtual networks are maintained, and resource over-provisioning is minimized in the presence of uncertainty in UE locations and channel conditions. In addition, the mmW channels experience higher attenuation and blockage due to their small wavelengths compared to conventional sub-6 GHz channels. To compensate for the high pathloss, mmW systems typically use beamforming techniques. The directional communication in the presence of uncertainty in UE locations and channel conditions, make maintaining connectivity and performing initial access and cell discovery challenging. Our goal is to address these challenges and develop optimization frameworks to efficiently enable virtualization and mmW technologies in cellular networks.