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.

Vehicular communication networks are essential to the development of intelligent navigation systems and improvement of road safety. Unlike most terrestrial networks of today, vehicular networks are characterized by stringent reliability and latency requirements. In order to design efficient networks to meet these requirements, it is important to understand the system-level performance of vehicular networks. Stochastic geometry has recently emerged as a powerful tool for the modeling and analysis of wireless communication networks. However, the canonical spatial models such as the 2D Poisson point process (PPP) does not capture the peculiar spatial layout of vehicular networks, where the locations of vehicular nodes are restricted to roadways. Motivated by this, we consider a doubly stochastic spatial model that captures the spatial coupling between the vehicular nodes and the roads and analyze the performance of vehicular communication networks. We model the spatial layout of roads by a Poisson line process (PLP) and the locations of nodes on each line (road) by a 1D PPP, thereby forming a Cox process driven by a PLP or Poisson line Cox process (PLCP). In this dissertation, we develop the theory of the PLCP and apply it to study key performance metrics such as coverage probability and rate coverage for vehicular networks under different scenarios. First, we compute the signal-to-interference plus noise ratio (SINR)-based success probability of the typical communication link in a vehicular ad hoc network (VANET). Using this result, we also compute the area spectral efficiency (ASE) of the network. Our results show that the optimum transmission probability that maximizes the ASE of the network obtained for the Cox process differs significantly from that of the conventional 1D and 2D PPP models. Second, we calculate the signal-to-interference ratio (SIR)-based downlink coverage probability of the typical receiver in a vehicular network for the cellular network model in which each receiver node connects to its closest transmitting node in the network. The conditioning on the serving node imposes constraints on the spatial configuration of interfering nodes and also the underlying distribution of lines. We carefully handle these constraints using various fundamental distance properties of the PLCP and derive the exact expression for the coverage probability. Third, building further on the above mentioned works, we consider a more complex cellular vehicle-to-everything (C-V2X) communication network in which the vehicular nodes are served by roadside units (RSUs) as well as cellular macro base stations (MBSs). For this setup, we present the downlink coverage analysis of the typical receiver in the presence of shadowing effects. We address the technical challenges induced by the inclusion of shadowing effects by leveraging the asymptotic behavior of the Cox process. These results help us gain useful insights into the behavior of the networks as a function of key network parameters, such as the densities of the nodes and selection bias. Fourth, we characterize the load on the MBSs due to vehicular users, which is defined as the number of vehicular nodes that are served by the MBS. Since the limited network resources are shared by multiple users in the network, the load distribution is a key indicator of the demand of network resources. We first compute the distribution of the load on MBSs due to vehicular users in a single-tier vehicular network. Building on this, we characterize the load on both MBSs and RSUs in a heterogeneous C-V2X network. Using these results, we also compute the rate coverage of the typical receiver in the network. Fifth and last, we explore the applications of the PLCP that extend beyond vehicular communications. We derive the exact distribution of the shortest path distance between the typical point and its nearest neighbor in the sense of path distance in a Manhattan Poisson line Cox process (MPLCP), which is a special variant of the PLCP. The analytical framework developed in this work allows us to answer several important questions pertaining to transportation networks, urban planning, and personnel deployment. / Doctor of Philosophy / Vehicular communication networks are essential to the development of intelligent transportation systems (ITS) and improving road safety. As the in-vehicle sensors can assess only their immediate environment, vehicular nodes exchange information about critical events, such as accidents and sudden braking, with other vehicles, pedestrians, roadside infrastructure, and cellular base stations in order to make critical decisions in a timely manner. Considering the time-sensitive nature of this information, it is of paramount importance to design efficient communication networks that can support the exchange of this information with reliable and high-speed wireless links. Typically, prior to actual deployment, any design of a wireless network is subject to extensive analysis under various operational scenarios using computer simulations. However, it is not viable to rely entirely on simulations for the system design of highly complex systems, such as the vehicular networks. Hence, it is necessary to develop analytical methods that can complement simulators and also serve as a benchmark. One of the approaches that has gained popularity in the recent years for the modeling and analysis of large-scale wireless networks is the use of tools from stochastic geometry. In this approach, we endow the locations of wireless nodes with some distribution and analyze various aspects of the network by leveraging the properties of the distribution. Traditionally, wireless networks have been studied using simple spatial models in which the wireless nodes can lie anywhere on the domain of interest (often a 1D or a 2D plane). However, vehicular networks have a unique spatial geometry because the locations of vehicular nodes are restricted to roadways. Therefore, in order to model the locations of vehicular nodes in the network, we have to first model the underlying road systems. Further, we should also consider the randomness in the locations of vehicles on each road. So, we consider a doubly stochastic model called Poisson line Cox process (PLCP), in which the spatial layout of roads are modeled by random lines and the locations of vehicles on the roads are modeled by random set of points on these lines. As is usually the case in wireless networks, multiple vehicular nodes and roadside units (RSUs) operate at the same frequency due to the limited availability of radio frequency spectrum, which causes interference. Therefore, any receiver in the network obtains a signal that is a mixture of the desired signal from the intended transmitter and the interfering signals from the other transmitters. The ratio of the power of desired signal to the aggregate power of the interfering signals, which is called as the signal-to-interference ratio (SIR), depends on the locations of the transmitters with respect to the receiver. A receiver in the network is said to be in coverage if the SIR measured at the location of the receiver exceeds the required threshold to successfully decode the message. The probability of occurrence of this event is referred to as the coverage probability and it is one of the fundamental metrics that is used to characterize the performance of a wireless network. In our work, we have analytically characterized the coverage probability of the typical vehicular node in the network. This was the first work to present the coverage analysis of a vehicular network using the aforementioned doubly stochastic model. In addition to coverage probability, we have also explored other performance metrics such as data rate, which is the number of bits that can be successfully communicated per unit time, and spectral efficiency. Our analysis has revealed interesting trends in the coverage probability as a function of key system parameters such as the density of roads in a region (total length of roads per unit area), and the density of vehicles on the roads. We have shown that the vehicular nodes in areas with high density of roads have lower coverage than those in areas with sparsely distributed roads. On the other hand, the coverage probability of a vehicular node improves as the density of vehicles on the roads increases. Such insights are quite useful in the design and deployment of network infrastructure. While our research was primarily focused on communication networks, the utility of the spatial models considered in these works extends to other areas of engineering. For a special variant of the PLCP, we have derived the distribution of the shortest path distance between an arbitrary point and its nearest neighbor in the sense of path distance. The analytical framework developed in this work allows us to answer several important questions pertaining to infrastructure planning and personnel deployment.