Throughput Characterizations of Wireless Networks via Stochastic Geometry and Random Graph Theory

The shared medium of wireless communication networks presents many technical challenges that offer a rich modeling and design space across both physical and scheduling protocol layers. This dissertation is organized into tasks that characterize the throughput performance in such networks, with a secondary focus on the interference models employed therein. We examine the throughput ratio of greedy maximal scheduling (GMS) in wireless communication networks modeled as random graphs. A throughput ratio is a single-parameter characterization of the largest achievable fraction of the network capacity region. The throughput ratio of GMS is generally very difficult to obtain; however, it may be evaluated or bounded based on specific topology structures. We analyze the GMS throughput ratio in previously unexplored random graph families under the assumption of primary interference. Critical edge densities are shown to yield bounds on the range and expected GMS throughput ratio as the network grows large. We next focus on the increasing interest in the use of directional antennas to improve throughput in wireless networks. We propose a model for capturing the effects of antenna misdirection on coverage and throughput in large-scale directional networks within a stochastic geometry framework. We provide explicit expressions for communication outage as a function of network density and antenna beamwidth for idealized sector antenna patterns. These expressions are then employed in optimizations to maximize the spatial density of successful transmissions under ideal sector antennas. We supplement our analytical findings with numerical trends across more realistic antenna patterns. Finally, we characterize trade-offs between the protocol and physical interference models, each used in the prior tasks. A transmission is successful under the protocol model if the receiver is free of any single, significant interferer, while physical model feasibility accounts for multiple interference sources. The protocol model, parameterized by a guard zone radius, naturally forms a decision rule for estimating physical model feasibility. We combine binary hypothesis testing with stochastic geometry and characterize the guard zone achieving minimum protocol model prediction error. We conclude with guidelines for identifying environmental parameter regimes for which the protocol model is well suited as a proxy for the physical model.Ph.D., Electrical Engineering -- Drexel University, 201