With an ever-increasing amount of deployed base stations and new types of supported devices and services, cellular networks continue to evolve and densify constantly. These changes require us to revisit and improve classical mathematical models used to assess and optimize their performance. This thesis focuses on novel modeling of cellular networks that preserve their fundamental and critical properties and account for their evolution. We focus on two aspects: scaling laws in dense cellular networks and the data traffic dynamics caused by the interactions between the wireless nodes. We first focus on the distance-based attenuation, which is a critical aspect of dense wireless communications. As opposed to the ubiquitous power-law path loss, we propose a stretched exponential path loss model that is more suitable for short-range communication. In this model, the signal power attenuates over a distance r as e[superscript minus] [superscript alpha] [superscript r][superscript beta] where [alpha],[beta] are tunable parameters. Using field measurements, we show that this model is accurate for short to moderate distances in the range r Ε (5,300) meters. We use this model to analyze downlink cellular networks. Using stochastic geometry tools, we derive expressions for the coverage probability and the average area spectral efficiency (ASE). We prove that by over-densifying the network, the coverage probability is driven to zero, and the ASE saturates to a constant, which we derive in a closed-form. Then we extend this work to study the scaling laws of signal-to-interference-plus-noise ratio (SINR) and the ASE in dense networks under fairly general assumptions regarding the signal propagation and the network operation. We start by defining a class of physically feasible path loss models characterized by three simple properties: finite transmit power, the average received power is less than the transmit power and finite network interference. We show that this class of models includes the vast majority of the bounded models used in the literature. With this class of models, we propose a new approach to analyzing cellular networks' scaling laws. This asymptotic analysis relies on three assumptions: (1) interference is treated as noise; (2) the BS locations are drawn from a Poisson point process; (3) a physically feasible path loss model. We consider three possible definitions of the average ASE, all of which give units of bits per second per unit bandwidth per unit area. When there is no constraint on the minimum operational SINR and instantaneous full channel state information (CSI) is available at the transmitter, the average ASE is proven to saturate to a constant, which we derive in a closed-form. For the other two ASE definitions, wherein either a minimum SINR is enforced or CSI is not available, the average ASE is instead shown to collapse to zero at high BS density. We provide several familiar case studies for the class of considered path loss models and demonstrate that our results cover most previous models and results on ultradense networks as special cases. Then we extend this approach to account for multi-antenna cellular networks. We show that if the number of antennas scales at least linearly with the BSs density, then the SINR approaches a constant, and we restore the desired linear scaling of the ASE with densification. We show that this conclusion holds for cellular networks operating on the traditional frequency bands (sub-6 GHz) and mmWave bands. In the final part of this thesis, we focus on data traffic dynamics in wireless systems. Precisely, we characterize the stability, metastability, and the stationary regime of traffic dynamics in a single-cell uplink wireless system. The traffic is represented in terms of spatial birth-death processes, where users arrive as a Poisson point process in time and space, each with a file to transmit to the base station. Each user's service rate is based on its signal to interference plus noise ratio, where the interference is from other active users in the cell. Once the file is fully transmitted, the user leaves the cell. We derive the necessary and sufficient condition for network stability, independent of the specific bounded path loss function. A novel observation is that the network appears stable for a specific range of arrival rates for a possibly long time and then suddenly exhibits instability. This property, which is known in statistical physics but rarely observed in wireless communication, is called {\it metastability}. Finally, we propose two heuristic characterizations based on the mean-field interpretation of the network steady-state regime when it exists. The first-order approximation is very simple to compute but loose in some regimes. In contrast, the second-order approximation is more sophisticated but tight for the whole range of arrival ratesElectrical and Computer Engineerin
